12n
0568
(K12n
0568
)
A knot diagram
1
Linearized knot diagam
3 7 12 10 11 2 5 12 3 8 6 10
Solving Sequence
5,11 2,6
7 3 8 12 1 10 4 9
c
5
c
6
c
2
c
7
c
11
c
1
c
10
c
4
c
9
c
3
, c
8
, c
12
Ideals for irreducible components
2
of X
par
I
u
1
= h3.56196 × 10
180
u
75
− 6.92402 × 10
180
u
74
+ ··· + 4.56975 × 10
180
b − 7.18244 × 10
182
,
3.11091 × 10
181
u
75
− 7.34911 × 10
181
u
74
+ ··· + 1.32523 × 10
182
a − 3.27637 × 10
183
,
u
76
− 3u
75
+ ··· + 936u + 232i
I
u
2
= h248830399u
22
+ 208402801u
21
+ ··· + 79543084b − 1349697652,
410409361u
22
+ 348035792u
21
+ ··· + 79543084a − 2188204696, u
23
+ 2u
22
+ ··· − 8u − 8i
* 2 irreducible components of dim
C
= 0, with total 99 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
= h3.56 × 10
180
u
75
− 6.92 × 10
180
u
74
+ · · · + 4.57 × 10
180
b − 7.18 ×
10
182
, 3.11 × 10
181
u
75
− 7.35 × 10
181
u
74
+ · · · + 1.33 × 10
182
a − 3.28 ×
10
183
, u
76
− 3u
75
+ · · · + 936u + 232i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−0.234745u
75
+ 0.554555u
74
+ ··· + 169.599u + 24.7231
−0.779466u
75
+ 1.51519u
74
+ ··· + 787.398u + 157.174
a
6
=
1
u
2
a
7
=
0.498809u
75
− 0.947197u
74
+ ··· − 460.943u − 87.1424
1.15577u
75
− 2.09127u
74
+ ··· − 1178.23u − 242.449
a
3
=
0.913618u
75
− 1.62170u
74
+ ··· − 954.260u − 197.783
0.641894u
75
− 1.15647u
74
+ ··· − 655.502u − 136.716
a
8
=
−0.656963u
75
+ 1.14407u
74
+ ··· + 717.288u + 155.306
1.15577u
75
− 2.09127u
74
+ ··· − 1178.23u − 242.449
a
12
=
−u
−u
3
+ u
a
1
=
0.631741u
75
− 1.27025u
74
+ ··· − 563.644u − 116.446
0.404533u
75
− 0.758262u
74
+ ··· − 382.358u − 76.2189
a
10
=
−0.234311u
75
+ 0.585458u
74
+ ··· + 97.6788u + 10.2271
1.16020u
75
− 2.19526u
74
+ ··· − 1139.10u − 227.223
a
4
=
0.458281u
75
− 0.798480u
74
+ ··· − 499.398u − 103.931
0.480346u
75
− 0.857747u
74
+ ··· − 496.673u − 104.640
a
9
=
−1.15033u
75
+ 2.16962u
74
+ ··· + 1108.09u + 217.684
−1.71904u
75
+ 3.13616u
74
+ ··· + 1745.42u + 358.560
(ii) Obstruction class = −1
(iii) Cusp Shapes = −0.983457u
75
+ 1.79316u
74
+ ··· + 1053.18u + 204.030
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
4(4u
76
+ 181u
75
+ ··· + 50u + 1)
c
2
, c
6
2(2u
76
− u
75
+ ··· − 2u + 1)
c
3
u
76
− 7u
75
+ ··· + 842u + 773
c
4
u
76
+ u
75
+ ··· + 137983u + 158846
c
5
, c
11
u
76
− 3u
75
+ ··· + 936u + 232
c
7
u
76
− 5u
75
+ ··· − 19313u + 1532
c
8
u
76
− 4u
75
+ ··· + 20080608u + 2598032
c
9
2(2u
76
+ u
75
+ ··· + 296u + 712)
c
10
4(4u
76
+ 27u
75
+ ··· + 3218u + 419)
c
12
2(2u
76
+ 7u
75
+ ··· + 11068u + 1009)
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
76
+ 15y
75
+ ··· − 166y + 1)
c
2
, c
6
4(4y
76
− 181y
75
+ ··· − 50y + 1)
c
3
y
76
− 107y
75
+ ··· − 13723192y + 597529
c
4
y
76
+ 33y
75
+ ··· + 325811545407y + 25232051716
c
5
, c
11
y
76
− 51y
75
+ ··· − 1128512y + 53824
c
7
y
76
− 11y
75
+ ··· − 47423585y + 2347024
c
8
y
76
+ 62y
75
+ ··· + 198572181119104y + 6749770273024
c
9
4(4y
76
+ 367y
75
+ ··· + 3.78022 × 10
7
y + 506944)
c
10
16(16y
76
+ 487y
75
+ ··· + 8708976y + 175561)
c
12
4(4y
76
+ 331y
75
+ ··· + 2.10845 × 10
8
y + 1018081)
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.005098 + 1.009090I
a = 0.393251 + 0.810515I
b = −0.705606 + 0.017434I
−4.16391 − 4.94670I 0. + 3.45130I
u = −0.005098 − 1.009090I
a = 0.393251 − 0.810515I
b = −0.705606 − 0.017434I
−4.16391 + 4.94670I 0. − 3.45130I
u = 0.933682 + 0.297571I
a = −0.108605 − 0.446950I
b = 0.636825 + 0.264630I
−0.08245 − 4.80485I 0
u = 0.933682 − 0.297571I
a = −0.108605 + 0.446950I
b = 0.636825 − 0.264630I
−0.08245 + 4.80485I 0
u = 0.176764 + 1.009050I
a = −0.361751 − 0.893889I
b = 1.61810 + 0.10958I
1.70045 + 2.91637I 0
u = 0.176764 − 1.009050I
a = −0.361751 + 0.893889I
b = 1.61810 − 0.10958I
1.70045 − 2.91637I 0
u = 1.018160 + 0.180797I
a = −3.61763 + 0.47037I
b = −2.95467 − 0.94404I
−6.55599 − 2.35969I 0
u = 1.018160 − 0.180797I
a = −3.61763 − 0.47037I
b = −2.95467 + 0.94404I
−6.55599 + 2.35969I 0
u = −1.037780 + 0.050306I
a = −2.18608 − 0.36963I
b = −1.068720 − 0.752547I
−2.48276 + 0.74819I 0
u = −1.037780 − 0.050306I
a = −2.18608 + 0.36963I
b = −1.068720 + 0.752547I
−2.48276 − 0.74819I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.279819 + 0.894406I
a = −0.240842 − 0.954939I
b = 0.473947 + 0.149110I
2.20675 + 2.15189I −2.00000 − 6.97084I
u = −0.279819 − 0.894406I
a = −0.240842 + 0.954939I
b = 0.473947 − 0.149110I
2.20675 − 2.15189I −2.00000 + 6.97084I
u = −0.931439 + 0.093793I
a = 0.353517 − 0.205717I
b = −0.228533 + 0.380605I
−1.57052 + 0.52011I −4.24531 + 0.I
u = −0.931439 − 0.093793I
a = 0.353517 + 0.205717I
b = −0.228533 − 0.380605I
−1.57052 − 0.52011I −4.24531 + 0.I
u = −1.077730 + 0.076763I
a = 1.84215 + 0.42920I
b = 0.682352 − 0.497417I
−3.02707 − 0.18143I 0
u = −1.077730 − 0.076763I
a = 1.84215 − 0.42920I
b = 0.682352 + 0.497417I
−3.02707 + 0.18143I 0
u = −1.109660 + 0.203084I
a = 1.61262 + 1.92333I
b = 1.65697 + 2.09432I
−9.86665 + 5.91796I 0
u = −1.109660 − 0.203084I
a = 1.61262 − 1.92333I
b = 1.65697 − 2.09432I
−9.86665 − 5.91796I 0
u = 1.136350 + 0.003599I
a = −1.064320 − 0.075553I
b = −1.72518 − 0.75050I
−7.54536 + 1.24468I 0
u = 1.136350 − 0.003599I
a = −1.064320 + 0.075553I
b = −1.72518 + 0.75050I
−7.54536 − 1.24468I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.544396 + 1.000180I
a = −0.095435 + 0.415036I
b = 1.69336 + 0.10370I
−8.85105 + 1.75177I 0
u = −0.544396 − 1.000180I
a = −0.095435 − 0.415036I
b = 1.69336 − 0.10370I
−8.85105 − 1.75177I 0
u = 1.167580 + 0.149402I
a = 1.72845 − 0.61424I
b = 1.52072 − 0.86765I
−2.82519 − 4.47594I 0
u = 1.167580 − 0.149402I
a = 1.72845 + 0.61424I
b = 1.52072 + 0.86765I
−2.82519 + 4.47594I 0
u = 1.141340 + 0.356267I
a = −1.97705 + 0.57022I
b = −1.379620 − 0.269089I
−8.60220 − 8.16498I 0
u = 1.141340 − 0.356267I
a = −1.97705 − 0.57022I
b = −1.379620 + 0.269089I
−8.60220 + 8.16498I 0
u = 1.100400 + 0.514009I
a = 0.182278 − 0.554378I
b = 0.476968 − 0.410769I
−0.63838 − 5.02004I 0
u = 1.100400 − 0.514009I
a = 0.182278 + 0.554378I
b = 0.476968 + 0.410769I
−0.63838 + 5.02004I 0
u = 1.111630 + 0.510249I
a = 0.303809 − 0.263324I
b = 0.425849 − 0.400376I
−0.68506 − 5.04397I 0
u = 1.111630 − 0.510249I
a = 0.303809 + 0.263324I
b = 0.425849 + 0.400376I
−0.68506 + 5.04397I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.741491 + 0.975965I
a = 0.627850 − 0.813152I
b = 0.160474 + 1.091760I
0.664828 + 0.016710I 0
u = 0.741491 − 0.975965I
a = 0.627850 + 0.813152I
b = 0.160474 − 1.091760I
0.664828 − 0.016710I 0
u = 0.002030 + 1.272340I
a = 0.513090 + 0.516566I
b = −2.01029 − 0.25360I
−6.77946 + 10.25100I 0
u = 0.002030 − 1.272340I
a = 0.513090 − 0.516566I
b = −2.01029 + 0.25360I
−6.77946 − 10.25100I 0
u = −0.290112 + 1.251830I
a = 0.721546 − 0.371631I
b = −2.33695 − 0.28961I
−0.46245 − 2.32653I 0
u = −0.290112 − 1.251830I
a = 0.721546 + 0.371631I
b = −2.33695 + 0.28961I
−0.46245 + 2.32653I 0
u = 0.319419 + 0.638323I
a = 0.266507 + 0.149010I
b = 0.429896 + 0.399818I
1.58623 + 0.62032I 1.131389 − 0.019601I
u = 0.319419 − 0.638323I
a = 0.266507 − 0.149010I
b = 0.429896 − 0.399818I
1.58623 − 0.62032I 1.131389 + 0.019601I
u = 0.385520 + 0.578821I
a = 0.497687 − 0.253565I
b = 0.308115 + 0.179903I
1.44081 + 0.61682I 4.83546 + 0.93463I
u = 0.385520 − 0.578821I
a = 0.497687 + 0.253565I
b = 0.308115 − 0.179903I
1.44081 − 0.61682I 4.83546 − 0.93463I
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.214200 + 0.479278I
a = −0.030527 + 0.386320I
b = −0.171089 − 0.244683I
−0.85536 + 2.82110I 0
u = −1.214200 − 0.479278I
a = −0.030527 − 0.386320I
b = −0.171089 + 0.244683I
−0.85536 − 2.82110I 0
u = 1.274540 + 0.287916I
a = −2.15458 + 0.40448I
b = −2.52672 − 0.90327I
−6.55815 − 1.94136I 0
u = 1.274540 − 0.287916I
a = −2.15458 − 0.40448I
b = −2.52672 + 0.90327I
−6.55815 + 1.94136I 0
u = 0.194290 + 0.652674I
a = 0.004037 − 0.292078I
b = −1.108940 + 0.699571I
−5.77638 + 4.37759I −3.04054 − 1.90544I
u = 0.194290 − 0.652674I
a = 0.004037 + 0.292078I
b = −1.108940 − 0.699571I
−5.77638 − 4.37759I −3.04054 + 1.90544I
u = −1.316740 + 0.342524I
a = 2.22467 + 0.45472I
b = 2.84462 − 0.86702I
−3.74572 + 7.98813I 0
u = −1.316740 − 0.342524I
a = 2.22467 − 0.45472I
b = 2.84462 + 0.86702I
−3.74572 − 7.98813I 0
u = −0.540950 + 0.287850I
a = 1.59281 − 1.42860I
b = 1.005260 − 0.506933I
−8.08495 − 3.80008I −6.48316 + 2.78169I
u = −0.540950 − 0.287850I
a = 1.59281 + 1.42860I
b = 1.005260 + 0.506933I
−8.08495 + 3.80008I −6.48316 − 2.78169I
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.280390 + 0.542150I
a = −0.405570 + 0.444554I
b = −1.39952 + 0.78269I
−8.14535 − 0.29592I 0
u = 1.280390 − 0.542150I
a = −0.405570 − 0.444554I
b = −1.39952 − 0.78269I
−8.14535 + 0.29592I 0
u = 1.369510 + 0.269960I
a = 1.75943 − 0.21348I
b = 1.79429 + 1.07646I
−15.0106 − 5.5218I 0
u = 1.369510 − 0.269960I
a = 1.75943 + 0.21348I
b = 1.79429 − 1.07646I
−15.0106 + 5.5218I 0
u = −1.390460 + 0.141716I
a = −1.70864 − 0.95421I
b = −2.53555 − 0.75803I
−10.89910 − 1.69454I 0
u = −1.390460 − 0.141716I
a = −1.70864 + 0.95421I
b = −2.53555 + 0.75803I
−10.89910 + 1.69454I 0
u = 1.329630 + 0.472866I
a = 1.82348 − 0.90583I
b = 2.91957 + 0.23245I
−2.19507 − 8.22505I 0
u = 1.329630 − 0.472866I
a = 1.82348 + 0.90583I
b = 2.91957 − 0.23245I
−2.19507 + 8.22505I 0
u = −1.33351 + 0.50009I
a = 0.205326 − 0.345072I
b = 0.181642 + 0.317254I
−8.32222 + 10.32410I 0
u = −1.33351 − 0.50009I
a = 0.205326 + 0.345072I
b = 0.181642 − 0.317254I
−8.32222 − 10.32410I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.097023 + 0.516748I
a = −1.53614 + 0.33142I
b = 1.267050 + 0.268926I
0.63412 − 4.46156I −3.76825 + 6.77202I
u = 0.097023 − 0.516748I
a = −1.53614 − 0.33142I
b = 1.267050 − 0.268926I
0.63412 + 4.46156I −3.76825 − 6.77202I
u = −1.34581 + 0.61160I
a = −1.62036 − 0.84261I
b = −2.53126 + 1.02229I
−4.08423 + 8.86167I 0
u = −1.34581 − 0.61160I
a = −1.62036 + 0.84261I
b = −2.53126 − 1.02229I
−4.08423 − 8.86167I 0
u = 1.48533 + 0.07762I
a = −1.79656 + 0.60283I
b = −3.47474 + 0.80956I
−8.62358 + 1.01784I 0
u = 1.48533 − 0.07762I
a = −1.79656 − 0.60283I
b = −3.47474 − 0.80956I
−8.62358 − 1.01784I 0
u = 1.41487 + 0.58489I
a = −1.63665 + 0.81194I
b = −2.79765 − 0.68796I
−11.2576 − 16.6985I 0
u = 1.41487 − 0.58489I
a = −1.63665 − 0.81194I
b = −2.79765 + 0.68796I
−11.2576 + 16.6985I 0
u = −0.386897 + 0.249171I
a = 2.06957 − 0.41148I
b = −0.267376 + 0.524327I
−3.14659 + 1.15669I 0.68364 − 1.66386I
u = −0.386897 − 0.249171I
a = 2.06957 + 0.41148I
b = −0.267376 − 0.524327I
−3.14659 − 1.15669I 0.68364 + 1.66386I
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.30406 + 0.82899I
a = 1.05664 + 1.05525I
b = 2.16979 − 0.68015I
−10.94130 + 5.20376I 0
u = −1.30406 − 0.82899I
a = 1.05664 − 1.05525I
b = 2.16979 + 0.68015I
−10.94130 − 5.20376I 0
u = −0.420966 + 0.043691I
a = 1.177750 − 0.720907I
b = −0.633678 + 0.044005I
−1.261910 + 0.263190I −8.70761 + 0.23744I
u = −0.420966 − 0.043691I
a = 1.177750 + 0.720907I
b = −0.633678 − 0.044005I
−1.261910 − 0.263190I −8.70761 − 0.23744I
u = −1.65030 + 0.51603I
a = −1.148450 − 0.155755I
b = −1.90968 + 1.96171I
−12.01700 − 3.30289I 0
u = −1.65030 − 0.51603I
a = −1.148450 + 0.155755I
b = −1.90968 − 1.96171I
−12.01700 + 3.30289I 0
12
II. I
u
2
= h2.49 × 10
8
u
22
+ 2.08 × 10
8
u
21
+ · · · + 7.95 × 10
7
b − 1.35 × 10
9
, 4.10 ×
10
8
u
22
+3.48×10
8
u
21
+· · · +7.95×10
7
a−2.19×10
9
, u
23
+2u
22
+· · · − 8u −8i
(i) Arc colorings
a
5
=
1
0
a
11
=
0
u
a
2
=
−5.15959u
22
− 4.37544u
21
+ ··· + 13.1329u + 27.5097
−3.12825u
22
− 2.62000u
21
+ ··· + 7.89685u + 16.9681
a
6
=
1
u
2
a
7
=
5.96267u
22
+ 5.49417u
21
+ ··· − 13.9666u − 37.3530
3.71013u
22
+ 4.51949u
21
+ ··· − 2.41295u − 30.8696
a
3
=
0.180806u
22
+ 1.09306u
21
+ ··· + 4.41132u − 6.09049
2.40989u
22
+ 2.40623u
21
+ ··· − 5.49037u − 16.5146
a
8
=
2.25254u
22
+ 0.974685u
21
+ ··· − 11.5536u − 6.48339
3.71013u
22
+ 4.51949u
21
+ ··· − 2.41295u − 30.8696
a
12
=
−u
−u
3
+ u
a
1
=
−4.92777u
22
− 6.66663u
21
+ ··· − 3.35723u + 31.9947
−3.71013u
22
− 4.51949u
21
+ ··· + 2.41295u + 30.8696
a
10
=
−3.86653u
22
− 5.39577u
21
+ ··· − 1.15260u + 30.2425
1.89779u
22
+ 2.79821u
21
+ ··· + 0.830807u − 20.7597
a
4
=
−2.71997u
22
− 3.16714u
21
+ ··· + 3.22271u + 23.5905
5.45629u
22
+ 4.93488u
21
+ ··· − 15.1772u − 33.8649
a
9
=
4.16367u
22
+ 3.18690u
21
+ ··· − 13.2821u − 21.7105
2.88236u
22
+ 4.09623u
21
+ ··· + 1.72423u − 28.5228
(ii) Obstruction class = 1
(iii) Cusp Shapes =
5516374159
636344672
u
22
+
9107813537
636344672
u
21
+ ··· +
301737269
39771542
u −
9773924821
79543084
13
(iv) u-Polynomials at the component
14
Crossings u-Polynomials at each crossing
c
1
4(4u
23
− 65u
22
+ ··· + 15u − 1)
c
2
2(2u
23
+ u
22
+ ··· − 3u + 1)
c
3
u
23
+ 6u
22
+ ··· + 17u + 1
c
4
u
23
+ 3u
21
+ ··· + 33u + 14
c
5
u
23
+ 2u
22
+ ··· − 8u − 8
c
6
2(2u
23
− u
22
+ ··· − 3u − 1)
c
7
u
23
+ 2u
22
+ ··· − u − 4
c
8
u
23
− 3u
22
+ ··· + 40u − 16
c
9
2(2u
23
− 3u
22
+ ··· − 8u − 8)
c
10
4(4u
23
− 41u
22
+ ··· + 5u − 1)
c
11
u
23
− 2u
22
+ ··· − 8u + 8
c
12
2(2u
23
+ u
22
+ ··· − u + 1)
15
16
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
16(16y
23
− 321y
22
+ ··· − 13y −1)
c
2
, c
6
4(4y
23
− 65y
22
+ ··· + 15y −1)
c
3
y
23
− 22y
22
+ ··· − 11y −1
c
4
y
23
+ 6y
22
+ ··· + 1061y −196
c
5
, c
11
y
23
− 14y
22
+ ··· + 256y −64
c
7
y
23
+ 2y
22
+ ··· + 73y −16
c
8
y
23
+ 23y
22
+ ··· + 6080y −256
c
9
4(4y
23
+ 51y
22
+ ··· + 384y −64)
c
10
16(16y
23
− 297y
22
+ ··· − 3y −1)
c
12
4(4y
23
+ 31y
22
+ ··· + 13y −1)
17
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.356302 + 0.921246I
a = −0.426449 − 0.898055I
b = 1.81269 − 0.26418I
2.07565 + 3.56521I 0.83283 − 7.40934I
u = 0.356302 − 0.921246I
a = −0.426449 + 0.898055I
b = 1.81269 + 0.26418I
2.07565 − 3.56521I 0.83283 + 7.40934I
u = −0.659298 + 0.709797I
a = 0.183477 + 0.380951I
b = −0.351559 − 0.549190I
0.91405 − 1.41548I −1.11361 + 5.21408I
u = −0.659298 − 0.709797I
a = 0.183477 − 0.380951I
b = −0.351559 + 0.549190I
0.91405 + 1.41548I −1.11361 − 5.21408I
u = 1.04960
a = −2.61659
b = −0.614702
−3.12449 −70.7810
u = −0.974176 + 0.395630I
a = 1.57498 + 1.75261I
b = 1.40615 + 0.67428I
−8.68718 + 5.83308I −5.34407 − 4.88575I
u = −0.974176 − 0.395630I
a = 1.57498 − 1.75261I
b = 1.40615 − 0.67428I
−8.68718 − 5.83308I −5.34407 + 4.88575I
u = −0.969026 + 0.417007I
a = −0.357355 − 0.102308I
b = 0.217924 − 0.434540I
0.08939 + 5.69307I 0.41476 − 11.59398I
u = −0.969026 − 0.417007I
a = −0.357355 + 0.102308I
b = 0.217924 + 0.434540I
0.08939 − 5.69307I 0.41476 + 11.59398I
u = −0.446659 + 0.962675I
a = −0.182179 − 0.915290I
b = 0.156899 + 0.194953I
2.40763 + 1.37050I −0.171489 + 1.394959I
18
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.446659 − 0.962675I
a = −0.182179 + 0.915290I
b = 0.156899 − 0.194953I
2.40763 − 1.37050I −0.171489 − 1.394959I
u = 0.235891 + 0.795309I
a = 0.720914 − 0.951185I
b = −0.991580 + 0.519972I
−0.059835 − 1.122220I −4.89482 + 1.47895I
u = 0.235891 − 0.795309I
a = 0.720914 + 0.951185I
b = −0.991580 − 0.519972I
−0.059835 + 1.122220I −4.89482 − 1.47895I
u = 0.728014 + 0.278875I
a = −2.47522 + 1.35985I
b = −2.16573 − 0.15001I
−5.70885 − 2.28203I −0.70922 + 2.28852I
u = 0.728014 − 0.278875I
a = −2.47522 − 1.35985I
b = −2.16573 + 0.15001I
−5.70885 + 2.28203I −0.70922 − 2.28852I
u = −1.184950 + 0.568415I
a = 0.040381 + 0.403877I
b = −0.070996 − 0.158742I
−0.10085 + 4.15383I −1.76815 − 1.34475I
u = −1.184950 − 0.568415I
a = 0.040381 − 0.403877I
b = −0.070996 + 0.158742I
−0.10085 − 4.15383I −1.76815 + 1.34475I
u = 1.319470 + 0.481768I
a = 1.90814 − 0.84640I
b = 2.92161 + 0.56057I
−1.35982 − 8.75350I −1.07603 + 8.75787I
u = 1.319470 − 0.481768I
a = 1.90814 + 0.84640I
b = 2.92161 − 0.56057I
−1.35982 + 8.75350I −1.07603 − 8.75787I
u = −1.383620 + 0.262159I
a = −1.090950 − 0.766666I
b = −1.47323 − 0.28646I
−10.42060 − 2.61211I −7.27563 + 4.52171I
19
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.383620 − 0.262159I
a = −1.090950 + 0.766666I
b = −1.47323 + 0.28646I
−10.42060 + 2.61211I −7.27563 − 4.52171I
u = 1.45325 + 0.11507I
a = −2.33744 − 0.07338I
b = −4.15483 − 0.72662I
−8.84112 + 0.24124I −10.76982 + 2.03355I
u = 1.45325 − 0.11507I
a = −2.33744 + 0.07338I
b = −4.15483 + 0.72662I
−8.84112 − 0.24124I −10.76982 − 2.03355I
20
III. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
16(4u
23
− 65u
22
+ ··· + 15u − 1)(4u
76
+ 181u
75
+ ··· + 50u + 1)
c
2
4(2u
23
+ u
22
+ ··· − 3u + 1)(2u
76
− u
75
+ ··· − 2u + 1)
c
3
(u
23
+ 6u
22
+ ··· + 17u + 1)(u
76
− 7u
75
+ ··· + 842u + 773)
c
4
(u
23
+ 3u
21
+ ··· + 33u + 14)(u
76
+ u
75
+ ··· + 137983u + 158846)
c
5
(u
23
+ 2u
22
+ ··· − 8u − 8)(u
76
− 3u
75
+ ··· + 936u + 232)
c
6
4(2u
23
− u
22
+ ··· − 3u − 1)(2u
76
− u
75
+ ··· − 2u + 1)
c
7
(u
23
+ 2u
22
+ ··· − u − 4)(u
76
− 5u
75
+ ··· − 19313u + 1532)
c
8
(u
23
− 3u
22
+ ··· + 40u − 16)
· (u
76
− 4u
75
+ ··· + 20080608u + 2598032)
c
9
4(2u
23
− 3u
22
+ ··· − 8u − 8)(2u
76
+ u
75
+ ··· + 296u + 712)
c
10
16(4u
23
− 41u
22
+ ··· + 5u − 1)(4u
76
+ 27u
75
+ ··· + 3218u + 419)
c
11
(u
23
− 2u
22
+ ··· − 8u + 8)(u
76
− 3u
75
+ ··· + 936u + 232)
c
12
4(2u
23
+ u
22
+ ··· − u + 1)(2u
76
+ 7u
75
+ ··· + 11068u + 1009)
21
IV. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
256(16y
23
− 321y
22
+ ··· − 13y −1)(16y
76
+ 15y
75
+ ··· − 166y + 1)
c
2
, c
6
16(4y
23
− 65y
22
+ ··· + 15y −1)(4y
76
− 181y
75
+ ··· − 50y + 1)
c
3
(y
23
− 22y
22
+ ··· − 11y −1)
· (y
76
− 107y
75
+ ··· − 13723192y + 597529)
c
4
(y
23
+ 6y
22
+ ··· + 1061y −196)
· (y
76
+ 33y
75
+ ··· + 325811545407y + 25232051716)
c
5
, c
11
(y
23
− 14y
22
+ ··· + 256y −64)
· (y
76
− 51y
75
+ ··· − 1128512y + 53824)
c
7
(y
23
+ 2y
22
+ ··· + 73y −16)
· (y
76
− 11y
75
+ ··· − 47423585y + 2347024)
c
8
(y
23
+ 23y
22
+ ··· + 6080y −256)
· (y
76
+ 62y
75
+ ··· + 198572181119104y + 6749770273024)
c
9
16(4y
23
+ 51y
22
+ ··· + 384y −64)
· (4y
76
+ 367y
75
+ ··· + 37802176y + 506944)
c
10
256(16y
23
− 297y
22
+ ··· − 3y −1)
· (16y
76
+ 487y
75
+ ··· + 8708976y + 175561)
c
12
16(4y
23
+ 31y
22
+ ··· + 13y −1)
· (4y
76
+ 331y
75
+ ··· + 210844724y + 1018081)
22
