12n
0539
(K12n
0539
)
A knot diagram
1
Linearized knot diagam
3 6 11 12 2 9 5 4 6 1 8 9
Solving Sequence
2,6 3,9
7 10 1 11 5 8 12 4
c
2
c
6
c
9
c
1
c
10
c
5
c
7
c
12
c
4
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h1.71224 × 10
120
u
84
+ 1.40203 × 10
120
u
83
+ ··· + 3.73013 × 10
118
b − 2.07454 × 10
120
,
8.58971 × 10
120
u
84
+ 5.94299 × 10
120
u
83
+ ··· + 4.10314 × 10
119
a − 4.74408 × 10
120
,
u
85
− 24u
83
+ ··· + 10u + 1i
I
u
2
= h−10u
21
+ 53u
19
+ ··· + b − 15, −10u
21
+ 54u
19
+ ··· + a − 13, u
22
+ u
21
+ ··· − 2u + 1i
* 2 irreducible components of dim
C
= 0, with total 107 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
= h1.71 × 10
120
u
84
+ 1.40 × 10
120
u
83
+ · · · + 3.73 × 10
118
b − 2.07 ×
10
120
, 8.59 × 10
120
u
84
+ 5.94 × 10
120
u
83
+ · · · + 4.10 × 10
119
a − 4.74 ×
10
120
, u
85
− 24u
83
+ · · · + 10u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
−20.9345u
84
− 14.4840u
83
+ ··· + 267.776u + 11.5621
−45.9029u
84
− 37.5866u
83
+ ··· + 629.922u + 55.6158
a
7
=
11.1468u
84
+ 8.19621u
83
+ ··· − 72.3417u + 9.67525
18.6966u
84
+ 17.0401u
83
+ ··· − 217.270u − 19.2457
a
10
=
−20.9345u
84
− 14.4840u
83
+ ··· + 267.776u + 11.5621
−57.1007u
84
− 46.1321u
83
+ ··· + 795.697u + 70.0998
a
1
=
−u
2
+ 1
−u
4
a
11
=
−30.8822u
84
− 22.1361u
83
+ ··· + 408.995u + 23.4304
−46.8081u
84
− 37.9200u
83
+ ··· + 649.457u + 57.1070
a
5
=
u
u
a
8
=
3.64203u
84
+ 1.55727u
83
+ ··· + 23.6473u + 18.5192
11.1918u
84
+ 10.4012u
83
+ ··· − 121.281u − 10.4017
a
12
=
−8.59326u
84
− 8.98215u
83
+ ··· + 100.400u + 15.7211
−34.9414u
84
− 30.6980u
83
+ ··· + 434.117u + 39.2473
a
4
=
13.6180u
84
+ 13.8934u
83
+ ··· − 145.844u − 18.0597
48.0968u
84
+ 41.5976u
83
+ ··· − 603.928u − 54.4575
(ii) Obstruction class = −1
(iii) Cusp Shapes = 171.919u
84
+ 151.328u
83
+ ··· − 2175.77u − 192.981
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
85
+ 48u
84
+ ··· + 76u + 1
c
2
, c
5
u
85
− 24u
83
+ ··· + 10u − 1
c
3
u
85
− 22u
83
+ ··· − 68443u − 15487
c
4
u
85
+ 3u
84
+ ··· − 115u + 29
c
6
, c
9
u
85
+ 8u
84
+ ··· + 33526u + 4031
c
7
u
85
− 8u
84
+ ··· − 747u − 17
c
8
u
85
− 3u
84
+ ··· − 24u + 11
c
10
u
85
+ u
84
+ ··· − 653233343u − 56357257
c
11
u
85
+ 6u
84
+ ··· − 17u + 1
c
12
u
85
+ u
84
+ ··· − 7039u − 223
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
85
− 16y
84
+ ··· + 5764y −1
c
2
, c
5
y
85
− 48y
84
+ ··· + 76y −1
c
3
y
85
− 44y
84
+ ··· + 7600305635y −239847169
c
4
y
85
− 13y
84
+ ··· + 50693y −841
c
6
, c
9
y
85
− 84y
84
+ ··· + 4537701460y −16248961
c
7
y
85
− 40y
84
+ ··· + 290429y −289
c
8
y
85
− 13y
84
+ ··· + 6208y −121
c
10
y
85
+ 53y
84
+ ··· + 392522021882255677y −3176140416564049
c
11
y
85
+ 8y
84
+ ··· + 23y −1
c
12
y
85
+ 25y
84
+ ··· + 6405495y −49729
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.005353 + 1.000360I
a = 0.18285 − 1.48764I
b = 0.349188 − 0.373795I
−1.93409 + 0.60336I 0
u = 0.005353 − 1.000360I
a = 0.18285 + 1.48764I
b = 0.349188 + 0.373795I
−1.93409 − 0.60336I 0
u = 0.188620 + 0.969304I
a = 0.19737 + 1.77663I
b = −0.062291 + 0.128491I
−1.46515 + 11.85320I 0
u = 0.188620 − 0.969304I
a = 0.19737 − 1.77663I
b = −0.062291 − 0.128491I
−1.46515 − 11.85320I 0
u = −0.840878 + 0.483325I
a = 0.501916 − 1.283270I
b = 1.34341 − 1.06918I
3.51388 − 1.61241I 0
u = −0.840878 − 0.483325I
a = 0.501916 + 1.283270I
b = 1.34341 + 1.06918I
3.51388 + 1.61241I 0
u = 0.951828 + 0.159966I
a = 0.065586 − 0.374247I
b = 0.43709 + 2.16437I
−0.032156 − 0.597700I 0
u = 0.951828 − 0.159966I
a = 0.065586 + 0.374247I
b = 0.43709 − 2.16437I
−0.032156 + 0.597700I 0
u = 0.310483 + 0.990724I
a = 0.13435 − 1.57025I
b = −0.132367 − 0.293568I
−2.09244 + 2.43593I 0
u = 0.310483 − 0.990724I
a = 0.13435 + 1.57025I
b = −0.132367 + 0.293568I
−2.09244 − 2.43593I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.975011 + 0.393466I
a = 0.475549 + 0.820083I
b = 1.169380 − 0.022368I
1.41715 + 3.73569I 0
u = −0.975011 − 0.393466I
a = 0.475549 − 0.820083I
b = 1.169380 + 0.022368I
1.41715 − 3.73569I 0
u = 1.021460 + 0.278835I
a = 0.77446 + 2.18381I
b = 0.99233 + 2.23297I
1.68533 − 6.44110I 0
u = 1.021460 − 0.278835I
a = 0.77446 − 2.18381I
b = 0.99233 − 2.23297I
1.68533 + 6.44110I 0
u = −0.715395 + 0.783310I
a = 0.522346 + 0.160195I
b = 0.317448 − 0.195411I
3.70495 + 1.10586I 0
u = −0.715395 − 0.783310I
a = 0.522346 − 0.160195I
b = 0.317448 + 0.195411I
3.70495 − 1.10586I 0
u = −0.953739 + 0.471015I
a = −0.294966 + 1.084510I
b = 0.285466 + 0.666041I
1.52968 + 4.35650I 0
u = −0.953739 − 0.471015I
a = −0.294966 − 1.084510I
b = 0.285466 − 0.666041I
1.52968 − 4.35650I 0
u = −0.189972 + 0.915047I
a = 0.042038 + 1.307850I
b = 0.182832 − 0.146291I
0.27710 − 3.98155I 0
u = −0.189972 − 0.915047I
a = 0.042038 − 1.307850I
b = 0.182832 + 0.146291I
0.27710 + 3.98155I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.013401 + 0.933105I
a = −0.41356 + 1.56864I
b = −0.238256 − 0.042713I
−4.94846 − 4.99388I 0
u = −0.013401 − 0.933105I
a = −0.41356 − 1.56864I
b = −0.238256 + 0.042713I
−4.94846 + 4.99388I 0
u = 0.858709 + 0.306453I
a = 0.437696 + 0.079272I
b = −0.536251 − 0.628310I
−1.75635 − 1.24105I 0
u = 0.858709 − 0.306453I
a = 0.437696 − 0.079272I
b = −0.536251 + 0.628310I
−1.75635 + 1.24105I 0
u = 1.070350 + 0.241684I
a = −0.048326 − 0.800341I
b = −0.784925 + 0.086925I
−0.584139 − 1.214130I 0
u = 1.070350 − 0.241684I
a = −0.048326 + 0.800341I
b = −0.784925 − 0.086925I
−0.584139 + 1.214130I 0
u = 1.043000 + 0.381616I
a = −0.941223 + 0.060786I
b = −1.19962 − 1.11408I
0.85138 + 1.98117I 0
u = 1.043000 − 0.381616I
a = −0.941223 − 0.060786I
b = −1.19962 + 1.11408I
0.85138 − 1.98117I 0
u = −1.129960 + 0.104281I
a = −0.394497 + 0.932408I
b = −0.444109 + 0.587225I
−3.81181 + 3.18162I 0
u = −1.129960 − 0.104281I
a = −0.394497 − 0.932408I
b = −0.444109 − 0.587225I
−3.81181 − 3.18162I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.864367
a = 0.0715299
b = −0.541281
−1.42725 −6.10760
u = −1.080700 + 0.401420I
a = −0.165123 + 0.081421I
b = −0.78337 + 1.47583I
0.90179 + 8.56928I 0
u = −1.080700 − 0.401420I
a = −0.165123 − 0.081421I
b = −0.78337 − 1.47583I
0.90179 − 8.56928I 0
u = 0.832181
a = 0.926177
b = 2.91409
0.997166 −18.4890
u = −0.049225 + 0.830285I
a = 0.56528 − 1.89117I
b = −0.204200 − 0.163162I
−2.43502 − 3.30316I −5.23294 + 7.40607I
u = −0.049225 − 0.830285I
a = 0.56528 + 1.89117I
b = −0.204200 + 0.163162I
−2.43502 + 3.30316I −5.23294 − 7.40607I
u = 0.830826 + 0.826040I
a = −0.169302 + 0.010069I
b = −0.577550 + 0.509050I
3.76622 + 2.32030I 0
u = 0.830826 − 0.826040I
a = −0.169302 − 0.010069I
b = −0.577550 − 0.509050I
3.76622 − 2.32030I 0
u = 0.891925 + 0.810015I
a = −0.286571 + 0.262922I
b = 0.329641 − 0.110602I
3.57498 − 8.36975I 0
u = 0.891925 − 0.810015I
a = −0.286571 − 0.262922I
b = 0.329641 + 0.110602I
3.57498 + 8.36975I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.989802 + 0.710827I
a = 0.168409 + 0.465761I
b = 0.416900 + 0.454793I
2.86904 + 4.53419I 0
u = −0.989802 − 0.710827I
a = 0.168409 − 0.465761I
b = 0.416900 − 0.454793I
2.86904 − 4.53419I 0
u = −0.666265 + 0.344818I
a = −1.09970 + 1.54051I
b = −1.397150 + 0.053578I
4.07887 + 5.28332I 1.24117 − 5.02642I
u = −0.666265 − 0.344818I
a = −1.09970 − 1.54051I
b = −1.397150 − 0.053578I
4.07887 − 5.28332I 1.24117 + 5.02642I
u = 1.183110 + 0.402824I
a = 1.54579 + 0.12909I
b = 3.14640 − 0.15589I
−6.48173 − 3.55864I 0
u = 1.183110 − 0.402824I
a = 1.54579 − 0.12909I
b = 3.14640 + 0.15589I
−6.48173 + 3.55864I 0
u = −1.160000 + 0.524269I
a = −1.37812 − 0.72891I
b = −2.73159 − 1.13043I
−5.60017 + 4.82152I 0
u = −1.160000 − 0.524269I
a = −1.37812 + 0.72891I
b = −2.73159 + 1.13043I
−5.60017 − 4.82152I 0
u = 0.719223 + 0.060664I
a = −1.44270 − 2.37773I
b = −1.85713 − 1.14364I
3.11952 + 4.42569I −0.76135 − 6.20286I
u = 0.719223 − 0.060664I
a = −1.44270 + 2.37773I
b = −1.85713 + 1.14364I
3.11952 − 4.42569I −0.76135 + 6.20286I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.229530 + 0.438003I
a = 1.217770 − 0.384196I
b = 2.27464 − 1.11533I
−6.24720 − 1.14845I 0
u = 1.229530 − 0.438003I
a = 1.217770 + 0.384196I
b = 2.27464 + 1.11533I
−6.24720 + 1.14845I 0
u = −1.275120 + 0.282603I
a = −1.49840 − 0.21043I
b = −2.60608 − 0.26666I
−7.45533 + 1.39297I 0
u = −1.275120 − 0.282603I
a = −1.49840 + 0.21043I
b = −2.60608 + 0.26666I
−7.45533 − 1.39297I 0
u = −1.224310 + 0.482177I
a = −1.67152 + 0.03389I
b = −3.05540 + 0.28991I
−5.92815 + 8.04533I 0
u = −1.224310 − 0.482177I
a = −1.67152 − 0.03389I
b = −3.05540 − 0.28991I
−5.92815 − 8.04533I 0
u = 1.270180 + 0.354996I
a = −0.936675 + 0.026252I
b = −2.18853 + 0.30229I
−4.36713 − 0.22372I 0
u = 1.270180 − 0.354996I
a = −0.936675 − 0.026252I
b = −2.18853 − 0.30229I
−4.36713 + 0.22372I 0
u = −0.171412 + 0.657764I
a = −0.95991 − 2.23193I
b = −0.295373 + 0.036008I
−2.85946 − 0.19476I −5.29145 − 0.97537I
u = −0.171412 − 0.657764I
a = −0.95991 + 2.23193I
b = −0.295373 − 0.036008I
−2.85946 + 0.19476I −5.29145 + 0.97537I
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.456041 + 0.464462I
a = 1.193950 − 0.065927I
b = 1.034860 − 0.579589I
2.88974 − 0.39617I 2.71681 + 0.34590I
u = −0.456041 − 0.464462I
a = 1.193950 + 0.065927I
b = 1.034860 + 0.579589I
2.88974 + 0.39617I 2.71681 − 0.34590I
u = −1.235500 + 0.557498I
a = 1.126590 + 0.216852I
b = 2.36000 + 0.16189I
−2.90587 + 9.34845I 0
u = −1.235500 − 0.557498I
a = 1.126590 − 0.216852I
b = 2.36000 − 0.16189I
−2.90587 − 9.34845I 0
u = −1.276860 + 0.483646I
a = 1.272450 − 0.106001I
b = 2.66529 + 0.09834I
−8.82888 + 10.02930I 0
u = −1.276860 − 0.483646I
a = 1.272450 + 0.106001I
b = 2.66529 − 0.09834I
−8.82888 − 10.02930I 0
u = 1.288810 + 0.464947I
a = −1.144530 + 0.491479I
b = −2.26959 + 0.66922I
−8.97476 + 0.02482I 0
u = 1.288810 − 0.464947I
a = −1.144530 − 0.491479I
b = −2.26959 − 0.66922I
−8.97476 − 0.02482I 0
u = −1.330440 + 0.337617I
a = 1.283760 + 0.299388I
b = 2.40343 + 0.74368I
−6.44061 − 7.37054I 0
u = −1.330440 − 0.337617I
a = 1.283760 − 0.299388I
b = 2.40343 − 0.74368I
−6.44061 + 7.37054I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.250740 + 0.573265I
a = −1.53166 + 0.06635I
b = −2.88843 + 0.09759I
−4.7225 − 17.4174I 0
u = 1.250740 − 0.573265I
a = −1.53166 − 0.06635I
b = −2.88843 − 0.09759I
−4.7225 + 17.4174I 0
u = −1.302360 + 0.463258I
a = −1.243900 + 0.247243I
b = −2.16132 − 0.06403I
−6.10453 + 4.53838I 0
u = −1.302360 − 0.463258I
a = −1.243900 − 0.247243I
b = −2.16132 + 0.06403I
−6.10453 − 4.53838I 0
u = 1.241210 + 0.613061I
a = 1.362000 − 0.100699I
b = 2.43612 − 0.38495I
−5.01768 − 8.27806I 0
u = 1.241210 − 0.613061I
a = 1.362000 + 0.100699I
b = 2.43612 + 0.38495I
−5.01768 + 8.27806I 0
u = 1.307630 + 0.466435I
a = 1.46921 − 0.37040I
b = 2.33556 − 0.34225I
−6.08890 − 5.78678I 0
u = 1.307630 − 0.466435I
a = 1.46921 + 0.37040I
b = 2.33556 + 0.34225I
−6.08890 + 5.78678I 0
u = −0.440911 + 0.405001I
a = 0.792263 + 0.730144I
b = 1.142640 − 0.386053I
2.88774 − 0.20923I 1.242555 + 0.378473I
u = −0.440911 − 0.405001I
a = 0.792263 − 0.730144I
b = 1.142640 + 0.386053I
2.88774 + 0.20923I 1.242555 − 0.378473I
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.099952 + 0.429731I
a = 2.03358 + 0.01611I
b = −0.841544 + 0.483607I
3.44287 − 5.06710I 0.91675 + 5.72229I
u = −0.099952 − 0.429731I
a = 2.03358 − 0.01611I
b = −0.841544 − 0.483607I
3.44287 + 5.06710I 0.91675 − 5.72229I
u = 0.123525 + 0.400738I
a = 1.178250 − 0.064085I
b = 0.171595 − 0.506385I
−0.185084 − 1.355340I −1.97953 + 4.83531I
u = 0.123525 − 0.400738I
a = 1.178250 + 0.064085I
b = 0.171595 + 0.506385I
−0.185084 + 1.355340I −1.97953 − 4.83531I
u = −0.115053
a = −11.8433
b = −0.451096
−2.58472 2.24510
13
II. I
u
2
= h−10u
21
+ 53u
19
+ · · · + b − 15, −10u
21
+ 54u
19
+ · · · + a −
13, u
22
+ u
21
+ · · · − 2u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
9
=
10u
21
− 54u
19
+ ··· − 37u + 13
10u
21
− 53u
19
+ ··· − 32u + 15
a
7
=
−15u
21
− 5u
20
+ ··· + 37u − 10
−12u
21
− 5u
20
+ ··· + 50u − 14
a
10
=
10u
21
− 54u
19
+ ··· − 37u + 13
16u
21
+ 2u
20
+ ··· − 62u + 25
a
1
=
−u
2
+ 1
−u
4
a
11
=
13u
21
− 3u
20
+ ··· − 40u + 18
16u
21
− 84u
19
+ ··· − 48u + 21
a
5
=
u
u
a
8
=
−22u
21
− 5u
20
+ ··· + 46u − 13
−19u
21
− 5u
20
+ ··· + 59u − 17
a
12
=
−13u
21
+ 69u
19
+ ··· + 44u − 18
−15u
21
− 6u
20
+ ··· + 50u − 11
a
4
=
2u
19
− 9u
17
+ ··· + 11u − 3
6u
21
+ 2u
20
+ ··· − u
2
− 13u
(ii) Obstruction class = 1
(iii) Cusp Shapes
= 20u
21
− u
20
− 104u
19
+ 2u
18
+ 303u
17
+ 3u
16
− 565u
15
− 59u
14
+ 755u
13
+ 203u
12
−
679u
11
−410u
10
+362u
9
+572u
8
+11u
7
−551u
6
−238u
5
+388u
4
+209u
3
−192u
2
−89u+43
14
(iv) u-Polynomials at the component
15
Crossings u-Polynomials at each crossing
c
1
u
22
− 11u
21
+ ··· − 16u + 1
c
2
u
22
+ u
21
+ ··· − 2u + 1
c
3
u
22
+ u
21
+ ··· − 15u + 5
c
4
u
22
− 5u
19
+ ··· + u − 1
c
5
u
22
− u
21
+ ··· + 2u + 1
c
6
u
22
− 11u
21
+ ··· − 10u + 1
c
7
u
22
+ 3u
21
+ ··· + 189u + 23
c
8
u
22
− 4u
20
+ ··· + 8u
2
− 1
c
9
u
22
+ 11u
21
+ ··· + 10u + 1
c
10
u
22
+ 2u
21
+ ··· − 489u − 179
c
11
u
22
− u
21
+ ··· − 7u − 1
c
12
u
22
+ 4u
21
+ ··· − 5u − 5
16
17
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
22
+ 5y
21
+ ··· − 52y + 1
c
2
, c
5
y
22
− 11y
21
+ ··· − 16y + 1
c
3
y
22
− 15y
21
+ ··· − 755y + 25
c
4
y
22
+ 24y
20
+ ··· − 9y + 1
c
6
, c
9
y
22
− 3y
21
+ ··· + 12y + 1
c
7
y
22
− 15y
21
+ ··· − 11893y + 529
c
8
y
22
− 8y
21
+ ··· − 16y + 1
c
10
y
22
+ 6y
21
+ ··· + 57303y + 32041
c
11
y
22
+ 5y
21
+ ··· − 3y + 1
c
12
y
22
+ 6y
21
+ ··· − 455y + 25
18
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.979550 + 0.192965I
a = 0.049739 − 0.317281I
b = 0.07427 + 1.88292I
−0.110842 − 0.638882I −39.2337 − 0.4195I
u = 0.979550 − 0.192965I
a = 0.049739 + 0.317281I
b = 0.07427 − 1.88292I
−0.110842 + 0.638882I −39.2337 + 0.4195I
u = −0.723270 + 0.716834I
a = 0.397388 − 0.005884I
b = 0.436175 − 0.704061I
4.11163 + 0.63723I 6.54002 + 1.19849I
u = −0.723270 − 0.716834I
a = 0.397388 + 0.005884I
b = 0.436175 + 0.704061I
4.11163 − 0.63723I 6.54002 − 1.19849I
u = −0.908952 + 0.290032I
a = 0.38486 − 2.07167I
b = 0.058682 − 1.072120I
2.62294 + 5.98882I −0.92980 − 8.33780I
u = −0.908952 − 0.290032I
a = 0.38486 + 2.07167I
b = 0.058682 + 1.072120I
2.62294 − 5.98882I −0.92980 + 8.33780I
u = −0.193236 + 0.923126I
a = 0.06481 + 1.71985I
b = 0.034564 + 0.268808I
−2.05997 − 1.85851I −3.94257 − 0.91516I
u = −0.193236 − 0.923126I
a = 0.06481 − 1.71985I
b = 0.034564 − 0.268808I
−2.05997 + 1.85851I −3.94257 + 0.91516I
u = 0.827042 + 0.682329I
a = 0.652080 + 0.805407I
b = 0.478838 + 0.307764I
5.15735 + 2.30312I 3.06418 − 2.18439I
u = 0.827042 − 0.682329I
a = 0.652080 − 0.805407I
b = 0.478838 − 0.307764I
5.15735 − 2.30312I 3.06418 + 2.18439I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.867318 + 0.312804I
a = −1.25055 + 1.37179I
b = −1.71767 + 2.08935I
2.75033 − 3.38289I −3.52028 + 1.29488I
u = −0.867318 − 0.312804I
a = −1.25055 − 1.37179I
b = −1.71767 − 2.08935I
2.75033 + 3.38289I −3.52028 − 1.29488I
u = 0.905224 + 0.651152I
a = −0.388636 − 0.909012I
b = −0.69139 − 1.25158I
4.90447 − 7.46002I 1.09193 + 6.89812I
u = 0.905224 − 0.651152I
a = −0.388636 + 0.909012I
b = −0.69139 + 1.25158I
4.90447 + 7.46002I 1.09193 − 6.89812I
u = −0.979142 + 0.678373I
a = 0.039106 + 0.356080I
b = 0.531614 + 0.013462I
3.32463 + 4.72683I 7.75293 − 7.21359I
u = −0.979142 − 0.678373I
a = 0.039106 − 0.356080I
b = 0.531614 − 0.013462I
3.32463 − 4.72683I 7.75293 + 7.21359I
u = 1.218980 + 0.391873I
a = −1.42856 + 0.23693I
b = −2.66587 + 0.61693I
−6.40706 − 2.19213I −7.62094 + 1.94263I
u = 1.218980 − 0.391873I
a = −1.42856 − 0.23693I
b = −2.66587 − 0.61693I
−6.40706 + 2.19213I −7.62094 − 1.94263I
u = −1.249940 + 0.521685I
a = 1.51302 + 0.09874I
b = 2.66597 + 0.12109I
−5.41252 + 7.14535I −5.55491 − 4.26248I
u = −1.249940 − 0.521685I
a = 1.51302 − 0.09874I
b = 2.66597 − 0.12109I
−5.41252 − 7.14535I −5.55491 + 4.26248I
20
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.594637
a = −2.04766
b = −0.0406902
−2.98320 −18.2720
u = 0.387486
a = −1.01885
b = 1.63034
1.67065 −3.02160
21
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
22
− 11u
21
+ ··· − 16u + 1)(u
85
+ 48u
84
+ ··· + 76u + 1)
c
2
(u
22
+ u
21
+ ··· − 2u + 1)(u
85
− 24u
83
+ ··· + 10u − 1)
c
3
(u
22
+ u
21
+ ··· − 15u + 5)(u
85
− 22u
83
+ ··· − 68443u − 15487)
c
4
(u
22
− 5u
19
+ ··· + u − 1)(u
85
+ 3u
84
+ ··· − 115u + 29)
c
5
(u
22
− u
21
+ ··· + 2u + 1)(u
85
− 24u
83
+ ··· + 10u − 1)
c
6
(u
22
− 11u
21
+ ··· − 10u + 1)(u
85
+ 8u
84
+ ··· + 33526u + 4031)
c
7
(u
22
+ 3u
21
+ ··· + 189u + 23)(u
85
− 8u
84
+ ··· − 747u − 17)
c
8
(u
22
− 4u
20
+ ··· + 8u
2
− 1)(u
85
− 3u
84
+ ··· − 24u + 11)
c
9
(u
22
+ 11u
21
+ ··· + 10u + 1)(u
85
+ 8u
84
+ ··· + 33526u + 4031)
c
10
(u
22
+ 2u
21
+ ··· − 489u − 179)
· (u
85
+ u
84
+ ··· − 653233343u − 56357257)
c
11
(u
22
− u
21
+ ··· − 7u − 1)(u
85
+ 6u
84
+ ··· − 17u + 1)
c
12
(u
22
+ 4u
21
+ ··· − 5u − 5)(u
85
+ u
84
+ ··· − 7039u − 223)
22
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
22
+ 5y
21
+ ··· − 52y + 1)(y
85
− 16y
84
+ ··· + 5764y −1)
c
2
, c
5
(y
22
− 11y
21
+ ··· − 16y + 1)(y
85
− 48y
84
+ ··· + 76y −1)
c
3
(y
22
− 15y
21
+ ··· − 755y + 25)
· (y
85
− 44y
84
+ ··· + 7600305635y −239847169)
c
4
(y
22
+ 24y
20
+ ··· − 9y + 1)(y
85
− 13y
84
+ ··· + 50693y −841)
c
6
, c
9
(y
22
− 3y
21
+ ··· + 12y + 1)
· (y
85
− 84y
84
+ ··· + 4537701460y −16248961)
c
7
(y
22
− 15y
21
+ ··· − 11893y + 529)
· (y
85
− 40y
84
+ ··· + 290429y −289)
c
8
(y
22
− 8y
21
+ ··· − 16y + 1)(y
85
− 13y
84
+ ··· + 6208y −121)
c
10
(y
22
+ 6y
21
+ ··· + 57303y + 32041)
· (y
85
+ 53y
84
+ ··· + 392522021882255677y −3176140416564049)
c
11
(y
22
+ 5y
21
+ ··· − 3y + 1)(y
85
+ 8y
84
+ ··· + 23y −1)
c
12
(y
22
+ 6y
21
+ ··· − 455y + 25)
· (y
85
+ 25y
84
+ ··· + 6405495y −49729)
23
