12n
0761
(K12n
0761
)
A knot diagram
1
Linearized knot diagam
4 7 9 7 11 3 12 3 1 8 5 10
Solving Sequence
10,12
1
3,9
4 8 7 5 2 6 11
c
12
c
9
c
3
c
8
c
7
c
4
c
2
c
6
c
11
c
1
, c
5
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h3.97870 × 10
127
u
63
+ 7.30559 × 10
127
u
62
+ ··· + 2.80101 × 10
129
b − 2.17236 × 10
129
,
9.34021 × 10
128
u
63
+ 2.00908 × 10
129
u
62
+ ··· + 2.80101 × 10
129
a + 1.33402 × 10
131
, u
64
+ 2u
63
+ ··· + 52u − 1i
I
u
2
= h5.31075 × 10
16
u
33
− 2.70900 × 10
17
u
32
+ ··· + 1.01071 × 10
18
b + 7.36359 × 10
17
,
− 1.67036 × 10
19
u
33
+ 2.51183 × 10
19
u
32
+ ··· + 5.55891 × 10
19
a + 7.28093 × 10
19
,
u
34
− 3u
33
+ ··· − 27u + 5i
* 2 irreducible components of dim
C
= 0, with total 98 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
= h3.98 × 10
127
u
63
+ 7.31 × 10
127
u
62
+ · · · + 2.80 × 10
129
b − 2.17 ×
10
129
, 9.34 × 10
128
u
63
+ 2.01 × 10
129
u
62
+ · · · + 2.80 × 10
129
a + 1.33 ×
10
131
, u
64
+ 2u
63
+ · · · + 52u − 1i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
3
=
−0.333459u
63
− 0.717269u
62
+ ··· − 501.805u − 47.6263
−0.0142045u
63
− 0.0260820u
62
+ ··· − 6.72756u + 0.775564
a
9
=
−u
u
3
+ u
a
4
=
−0.345609u
63
− 0.726001u
62
+ ··· − 502.999u − 47.5965
−0.0219766u
63
− 0.0285431u
62
+ ··· − 4.71159u + 0.730182
a
8
=
1.02497u
63
+ 2.00739u
62
+ ··· + 780.201u + 32.8037
−0.0511564u
63
− 0.107939u
62
+ ··· − 26.5733u − 0.0850152
a
7
=
0.973811u
63
+ 1.89945u
62
+ ··· + 753.627u + 32.7187
−0.0511564u
63
− 0.107939u
62
+ ··· − 26.5733u − 0.0850152
a
5
=
−1.11384u
63
− 2.14207u
62
+ ··· − 740.710u − 40.0935
0.0736073u
63
+ 0.141737u
62
+ ··· + 25.8132u + 0.162424
a
2
=
−0.163667u
63
− 0.369101u
62
+ ··· − 315.105u − 29.4435
−0.0202597u
63
− 0.0325595u
62
+ ··· − 4.23987u + 0.489100
a
6
=
1.29798u
63
+ 2.57666u
62
+ ··· + 1114.78u + 53.0891
−0.0501939u
63
− 0.101574u
62
+ ··· − 31.4978u − 0.323632
a
11
=
−1.29596u
63
− 2.48504u
62
+ ··· − 761.398u − 18.2978
0.0772814u
63
+ 0.139583u
62
+ ··· + 40.7050u − 0.311959
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.422995u
63
− 0.770299u
62
+ ··· − 106.004u − 6.77653
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
64
− 6u
63
+ ··· − 11638u + 1297
c
2
, c
6
u
64
+ 3u
63
+ ··· + 274122u + 178861
c
3
, c
8
u
64
− u
63
+ ··· − 514u + 43
c
4
u
64
− 7u
63
+ ··· + 35883u − 2633
c
5
, c
11
u
64
+ u
63
+ ··· − 146u − 61
c
7
u
64
+ 2u
63
+ ··· − 1926u − 359
c
9
, c
12
u
64
+ 2u
63
+ ··· + 52u − 1
c
10
u
64
− 8u
63
+ ··· + 360305u − 493889
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
64
− 102y
63
+ ··· − 115080144y + 1682209
c
2
, c
6
y
64
− 97y
63
+ ··· − 66879492684y + 31991257321
c
3
, c
8
y
64
− 65y
63
+ ··· − 189118y + 1849
c
4
y
64
− 103y
63
+ ··· − 1148483033y + 6932689
c
5
, c
11
y
64
+ 61y
63
+ ··· − 160274y + 3721
c
7
y
64
− 20y
63
+ ··· + 12391674y + 128881
c
9
, c
12
y
64
+ 56y
63
+ ··· − 4566y + 1
c
10
y
64
− 36y
63
+ ··· − 918166302603y + 243926344321
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.007940 + 0.142695I
a = 1.72681 + 0.33227I
b = −2.14827 − 0.38605I
−5.44537 + 1.27224I 0
u = −1.007940 − 0.142695I
a = 1.72681 − 0.33227I
b = −2.14827 + 0.38605I
−5.44537 − 1.27224I 0
u = 0.249944 + 0.990791I
a = 0.640684 + 0.292773I
b = 1.131970 − 0.306003I
0.77396 + 1.88121I 0
u = 0.249944 − 0.990791I
a = 0.640684 − 0.292773I
b = 1.131970 + 0.306003I
0.77396 − 1.88121I 0
u = 0.550861 + 0.895713I
a = 0.776838 + 0.264285I
b = 0.537876 − 1.046190I
0.74786 + 1.74560I 0
u = 0.550861 − 0.895713I
a = 0.776838 − 0.264285I
b = 0.537876 + 1.046190I
0.74786 − 1.74560I 0
u = 0.249663 + 0.860286I
a = −0.007952 − 0.255517I
b = −1.346110 + 0.066798I
1.46998 − 0.09365I −6.05569 − 0.75235I
u = 0.249663 − 0.860286I
a = −0.007952 + 0.255517I
b = −1.346110 − 0.066798I
1.46998 + 0.09365I −6.05569 + 0.75235I
u = 0.816030 + 0.352936I
a = 1.065950 − 0.372916I
b = −1.21954 − 0.72193I
1.34471 + 1.67458I 4.89337 − 2.28509I
u = 0.816030 − 0.352936I
a = 1.065950 + 0.372916I
b = −1.21954 + 0.72193I
1.34471 − 1.67458I 4.89337 + 2.28509I
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.457483 + 1.043140I
a = 0.204342 + 0.373914I
b = 0.698972 − 0.215128I
−0.48463 + 2.79065I 0
u = 0.457483 − 1.043140I
a = 0.204342 − 0.373914I
b = 0.698972 + 0.215128I
−0.48463 − 2.79065I 0
u = −0.492479 + 1.105960I
a = 0.363473 − 0.562434I
b = 0.483288 + 0.305590I
−3.32128 − 6.55734I 0
u = −0.492479 − 1.105960I
a = 0.363473 + 0.562434I
b = 0.483288 − 0.305590I
−3.32128 + 6.55734I 0
u = 0.258616 + 1.235310I
a = 1.77466 − 1.22348I
b = −0.172078 − 0.546913I
−16.2576 + 2.1070I 0
u = 0.258616 − 1.235310I
a = 1.77466 + 1.22348I
b = −0.172078 + 0.546913I
−16.2576 − 2.1070I 0
u = 0.696765 + 0.232307I
a = −1.16792 + 1.33211I
b = 0.171332 − 0.345569I
−13.19110 + 1.27884I −7.41673 − 0.45833I
u = 0.696765 − 0.232307I
a = −1.16792 − 1.33211I
b = 0.171332 + 0.345569I
−13.19110 − 1.27884I −7.41673 + 0.45833I
u = −0.682790 + 0.263870I
a = 0.438693 − 0.369280I
b = −0.342223 + 0.086473I
−0.95985 + 2.04685I −1.75065 − 3.12369I
u = −0.682790 − 0.263870I
a = 0.438693 + 0.369280I
b = −0.342223 − 0.086473I
−0.95985 − 2.04685I −1.75065 + 3.12369I
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.174623 + 1.260770I
a = −2.35850 + 0.45076I
b = −1.53794 − 0.61406I
−11.49590 + 1.71321I 0
u = −0.174623 − 1.260770I
a = −2.35850 − 0.45076I
b = −1.53794 + 0.61406I
−11.49590 − 1.71321I 0
u = −0.306605 + 1.249510I
a = 0.200371 + 0.206893I
b = 0.627190 + 0.049373I
−5.37789 − 1.23730I 0
u = −0.306605 − 1.249510I
a = 0.200371 − 0.206893I
b = 0.627190 − 0.049373I
−5.37789 + 1.23730I 0
u = −1.285920 + 0.192101I
a = −1.42596 − 0.15956I
b = 2.57629 − 0.75755I
−15.2764 − 8.8264I 0
u = −1.285920 − 0.192101I
a = −1.42596 + 0.15956I
b = 2.57629 + 0.75755I
−15.2764 + 8.8264I 0
u = −0.656758
a = −1.69115
b = 0.229294
−7.54151 −19.1290
u = 0.030952 + 1.346990I
a = −0.59570 − 1.40447I
b = −0.841490 − 0.064539I
−5.51440 + 0.30301I 0
u = 0.030952 − 1.346990I
a = −0.59570 + 1.40447I
b = −0.841490 + 0.064539I
−5.51440 − 0.30301I 0
u = 0.016235 + 1.351670I
a = −0.74947 + 1.55560I
b = −0.902586 + 0.406360I
−8.88905 + 3.84557I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.016235 − 1.351670I
a = −0.74947 − 1.55560I
b = −0.902586 − 0.406360I
−8.88905 − 3.84557I 0
u = 0.895451 + 1.019690I
a = 0.417165 + 0.878340I
b = 1.62581 − 2.01395I
0.31944 + 4.24899I 0
u = 0.895451 − 1.019690I
a = 0.417165 − 0.878340I
b = 1.62581 + 2.01395I
0.31944 − 4.24899I 0
u = −0.387601 + 1.301540I
a = −0.48828 − 2.11903I
b = 1.79526 − 0.66734I
−9.22324 − 6.23066I 0
u = −0.387601 − 1.301540I
a = −0.48828 + 2.11903I
b = 1.79526 + 0.66734I
−9.22324 + 6.23066I 0
u = −0.254005 + 1.347870I
a = 0.707175 + 1.216390I
b = −0.250688 + 0.217652I
−11.89940 − 3.29862I 0
u = −0.254005 − 1.347870I
a = 0.707175 − 1.216390I
b = −0.250688 − 0.217652I
−11.89940 + 3.29862I 0
u = −0.089807 + 1.382760I
a = −0.33602 + 1.52963I
b = −0.830903 + 0.034127I
−9.26019 − 5.11499I 0
u = −0.089807 − 1.382760I
a = −0.33602 − 1.52963I
b = −0.830903 − 0.034127I
−9.26019 + 5.11499I 0
u = 0.142080 + 1.389040I
a = −0.957401 + 0.071022I
b = −1.53212 + 0.09517I
−7.50523 + 2.04977I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.142080 − 1.389040I
a = −0.957401 − 0.071022I
b = −1.53212 − 0.09517I
−7.50523 − 2.04977I 0
u = 1.46014
a = −1.47207
b = 3.47659
−9.73353 0
u = −0.17379 + 1.44995I
a = −0.206285 − 0.120922I
b = −1.49106 + 0.16967I
−14.0649 − 6.1119I 0
u = −0.17379 − 1.44995I
a = −0.206285 + 0.120922I
b = −1.49106 − 0.16967I
−14.0649 + 6.1119I 0
u = 0.31970 + 1.42902I
a = 0.13246 + 1.67735I
b = 1.60069 + 0.52413I
−4.28551 + 5.79817I 0
u = 0.31970 − 1.42902I
a = 0.13246 − 1.67735I
b = 1.60069 − 0.52413I
−4.28551 − 5.79817I 0
u = 0.27320 + 1.45649I
a = 0.197724 − 1.052900I
b = −0.204744 + 0.178990I
−18.7460 + 4.8784I 0
u = 0.27320 − 1.45649I
a = 0.197724 + 1.052900I
b = −0.204744 − 0.178990I
−18.7460 − 4.8784I 0
u = −0.426812 + 0.260862I
a = −2.07816 + 1.63560I
b = 1.48606 − 0.39290I
−8.33818 − 3.82630I −4.41107 + 3.39985I
u = −0.426812 − 0.260862I
a = −2.07816 − 1.63560I
b = 1.48606 + 0.39290I
−8.33818 + 3.82630I −4.41107 − 3.39985I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.097833 + 0.474622I
a = −0.827808 + 0.678647I
b = 0.294933 + 0.730719I
−1.319160 − 0.440236I −9.35435 + 2.21690I
u = −0.097833 − 0.474622I
a = −0.827808 − 0.678647I
b = 0.294933 − 0.730719I
−1.319160 + 0.440236I −9.35435 − 2.21690I
u = −0.37887 + 1.50747I
a = 0.154569 − 1.209630I
b = 1.96550 − 0.01342I
−10.95380 − 3.84815I 0
u = −0.37887 − 1.50747I
a = 0.154569 + 1.209630I
b = 1.96550 + 0.01342I
−10.95380 + 3.84815I 0
u = 0.434862
a = −1.15792
b = 1.73830
−2.71311 4.97120
u = −0.53243 + 1.51468I
a = 0.17579 + 1.53528I
b = −2.26321 + 0.64860I
18.7748 − 15.2291I 0
u = −0.53243 − 1.51468I
a = 0.17579 − 1.53528I
b = −2.26321 − 0.64860I
18.7748 + 15.2291I 0
u = −0.78553 + 1.46938I
a = −0.008826 + 1.081540I
b = −2.98528 − 0.34680I
−19.0465 + 1.4457I 0
u = −0.78553 − 1.46938I
a = −0.008826 − 1.081540I
b = −2.98528 + 0.34680I
−19.0465 − 1.4457I 0
u = 0.63716 + 1.58515I
a = 0.076750 − 1.383190I
b = −2.87479 − 0.66509I
−14.8125 + 7.4988I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.63716 − 1.58515I
a = 0.076750 + 1.383190I
b = −2.87479 + 0.66509I
−14.8125 − 7.4988I 0
u = −0.143681 + 0.044279I
a = −7.87520 − 3.81313I
b = 0.894949 + 0.189533I
−4.43324 − 4.09803I −12.1941 + 7.4744I
u = −0.143681 − 0.044279I
a = −7.87520 + 3.81313I
b = 0.894949 − 0.189533I
−4.43324 + 4.09803I −12.1941 − 7.4744I
u = 0.0149078
a = −55.6188
b = 0.661638
−1.19438 −8.68390
11
II. I
u
2
= h5.31 × 10
16
u
33
− 2.71 × 10
17
u
32
+ · · · + 1.01 × 10
18
b + 7.36 ×
10
17
, −1.67 × 10
19
u
33
+ 2.51 × 10
19
u
32
+ · · · + 5.56 × 10
19
a + 7.28 ×
10
19
, u
34
− 3u
33
+ · · · − 27u + 5i
(i) Arc colorings
a
10
=
0
u
a
12
=
1
0
a
1
=
1
−u
2
a
3
=
0.300484u
33
− 0.451857u
32
+ ··· − 11.2848u − 1.30978
−0.0525447u
33
+ 0.268029u
32
+ ··· + 12.0496u − 0.728556
a
9
=
−u
u
3
+ u
a
4
=
0.597381u
33
− 0.951533u
32
+ ··· − 11.1959u − 1.06778
0.0496895u
33
+ 0.346387u
32
+ ··· + 2.88773u + 0.984526
a
8
=
0.103858u
33
− 0.753674u
32
+ ··· + 12.6796u − 0.00462628
0.399254u
33
− 1.22377u
32
+ ··· + 13.6644u − 2.75474
a
7
=
0.503112u
33
− 1.97744u
32
+ ··· + 26.3439u − 2.75937
0.399254u
33
− 1.22377u
32
+ ··· + 13.6644u − 2.75474
a
5
=
0.880333u
33
− 1.84770u
32
+ ··· − 20.5109u + 2.14763
0.892975u
33
− 2.88608u
32
+ ··· + 13.6187u − 0.688373
a
2
=
0.331457u
33
− 0.303393u
32
+ ··· − 8.35774u − 2.18935
−1.05254u
33
+ 3.26803u
32
+ ··· + 7.04961u + 0.271444
a
6
=
0.0728670u
33
− 1.48623u
32
+ ··· + 50.8761u − 12.0674
−0.345156u
33
+ 1.22456u
32
+ ··· − 12.7354u + 2.73846
a
11
=
−1.00426u
33
+ 3.93758u
32
+ ··· − 30.1763u + 2.98429
0.169389u
33
− 0.104604u
32
+ ··· − 11.8324u + 2.91177
(ii) Obstruction class = 1
(iii) Cusp Shapes = −
2163458071743622590
11117810484131810393
u
33
+
36568167913572040564
11117810484131810393
u
32
+ ··· −
1342205609064896559183
11117810484131810393
u +
46639162711066437378
11117810484131810393
12
(iv) u-Polynomials at the component
13
Crossings u-Polynomials at each crossing
c
1
u
34
− 15u
33
+ ··· + 467u − 53
c
2
u
34
+ 2u
33
+ ··· + 3u − 1
c
3
u
34
− 11u
32
+ ··· − 7u + 3
c
4
u
34
− 12u
33
+ ··· − 1360u + 175
c
5
u
34
+ 12u
32
+ ··· + 5u − 3
c
6
u
34
− 2u
33
+ ··· − 3u − 1
c
7
u
34
+ u
33
+ ··· − u − 1
c
8
u
34
− 11u
32
+ ··· + 7u + 3
c
9
u
34
+ 3u
33
+ ··· + 27u + 5
c
10
u
34
+ 3u
33
+ ··· + 678u + 173
c
11
u
34
+ 12u
32
+ ··· − 5u − 3
c
12
u
34
− 3u
33
+ ··· − 27u + 5
14
15
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
34
− 43y
33
+ ··· − 6831y + 2809
c
2
, c
6
y
34
− 18y
33
+ ··· + 13y + 1
c
3
, c
8
y
34
− 22y
33
+ ··· − 217y + 9
c
4
y
34
− 36y
33
+ ··· − 651200y + 30625
c
5
, c
11
y
34
+ 24y
33
+ ··· + 143y + 9
c
7
y
34
+ 3y
33
+ ··· − 25y + 1
c
9
, c
12
y
34
+ 27y
33
+ ··· − 309y + 25
c
10
y
34
− y
33
+ ··· + 164154y + 29929
16
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.766380 + 0.506457I
a = 0.117856 − 0.160082I
b = 0.623438 + 0.869619I
−2.27085 + 1.95626I −9.24623 − 1.70967I
u = −0.766380 − 0.506457I
a = 0.117856 + 0.160082I
b = 0.623438 − 0.869619I
−2.27085 − 1.95626I −9.24623 + 1.70967I
u = −0.308433 + 1.080170I
a = 1.322530 + 0.396036I
b = −0.434514 − 0.496250I
−15.6918 − 1.2800I −10.72860 − 1.32316I
u = −0.308433 − 1.080170I
a = 1.322530 − 0.396036I
b = −0.434514 + 0.496250I
−15.6918 + 1.2800I −10.72860 + 1.32316I
u = 0.875882
a = −1.41620
b = 0.837071
−7.06851 −1.41880
u = 0.781874 + 0.374349I
a = 0.828422 − 0.587983I
b = −0.959535 − 0.479817I
0.74361 + 1.92657I −7.44260 − 5.71922I
u = 0.781874 − 0.374349I
a = 0.828422 + 0.587983I
b = −0.959535 + 0.479817I
0.74361 − 1.92657I −7.44260 + 5.71922I
u = 0.517506 + 1.024060I
a = −0.205606 + 0.227297I
b = 0.603730 − 0.117604I
−1.01482 + 2.80754I −12.27145 − 3.23297I
u = 0.517506 − 1.024060I
a = −0.205606 − 0.227297I
b = 0.603730 + 0.117604I
−1.01482 − 2.80754I −12.27145 + 3.23297I
u = −0.530685 + 1.059380I
a = −0.133097 + 0.342424I
b = −0.180839 + 0.401786I
−3.95149 − 6.85543I −13.0643 + 9.1794I
17
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.530685 − 1.059380I
a = −0.133097 − 0.342424I
b = −0.180839 − 0.401786I
−3.95149 + 6.85543I −13.0643 − 9.1794I
u = −0.106988 + 0.793293I
a = −1.92839 − 1.12133I
b = 1.46699 − 0.64171I
−9.43550 − 3.53143I −12.56667 + 1.79470I
u = −0.106988 − 0.793293I
a = −1.92839 + 1.12133I
b = 1.46699 + 0.64171I
−9.43550 + 3.53143I −12.56667 − 1.79470I
u = 0.025886 + 1.204170I
a = 0.303685 + 0.255539I
b = 1.49078 + 0.03844I
−0.191346 − 0.659027I −11.01369 + 0.18041I
u = 0.025886 − 1.204170I
a = 0.303685 − 0.255539I
b = 1.49078 − 0.03844I
−0.191346 + 0.659027I −11.01369 − 0.18041I
u = −0.037809 + 1.237270I
a = −1.94630 + 1.18242I
b = −1.70472 − 0.14443I
−11.27710 + 2.89887I −12.37719 − 4.00125I
u = −0.037809 − 1.237270I
a = −1.94630 − 1.18242I
b = −1.70472 + 0.14443I
−11.27710 − 2.89887I −12.37719 + 4.00125I
u = 0.094901 + 0.727736I
a = −0.450339 − 0.582207I
b = −1.280430 + 0.124276I
1.74291 + 1.07503I −2.00434 − 5.12506I
u = 0.094901 − 0.727736I
a = −0.450339 + 0.582207I
b = −1.280430 − 0.124276I
1.74291 − 1.07503I −2.00434 + 5.12506I
u = 0.825233 + 0.992874I
a = 0.951049 + 0.073749I
b = 0.06217 − 2.04842I
0.00735 + 2.45343I −9.65678 − 4.01473I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.825233 − 0.992874I
a = 0.951049 − 0.073749I
b = 0.06217 + 2.04842I
0.00735 − 2.45343I −9.65678 + 4.01473I
u = −0.565426 + 0.391970I
a = 2.10301 + 0.78370I
b = −1.176150 + 0.693946I
−4.00587 + 3.40968I −6.81173 + 0.18467I
u = −0.565426 − 0.391970I
a = 2.10301 − 0.78370I
b = −1.176150 − 0.693946I
−4.00587 − 3.40968I −6.81173 − 0.18467I
u = −0.300164 + 1.301050I
a = −0.04683 − 1.87237I
b = 1.48880 − 0.09537I
−7.27855 − 6.80519I −8.88118 + 6.12054I
u = −0.300164 − 1.301050I
a = −0.04683 + 1.87237I
b = 1.48880 + 0.09537I
−7.27855 + 6.80519I −8.88118 − 6.12054I
u = 0.922425 + 1.028280I
a = 0.348151 + 1.114270I
b = 2.20817 − 2.16137I
−0.10540 + 4.13873I −15.7530 − 3.7448I
u = 0.922425 − 1.028280I
a = 0.348151 − 1.114270I
b = 2.20817 + 2.16137I
−0.10540 − 4.13873I −15.7530 + 3.7448I
u = −0.12017 + 1.41349I
a = −1.135870 − 0.798894I
b = −1.191820 − 0.590009I
−8.82752 − 0.38879I −12.56677 + 0.I
u = −0.12017 − 1.41349I
a = −1.135870 + 0.798894I
b = −1.191820 + 0.590009I
−8.82752 + 0.38879I −12.56677 + 0.I
u = 0.22660 + 1.42133I
a = 0.60486 − 1.42107I
b = −0.273567 − 0.658396I
−12.19970 + 3.90061I −14.5545 − 6.4432I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.22660 − 1.42133I
a = 0.60486 + 1.42107I
b = −0.273567 + 0.658396I
−12.19970 − 3.90061I −14.5545 + 6.4432I
u = 0.30041 + 1.44450I
a = 0.10153 + 1.65659I
b = 1.37530 + 0.62619I
−5.07286 + 5.81700I −12.74429 + 0.I
u = 0.30041 − 1.44450I
a = 0.10153 − 1.65659I
b = 1.37530 − 0.62619I
−5.07286 − 5.81700I −12.74429 + 0.I
u = 0.206565
a = −4.45311
b = 1.92730
−3.05706 −19.2140
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
(u
34
− 15u
33
+ ··· + 467u − 53)(u
64
− 6u
63
+ ··· − 11638u + 1297)
c
2
(u
34
+ 2u
33
+ ··· + 3u − 1)(u
64
+ 3u
63
+ ··· + 274122u + 178861)
c
3
(u
34
− 11u
32
+ ··· − 7u + 3)(u
64
− u
63
+ ··· − 514u + 43)
c
4
(u
34
− 12u
33
+ ··· − 1360u + 175)(u
64
− 7u
63
+ ··· + 35883u − 2633)
c
5
(u
34
+ 12u
32
+ ··· + 5u − 3)(u
64
+ u
63
+ ··· − 146u − 61)
c
6
(u
34
− 2u
33
+ ··· − 3u − 1)(u
64
+ 3u
63
+ ··· + 274122u + 178861)
c
7
(u
34
+ u
33
+ ··· − u − 1)(u
64
+ 2u
63
+ ··· − 1926u − 359)
c
8
(u
34
− 11u
32
+ ··· + 7u + 3)(u
64
− u
63
+ ··· − 514u + 43)
c
9
(u
34
+ 3u
33
+ ··· + 27u + 5)(u
64
+ 2u
63
+ ··· + 52u − 1)
c
10
(u
34
+ 3u
33
+ ··· + 678u + 173)
· (u
64
− 8u
63
+ ··· + 360305u − 493889)
c
11
(u
34
+ 12u
32
+ ··· − 5u − 3)(u
64
+ u
63
+ ··· − 146u − 61)
c
12
(u
34
− 3u
33
+ ··· − 27u + 5)(u
64
+ 2u
63
+ ··· + 52u − 1)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
(y
34
− 43y
33
+ ··· − 6831y + 2809)
· (y
64
− 102y
63
+ ··· − 115080144y + 1682209)
c
2
, c
6
(y
34
− 18y
33
+ ··· + 13y + 1)
· (y
64
− 97y
63
+ ··· − 66879492684y + 31991257321)
c
3
, c
8
(y
34
− 22y
33
+ ··· − 217y + 9)(y
64
− 65y
63
+ ··· − 189118y + 1849)
c
4
(y
34
− 36y
33
+ ··· − 651200y + 30625)
· (y
64
− 103y
63
+ ··· − 1148483033y + 6932689)
c
5
, c
11
(y
34
+ 24y
33
+ ··· + 143y + 9)(y
64
+ 61y
63
+ ··· − 160274y + 3721)
c
7
(y
34
+ 3y
33
+ ··· − 25y + 1)
· (y
64
− 20y
63
+ ··· + 12391674y + 128881)
c
9
, c
12
(y
34
+ 27y
33
+ ··· − 309y + 25)(y
64
+ 56y
63
+ ··· − 4566y + 1)
c
10
(y
34
− y
33
+ ··· + 164154y + 29929)
· (y
64
− 36y
63
+ ··· − 918166302603y + 243926344321)
22
