12a
1187
(K12a
1187
)
A knot diagram
1
Linearized knot diagam
4 10 11 8 2 3 1 5 12 6 7 9
Solving Sequence
5,8
9
1,4
2 6 7 12 10 11 3
c
8
c
4
c
1
c
5
c
7
c
12
c
9
c
11
c
3
c
2
, c
6
, c
10
Ideals for irreducible components
2
of X
par
I
u
1
= h1.43694 × 10
1247
u
202
+ 6.99654 × 10
1246
u
201
+ ··· + 2.59373 × 10
1248
b − 4.94103 × 10
1250
,
2.06789 × 10
1251
u
202
+ 4.73176 × 10
1250
u
201
+ ··· + 1.89887 × 10
1252
a + 5.27296 × 10
1254
,
u
203
+ 2u
202
+ ··· − 80511u − 7321i
I
u
2
= h1.31314 × 10
60
u
49
+ 1.32815 × 10
60
u
48
+ ··· + 7.86550 × 10
58
b + 6.20943 × 10
59
,
− 1.47583 × 10
60
u
49
− 1.56407 × 10
60
u
48
+ ··· + 7.86550 × 10
58
a − 7.12810 × 10
59
, u
50
+ u
49
+ ··· − u + 1i
I
u
3
= h2b − 3, 2a + 5, u − 1i
I
u
4
= hb, a + 1, u − 1i
* 4 irreducible components of dim
C
= 0, with total 255 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
= h1.44 × 10
1247
u
202
+ 7.00 × 10
1246
u
201
+ · · · + 2.59 × 10
1248
b − 4.94 ×
10
1250
, 2.07 × 10
1251
u
202
+ 4.73 × 10
1250
u
201
+ · · · + 1.90 × 10
1252
a + 5.27 ×
10
1254
, u
203
+ 2u
202
+ · · · − 80511u − 7321i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
1
=
−0.108901u
202
− 0.0249188u
201
+ ··· − 1382.26u − 277.689
−0.0554007u
202
− 0.0269748u
201
+ ··· + 2118.49u + 190.499
a
4
=
−u
u
a
2
=
0.242892u
202
+ 0.297981u
201
+ ··· − 22457.6u − 2303.48
−0.407194u
202
− 0.349875u
201
+ ··· + 23193.8u + 2216.29
a
6
=
0.205842u
202
+ 0.222492u
201
+ ··· − 20845.4u − 2152.38
−0.562734u
202
− 0.554116u
201
+ ··· + 41834.2u + 4150.50
a
7
=
−0.408983u
202
− 0.416467u
201
+ ··· + 27287.1u + 2750.97
0.227279u
202
+ 0.265027u
201
+ ··· − 17597.8u − 1856.07
a
12
=
0.200303u
202
+ 0.240294u
201
+ ··· − 18232.7u − 1880.28
−0.433780u
202
− 0.408627u
201
+ ··· + 28290.9u + 2776.24
a
10
=
0.355570u
202
+ 0.433197u
201
+ ··· − 31605.2u − 3205.28
0.759767u
202
+ 0.907805u
201
+ ··· − 65585.9u − 6627.87
a
11
=
−1.63450u
202
− 1.74050u
201
+ ··· + 124864.u + 12504.6
1.60647u
202
+ 1.79540u
201
+ ··· − 129709.u − 13101.6
a
3
=
0.321269u
202
+ 0.329106u
201
+ ··· − 22483.3u − 2240.10
0.389626u
202
+ 0.455494u
201
+ ··· − 31040.9u − 3095.52
(ii) Obstruction class = −1
(iii) Cusp Shapes = −12.4193u
202
− 15.9063u
201
+ ··· + 1.19388 × 10
6
u + 123342.
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
203
+ 10u
202
+ ··· − 1413591u + 4819
c
2
u
203
+ 3u
202
+ ··· + 62u + 1
c
3
u
203
+ u
202
+ ··· − 274u + 16
c
4
, c
8
u
203
− 2u
202
+ ··· − 80511u + 7321
c
5
2(2u
203
+ u
202
+ ··· − 8.22687 × 10
10
u + 4.61846 × 10
9
)
c
6
2(2u
203
− 7u
202
+ ··· + 4u + 11)
c
7
2(2u
203
+ 5u
202
+ ··· + 2459520u + 382966)
c
9
, c
12
u
203
− 8u
202
+ ··· − 1110488u + 1091189
c
10
u
203
− 4u
201
+ ··· − 1855u + 158
c
11
u
203
+ 3u
202
+ ··· + 6685893u + 3717382
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
203
+ 42y
202
+ ··· + 1989941534611y −23222761
c
2
y
203
+ 25y
202
+ ··· + 194y −1
c
3
y
203
+ 9y
202
+ ··· + 36740y −256
c
4
, c
8
y
203
− 110y
202
+ ··· + 5254435841y −53597041
c
5
4(4y
203
− 225y
202
+ ··· − 1.19976 × 10
21
y −2.13302 × 10
19
)
c
6
4(4y
203
− 89y
202
+ ··· + 3822y −121)
c
7
4(4y
203
− 49y
202
+ ··· + 2.41353 × 10
12
y −1.46663 × 10
11
)
c
9
, c
12
y
203
+ 142y
202
+ ··· − 192816319316354y −1190693433721
c
10
y
203
− 8y
202
+ ··· + 2071797y −24964
c
11
y
203
− 19y
202
+ ··· + 1958373122289601y −13818928933924
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.415362 + 0.899292I
a = −0.207812 + 0.662700I
b = −1.01362 − 1.05022I
−3.87742 + 6.13429I 0
u = −0.415362 − 0.899292I
a = −0.207812 − 0.662700I
b = −1.01362 + 1.05022I
−3.87742 − 6.13429I 0
u = −0.894875 + 0.420192I
a = 2.31810 − 0.46068I
b = −0.275272 + 0.760522I
−2.96780 − 12.19750I 0
u = −0.894875 − 0.420192I
a = 2.31810 + 0.46068I
b = −0.275272 − 0.760522I
−2.96780 + 12.19750I 0
u = 0.957452 + 0.245768I
a = −1.97389 − 1.04777I
b = 0.436871 + 0.247251I
0.07450 + 5.23115I 0
u = 0.957452 − 0.245768I
a = −1.97389 + 1.04777I
b = 0.436871 − 0.247251I
0.07450 − 5.23115I 0
u = −0.942656 + 0.291960I
a = 1.36836 + 1.40017I
b = −1.75070 − 1.53821I
−1.18988 − 1.42649I 0
u = −0.942656 − 0.291960I
a = 1.36836 − 1.40017I
b = −1.75070 + 1.53821I
−1.18988 + 1.42649I 0
u = −0.944282 + 0.280052I
a = −2.40162 + 0.54478I
b = 1.128980 − 0.281371I
−1.69095 − 4.88437I 0
u = −0.944282 − 0.280052I
a = −2.40162 − 0.54478I
b = 1.128980 + 0.281371I
−1.69095 + 4.88437I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.955121 + 0.229896I
a = −0.69761 + 1.69525I
b = 0.077342 + 0.607569I
−2.40362 − 6.14299I 0
u = −0.955121 − 0.229896I
a = −0.69761 − 1.69525I
b = 0.077342 − 0.607569I
−2.40362 + 6.14299I 0
u = 0.873412 + 0.437921I
a = −2.21088 + 0.44149I
b = 1.58276 + 0.07708I
−4.33235 + 7.06722I 0
u = 0.873412 − 0.437921I
a = −2.21088 − 0.44149I
b = 1.58276 − 0.07708I
−4.33235 − 7.06722I 0
u = −0.922495 + 0.317669I
a = 2.32477 − 0.59364I
b = −1.55662 + 0.79349I
−0.711081 + 0.821444I 0
u = −0.922495 − 0.317669I
a = 2.32477 + 0.59364I
b = −1.55662 − 0.79349I
−0.711081 − 0.821444I 0
u = −1.02967
a = −2.73050
b = 2.07191
3.17175 0
u = 0.908540 + 0.485793I
a = 1.91311 + 0.40720I
b = −0.183286 − 0.925721I
−4.45106 + 3.58775I 0
u = 0.908540 − 0.485793I
a = 1.91311 − 0.40720I
b = −0.183286 + 0.925721I
−4.45106 − 3.58775I 0
u = 0.002924 + 0.969557I
a = 0.215865 − 0.353356I
b = −0.755237 − 0.103120I
1.197420 + 0.343471I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.002924 − 0.969557I
a = 0.215865 + 0.353356I
b = −0.755237 + 0.103120I
1.197420 − 0.343471I 0
u = 0.962951 + 0.368378I
a = 0.369831 − 0.789035I
b = −0.152701 − 0.978174I
−1.62798 + 3.27127I 0
u = 0.962951 − 0.368378I
a = 0.369831 + 0.789035I
b = −0.152701 + 0.978174I
−1.62798 − 3.27127I 0
u = −0.969947 + 0.369188I
a = 1.049870 + 0.082946I
b = −0.996577 + 0.501260I
1.88034 − 0.84617I 0
u = −0.969947 − 0.369188I
a = 1.049870 − 0.082946I
b = −0.996577 − 0.501260I
1.88034 + 0.84617I 0
u = 0.925121 + 0.470981I
a = −1.39409 − 0.32714I
b = 0.314429 − 0.093935I
−4.24178 + 5.99564I 0
u = 0.925121 − 0.470981I
a = −1.39409 + 0.32714I
b = 0.314429 + 0.093935I
−4.24178 − 5.99564I 0
u = −0.110478 + 0.947327I
a = −0.132327 − 0.741192I
b = −0.332324 + 0.434466I
−2.14005 − 2.25458I 0
u = −0.110478 − 0.947327I
a = −0.132327 + 0.741192I
b = −0.332324 − 0.434466I
−2.14005 + 2.25458I 0
u = 0.954179 + 0.433018I
a = 2.31534 + 0.68001I
b = −1.02239 − 1.44882I
−3.96433 + 2.21418I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.954179 − 0.433018I
a = 2.31534 − 0.68001I
b = −1.02239 + 1.44882I
−3.96433 − 2.21418I 0
u = −0.884096 + 0.332899I
a = −2.27083 + 1.15862I
b = 0.348050 − 1.059630I
−3.37792 − 2.31299I 0
u = −0.884096 − 0.332899I
a = −2.27083 − 1.15862I
b = 0.348050 + 1.059630I
−3.37792 + 2.31299I 0
u = 0.429512 + 0.967202I
a = 0.371661 + 0.539858I
b = 0.647467 − 0.921815I
−3.67535 − 0.55845I 0
u = 0.429512 − 0.967202I
a = 0.371661 − 0.539858I
b = 0.647467 + 0.921815I
−3.67535 + 0.55845I 0
u = 0.891779 + 0.268410I
a = 0.53167 − 1.78020I
b = −1.02805 + 2.30859I
−2.10369 + 11.24030I 0
u = 0.891779 − 0.268410I
a = 0.53167 + 1.78020I
b = −1.02805 − 2.30859I
−2.10369 − 11.24030I 0
u = −0.260923 + 1.047260I
a = 0.410929 + 0.209505I
b = 0.537624 − 0.746484I
−1.07835 − 6.96206I 0
u = −0.260923 − 1.047260I
a = 0.410929 − 0.209505I
b = 0.537624 + 0.746484I
−1.07835 + 6.96206I 0
u = −0.901398 + 0.148091I
a = −4.45131 + 0.77868I
b = 3.21285 − 0.84558I
−1.91204 − 0.43767I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.901398 − 0.148091I
a = −4.45131 − 0.77868I
b = 3.21285 + 0.84558I
−1.91204 + 0.43767I 0
u = 1.024860 + 0.385707I
a = 0.886805 − 0.318550I
b = −0.402786 − 0.843476I
−0.80214 + 3.54108I 0
u = 1.024860 − 0.385707I
a = 0.886805 + 0.318550I
b = −0.402786 + 0.843476I
−0.80214 − 3.54108I 0
u = −0.364898 + 0.817401I
a = −0.190010 − 0.027234I
b = −0.873020 − 0.277556I
0.65598 + 1.89187I 0
u = −0.364898 − 0.817401I
a = −0.190010 + 0.027234I
b = −0.873020 + 0.277556I
0.65598 − 1.89187I 0
u = 0.766108 + 0.454282I
a = 1.93240 + 0.48297I
b = −0.426037 − 0.609026I
−3.21700 − 1.11661I 0
u = 0.766108 − 0.454282I
a = 1.93240 − 0.48297I
b = −0.426037 + 0.609026I
−3.21700 + 1.11661I 0
u = 0.877362 + 0.121716I
a = 0.475549 + 0.912419I
b = −0.335112 + 1.041390I
−0.55840 − 3.52404I 0
u = 0.877362 − 0.121716I
a = 0.475549 − 0.912419I
b = −0.335112 − 1.041390I
−0.55840 + 3.52404I 0
u = 1.094060 + 0.220920I
a = −0.341521 + 1.071550I
b = 0.618269 − 0.016875I
1.26413 − 3.68221I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.094060 − 0.220920I
a = −0.341521 − 1.071550I
b = 0.618269 + 0.016875I
1.26413 + 3.68221I 0
u = 0.800482 + 0.361672I
a = −0.039714 + 0.229737I
b = 0.09793 − 1.43360I
−3.18474 + 4.65311I 0
u = 0.800482 − 0.361672I
a = −0.039714 − 0.229737I
b = 0.09793 + 1.43360I
−3.18474 − 4.65311I 0
u = 1.075270 + 0.330353I
a = −1.40397 + 0.83922I
b = 0.804313 + 0.822245I
4.06060 + 2.22713I 0
u = 1.075270 − 0.330353I
a = −1.40397 − 0.83922I
b = 0.804313 − 0.822245I
4.06060 − 2.22713I 0
u = 0.042996 + 0.873531I
a = −0.071817 + 0.645604I
b = 0.944670 + 0.424541I
0.18540 + 10.12770I 0
u = 0.042996 − 0.873531I
a = −0.071817 − 0.645604I
b = 0.944670 − 0.424541I
0.18540 − 10.12770I 0
u = −0.832254 + 0.246913I
a = −0.678227 + 0.454447I
b = −0.04173 − 1.90311I
−3.69799 − 0.33400I 0
u = −0.832254 − 0.246913I
a = −0.678227 − 0.454447I
b = −0.04173 + 1.90311I
−3.69799 + 0.33400I 0
u = 0.816391 + 0.287618I
a = −3.04409 − 0.84894I
b = 1.54769 + 0.98598I
−2.30645 − 8.68082I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.816391 − 0.287618I
a = −3.04409 + 0.84894I
b = 1.54769 − 0.98598I
−2.30645 + 8.68082I 0
u = −0.857881 + 0.074344I
a = −1.04252 − 3.43027I
b = 0.99926 + 3.69436I
−1.80683 − 2.95019I 0
u = −0.857881 − 0.074344I
a = −1.04252 + 3.43027I
b = 0.99926 − 3.69436I
−1.80683 + 2.95019I 0
u = −1.139700 + 0.067593I
a = −0.520122 − 1.027930I
b = 0.39701 + 1.50364I
2.89468 − 0.55993I 0
u = −1.139700 − 0.067593I
a = −0.520122 + 1.027930I
b = 0.39701 − 1.50364I
2.89468 + 0.55993I 0
u = 0.213387 + 1.122050I
a = −0.006654 − 0.400905I
b = −0.729469 + 0.863645I
−2.71993 − 6.98469I 0
u = 0.213387 − 1.122050I
a = −0.006654 + 0.400905I
b = −0.729469 − 0.863645I
−2.71993 + 6.98469I 0
u = 0.865936 + 0.759763I
a = −0.824712 + 1.043820I
b = 1.50845 + 0.02805I
2.60381 − 2.66941I 0
u = 0.865936 − 0.759763I
a = −0.824712 − 1.043820I
b = 1.50845 − 0.02805I
2.60381 + 2.66941I 0
u = −0.010172 + 0.845425I
a = −0.0798615 + 0.0371923I
b = −0.576223 + 0.925142I
−0.70649 − 4.59585I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.010172 − 0.845425I
a = −0.0798615 − 0.0371923I
b = −0.576223 − 0.925142I
−0.70649 + 4.59585I 0
u = 0.343191 + 1.103690I
a = −0.016323 + 0.159304I
b = 0.504999 − 0.890514I
−5.38825 − 3.22534I 0
u = 0.343191 − 1.103690I
a = −0.016323 − 0.159304I
b = 0.504999 + 0.890514I
−5.38825 + 3.22534I 0
u = −0.815581 + 0.185129I
a = 2.39613 − 1.59847I
b = −0.133508 − 0.163263I
−2.93557 + 4.13930I 0
u = −0.815581 − 0.185129I
a = 2.39613 + 1.59847I
b = −0.133508 + 0.163263I
−2.93557 − 4.13930I 0
u = 0.638771 + 0.534022I
a = 0.91341 − 1.16299I
b = −0.992251 + 0.995041I
−4.98129 − 3.10031I 0
u = 0.638771 − 0.534022I
a = 0.91341 + 1.16299I
b = −0.992251 − 0.995041I
−4.98129 + 3.10031I 0
u = −1.101910 + 0.395880I
a = 1.371280 + 0.233194I
b = −0.403056 + 0.715267I
0.80956 + 1.89714I 0
u = −1.101910 − 0.395880I
a = 1.371280 − 0.233194I
b = −0.403056 − 0.715267I
0.80956 − 1.89714I 0
u = −0.269452 + 0.780049I
a = 0.473111 + 0.407573I
b = −0.753563 + 0.404096I
1.41980 − 1.71904I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.269452 − 0.780049I
a = 0.473111 − 0.407573I
b = −0.753563 − 0.404096I
1.41980 + 1.71904I 0
u = −1.138150 + 0.299210I
a = 1.35093 + 0.62856I
b = −1.29931 + 0.77251I
6.23829 + 1.55497I 0
u = −1.138150 − 0.299210I
a = 1.35093 − 0.62856I
b = −1.29931 − 0.77251I
6.23829 − 1.55497I 0
u = 0.265605 + 1.147240I
a = 0.212614 + 0.344904I
b = 0.865737 − 0.876846I
−4.38293 − 6.78563I 0
u = 0.265605 − 1.147240I
a = 0.212614 − 0.344904I
b = 0.865737 + 0.876846I
−4.38293 + 6.78563I 0
u = −0.679012 + 0.462133I
a = 0.139102 + 0.479048I
b = 0.180311 + 1.399900I
−3.60861 + 8.48201I 0
u = −0.679012 − 0.462133I
a = 0.139102 − 0.479048I
b = 0.180311 − 1.399900I
−3.60861 − 8.48201I 0
u = −0.792909 + 0.204172I
a = 1.37194 + 0.46338I
b = −1.14683 − 1.24395I
−2.34259 + 2.56087I 0
u = −0.792909 − 0.204172I
a = 1.37194 − 0.46338I
b = −1.14683 + 1.24395I
−2.34259 − 2.56087I 0
u = −0.271401 + 1.154710I
a = 0.099871 − 0.368449I
b = 0.889741 + 0.903006I
−3.6186 + 15.5237I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.271401 − 1.154710I
a = 0.099871 + 0.368449I
b = 0.889741 − 0.903006I
−3.6186 − 15.5237I 0
u = −0.435292 + 1.111970I
a = 0.069919 + 0.485187I
b = −0.951304 − 0.672703I
−2.02991 + 5.84353I 0
u = −0.435292 − 1.111970I
a = 0.069919 − 0.485187I
b = −0.951304 + 0.672703I
−2.02991 − 5.84353I 0
u = 1.182400 + 0.190935I
a = −1.50368 + 0.33525I
b = 1.097070 + 0.323858I
5.83772 + 0.71294I 0
u = 1.182400 − 0.190935I
a = −1.50368 − 0.33525I
b = 1.097070 − 0.323858I
5.83772 − 0.71294I 0
u = −1.081480 + 0.537328I
a = −1.187790 − 0.745245I
b = 1.141800 − 0.682033I
2.84415 − 6.88891I 0
u = −1.081480 − 0.537328I
a = −1.187790 + 0.745245I
b = 1.141800 + 0.682033I
2.84415 + 6.88891I 0
u = 1.188680 + 0.256751I
a = 1.51320 − 0.22088I
b = −1.34257 − 0.86489I
6.88601 + 7.01460I 0
u = 1.188680 − 0.256751I
a = 1.51320 + 0.22088I
b = −1.34257 + 0.86489I
6.88601 − 7.01460I 0
u = −1.22377
a = 0.667574
b = −0.664785
2.12975 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.052728 + 0.773471I
a = 0.592347 − 0.222276I
b = 0.632140 + 0.717279I
1.18303 − 1.12212I 0
u = 0.052728 − 0.773471I
a = 0.592347 + 0.222276I
b = 0.632140 − 0.717279I
1.18303 + 1.12212I 0
u = 0.556308 + 0.530621I
a = 0.349625 − 0.423029I
b = 0.05029 − 1.42849I
−5.43601 + 0.55026I 0
u = 0.556308 − 0.530621I
a = 0.349625 + 0.423029I
b = 0.05029 + 1.42849I
−5.43601 − 0.55026I 0
u = 0.065083 + 0.765139I
a = 0.448016 − 0.636943I
b = 0.794968 − 0.365390I
−1.11795 − 3.00739I 0
u = 0.065083 − 0.765139I
a = 0.448016 + 0.636943I
b = 0.794968 + 0.365390I
−1.11795 + 3.00739I 0
u = 0.534570 + 0.538984I
a = 1.001020 + 0.057489I
b = −0.025673 + 0.876688I
−5.32769 − 1.89571I 0
u = 0.534570 − 0.538984I
a = 1.001020 − 0.057489I
b = −0.025673 − 0.876688I
−5.32769 + 1.89571I 0
u = 1.249960 + 0.086661I
a = −0.951881 + 0.548912I
b = 0.693915 + 0.234454I
4.91107 − 2.60938I 0
u = 1.249960 − 0.086661I
a = −0.951881 − 0.548912I
b = 0.693915 − 0.234454I
4.91107 + 2.60938I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.013070 + 0.753633I
a = −0.818664 − 0.742042I
b = 1.071270 + 0.063927I
1.57323 − 4.08247I 0
u = −1.013070 − 0.753633I
a = −0.818664 + 0.742042I
b = 1.071270 − 0.063927I
1.57323 + 4.08247I 0
u = 0.573407 + 0.450637I
a = 0.926937 + 0.857517I
b = 0.30459 − 1.77109I
−5.09680 + 1.51428I 0
u = 0.573407 − 0.450637I
a = 0.926937 − 0.857517I
b = 0.30459 + 1.77109I
−5.09680 − 1.51428I 0
u = −1.218510 + 0.433303I
a = 1.78226 − 0.25562I
b = −1.54961 + 1.20248I
4.89627 − 3.18817I 0
u = −1.218510 − 0.433303I
a = 1.78226 + 0.25562I
b = −1.54961 − 1.20248I
4.89627 + 3.18817I 0
u = 1.205960 + 0.471831I
a = 1.140010 − 0.464165I
b = −0.968014 − 0.917263I
2.23510 + 7.55638I 0
u = 1.205960 − 0.471831I
a = 1.140010 + 0.464165I
b = −0.968014 + 0.917263I
2.23510 − 7.55638I 0
u = 1.076910 + 0.731633I
a = 1.104930 − 0.772223I
b = −1.64432 − 0.24010I
3.35185 + 8.56193I 0
u = 1.076910 − 0.731633I
a = 1.104930 + 0.772223I
b = −1.64432 + 0.24010I
3.35185 − 8.56193I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.205910 + 0.499036I
a = 0.349419 − 0.637805I
b = −0.760091 − 0.280949I
4.44591 + 5.77896I 0
u = 1.205910 − 0.499036I
a = 0.349419 + 0.637805I
b = −0.760091 + 0.280949I
4.44591 − 5.77896I 0
u = −1.197130 + 0.521600I
a = 1.075450 + 0.236061I
b = −1.251450 + 0.306299I
2.20417 − 1.19635I 0
u = −1.197130 − 0.521600I
a = 1.075450 − 0.236061I
b = −1.251450 − 0.306299I
2.20417 + 1.19635I 0
u = 1.250610 + 0.403240I
a = −0.598433 − 0.572420I
b = 0.266291 + 1.274600I
1.74199 + 9.64376I 0
u = 1.250610 − 0.403240I
a = −0.598433 + 0.572420I
b = 0.266291 − 1.274600I
1.74199 − 9.64376I 0
u = 1.243750 + 0.426958I
a = −1.53999 − 0.22937I
b = 1.249270 + 0.627583I
2.05540 + 6.79534I 0
u = 1.243750 − 0.426958I
a = −1.53999 + 0.22937I
b = 1.249270 − 0.627583I
2.05540 − 6.79534I 0
u = −0.513289 + 1.211570I
a = −0.127132 − 0.366399I
b = 0.574258 + 0.642685I
−7.06711 − 3.23454I 0
u = −0.513289 − 1.211570I
a = −0.127132 + 0.366399I
b = 0.574258 − 0.642685I
−7.06711 + 3.23454I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.261240 + 0.393809I
a = −1.44998 + 0.40183I
b = 0.949217 + 0.670181I
5.82658 + 5.77973I 0
u = 1.261240 − 0.393809I
a = −1.44998 − 0.40183I
b = 0.949217 − 0.670181I
5.82658 − 5.77973I 0
u = −1.172960 + 0.613642I
a = −1.82281 − 0.14442I
b = 1.54599 − 1.12914I
−1.49415 − 11.74120I 0
u = −1.172960 − 0.613642I
a = −1.82281 + 0.14442I
b = 1.54599 + 1.12914I
−1.49415 + 11.74120I 0
u = 0.675643
a = −2.52107
b = −0.236846
2.02655 0
u = 1.238130 + 0.473771I
a = −1.59437 − 0.18463I
b = 1.08643 + 1.18390I
2.98501 + 9.30926I 0
u = 1.238130 − 0.473771I
a = −1.59437 + 0.18463I
b = 1.08643 − 1.18390I
2.98501 − 9.30926I 0
u = −1.250080 + 0.465648I
a = 1.31986 + 0.54475I
b = −0.991665 + 0.829560I
4.0376 − 14.8468I 0
u = −1.250080 − 0.465648I
a = 1.31986 − 0.54475I
b = −0.991665 − 0.829560I
4.0376 + 14.8468I 0
u = −0.054257 + 0.661613I
a = −0.562765 + 0.865346I
b = 0.290493 + 0.871582I
−2.07189 − 5.72387I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.054257 − 0.661613I
a = −0.562765 − 0.865346I
b = 0.290493 − 0.871582I
−2.07189 + 5.72387I 0
u = 1.179620 + 0.636565I
a = 1.393230 − 0.006450I
b = −1.22409 − 1.11680I
−1.29940 + 6.41396I 0
u = 1.179620 − 0.636565I
a = 1.393230 + 0.006450I
b = −1.22409 + 1.11680I
−1.29940 − 6.41396I 0
u = −1.274130 + 0.427777I
a = −0.390987 − 0.214331I
b = 0.223897 − 0.703435I
1.83991 − 2.95394I 0
u = −1.274130 − 0.427777I
a = −0.390987 + 0.214331I
b = 0.223897 + 0.703435I
1.83991 + 2.95394I 0
u = −0.607400 + 0.219072I
a = −2.91038 − 1.07849I
b = 1.023400 + 0.374254I
−2.50491 − 0.93914I 0
u = −0.607400 − 0.219072I
a = −2.91038 + 1.07849I
b = 1.023400 − 0.374254I
−2.50491 + 0.93914I 0
u = 1.282490 + 0.448602I
a = −1.327440 + 0.245431I
b = 1.055040 + 0.280830I
5.31228 + 4.65426I 0
u = 1.282490 − 0.448602I
a = −1.327440 − 0.245431I
b = 1.055040 − 0.280830I
5.31228 − 4.65426I 0
u = −1.281500 + 0.461344I
a = −1.164950 − 0.538206I
b = 0.874887 − 0.510887I
5.24555 − 5.35358I 0
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.281500 − 0.461344I
a = −1.164950 + 0.538206I
b = 0.874887 + 0.510887I
5.24555 + 5.35358I 0
u = 1.303080 + 0.416173I
a = 1.62422 + 0.48159I
b = −1.50793 − 1.26810I
3.73766 + 11.68480I 0
u = 1.303080 − 0.416173I
a = 1.62422 − 0.48159I
b = −1.50793 + 1.26810I
3.73766 − 11.68480I 0
u = −1.304420 + 0.454028I
a = −0.141883 − 0.461984I
b = 0.318072 + 0.042269I
3.07900 − 0.31827I 0
u = −1.304420 − 0.454028I
a = −0.141883 + 0.461984I
b = 0.318072 − 0.042269I
3.07900 + 0.31827I 0
u = 1.230340 + 0.637651I
a = 1.41504 − 0.03909I
b = −0.926259 − 0.968381I
−2.54772 + 9.37229I 0
u = 1.230340 − 0.637651I
a = 1.41504 + 0.03909I
b = −0.926259 + 0.968381I
−2.54772 − 9.37229I 0
u = 1.307890 + 0.491037I
a = 0.976124 − 0.441253I
b = −1.132070 + 0.084049I
3.92694 − 5.04300I 0
u = 1.307890 − 0.491037I
a = 0.976124 + 0.441253I
b = −1.132070 − 0.084049I
3.92694 + 5.04300I 0
u = −1.223770 + 0.679062I
a = 1.347210 + 0.039797I
b = −1.051200 + 0.826646I
−4.54322 − 3.37296I 0
20
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.223770 − 0.679062I
a = 1.347210 − 0.039797I
b = −1.051200 − 0.826646I
−4.54322 + 3.37296I 0
u = −1.406340 + 0.080162I
a = 0.594314 + 0.235923I
b = −0.839831 + 0.337638I
2.38224 + 2.06034I 0
u = −1.406340 − 0.080162I
a = 0.594314 − 0.235923I
b = −0.839831 − 0.337638I
2.38224 − 2.06034I 0
u = −1.40691 + 0.15993I
a = −0.372017 − 0.543088I
b = 0.308061 − 0.099331I
3.53879 + 2.13558I 0
u = −1.40691 − 0.15993I
a = −0.372017 + 0.543088I
b = 0.308061 + 0.099331I
3.53879 − 2.13558I 0
u = −1.24401 + 0.68372I
a = −1.48786 − 0.24785I
b = 1.39493 − 0.83989I
0.61012 − 12.28850I 0
u = −1.24401 − 0.68372I
a = −1.48786 + 0.24785I
b = 1.39493 + 0.83989I
0.61012 + 12.28850I 0
u = 1.28716 + 0.61038I
a = −1.57905 − 0.04886I
b = 1.30729 + 1.04740I
0.67097 + 13.08400I 0
u = 1.28716 − 0.61038I
a = −1.57905 + 0.04886I
b = 1.30729 − 1.04740I
0.67097 − 13.08400I 0
u = 0.513258 + 0.251212I
a = 2.83960 − 0.23058I
b = 0.073077 − 0.169275I
−2.97053 − 0.15806I 0
21
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.513258 − 0.251212I
a = 2.83960 + 0.23058I
b = 0.073077 + 0.169275I
−2.97053 + 0.15806I 0
u = 1.28306 + 0.63744I
a = 1.53530 − 0.00970I
b = −1.36477 − 1.22866I
−1.14839 + 13.07000I 0
u = 1.28306 − 0.63744I
a = 1.53530 + 0.00970I
b = −1.36477 + 1.22866I
−1.14839 − 13.07000I 0
u = −1.40372 + 0.31591I
a = −0.792881 + 0.800536I
b = 0.577716 − 1.230100I
1.38175 − 1.95752I 0
u = −1.40372 − 0.31591I
a = −0.792881 − 0.800536I
b = 0.577716 + 1.230100I
1.38175 + 1.95752I 0
u = −1.28698 + 0.64633I
a = 1.58437 + 0.03359I
b = −1.37421 + 1.16127I
−0.3936 − 21.8727I 0
u = −1.28698 − 0.64633I
a = 1.58437 − 0.03359I
b = −1.37421 − 1.16127I
−0.3936 + 21.8727I 0
u = 0.35989 + 1.41070I
a = −0.007257 − 0.355529I
b = −0.529463 + 0.529576I
−6.59977 − 4.77761I 0
u = 0.35989 − 1.41070I
a = −0.007257 + 0.355529I
b = −0.529463 − 0.529576I
−6.59977 + 4.77761I 0
u = −1.11486 + 0.95215I
a = −0.668965 − 0.460897I
b = 1.003180 − 0.449210I
1.88854 − 6.49373I 0
22
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.11486 − 0.95215I
a = −0.668965 + 0.460897I
b = 1.003180 + 0.449210I
1.88854 + 6.49373I 0
u = 0.303556 + 0.437243I
a = 1.19782 − 1.34934I
b = 0.167026 − 0.477971I
−2.66082 + 0.01005I 0
u = 0.303556 − 0.437243I
a = 1.19782 + 1.34934I
b = 0.167026 + 0.477971I
−2.66082 − 0.01005I 0
u = 1.33693 + 0.69360I
a = −1.179050 − 0.079614I
b = 1.07542 + 0.94938I
−3.23328 + 11.93110I 0
u = 1.33693 − 0.69360I
a = −1.179050 + 0.079614I
b = 1.07542 − 0.94938I
−3.23328 − 11.93110I 0
u = −1.39782 + 0.58166I
a = −0.903378 − 0.227842I
b = 0.782382 − 0.184890I
4.32382 − 4.36197I 0
u = −1.39782 − 0.58166I
a = −0.903378 + 0.227842I
b = 0.782382 + 0.184890I
4.32382 + 4.36197I 0
u = −1.29354 + 0.80196I
a = 0.740786 + 0.262010I
b = −1.127660 + 0.333991I
2.74824 − 1.18727I 0
u = −1.29354 − 0.80196I
a = 0.740786 − 0.262010I
b = −1.127660 − 0.333991I
2.74824 + 1.18727I 0
u = 1.52314 + 0.09990I
a = 0.472288 − 0.431171I
b = −0.627983 − 0.061840I
3.13305 − 10.50110I 0
23
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.52314 − 0.09990I
a = 0.472288 + 0.431171I
b = −0.627983 + 0.061840I
3.13305 + 10.50110I 0
u = −0.070900 + 0.462386I
a = 1.66475 − 0.10332I
b = 0.952118 − 0.119605I
3.12794 − 4.43449I 8.44885 + 7.26104I
u = −0.070900 − 0.462386I
a = 1.66475 + 0.10332I
b = 0.952118 + 0.119605I
3.12794 + 4.43449I 8.44885 − 7.26104I
u = −1.53994 + 0.42816I
a = 0.020260 + 0.262022I
b = −0.278160 + 0.314783I
3.08513 + 0.35535I 0
u = −1.53994 − 0.42816I
a = 0.020260 − 0.262022I
b = −0.278160 − 0.314783I
3.08513 − 0.35535I 0
u = −0.103713 + 0.387544I
a = 1.199040 − 0.357427I
b = −0.117582 + 0.482643I
0.444059 − 1.261860I 4.91286 + 4.63218I
u = −0.103713 − 0.387544I
a = 1.199040 + 0.357427I
b = −0.117582 − 0.482643I
0.444059 + 1.261860I 4.91286 − 4.63218I
u = −0.07668 + 1.64017I
a = −0.065784 + 0.228145I
b = −0.152486 − 0.228209I
−4.67638 − 4.52811I 0
u = −0.07668 − 1.64017I
a = −0.065784 − 0.228145I
b = −0.152486 + 0.228209I
−4.67638 + 4.52811I 0
u = −0.110178 + 0.330566I
a = 1.16392 − 0.98764I
b = −0.109711 + 1.282780I
−2.39619 − 3.50536I −2.32903 + 1.77977I
24
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.110178 − 0.330566I
a = 1.16392 + 0.98764I
b = −0.109711 − 1.282780I
−2.39619 + 3.50536I −2.32903 − 1.77977I
u = −0.229828
a = 1.78238
b = −0.776172
1.64369 8.11750
u = −0.129423
a = 5.65008
b = −0.896993
1.59226 11.9420
25
II.
I
u
2
= h1.31×10
60
u
49
+1.33×10
60
u
48
+· · ·+7.87×10
58
b+6.21×10
59
, −1.48×
10
60
u
49
−1.56×10
60
u
48
+· · ·+7.87×10
58
a−7.13×10
59
, u
50
+u
49
+· · ·−u+1i
(i) Arc colorings
a
5
=
0
u
a
8
=
1
0
a
9
=
1
−u
2
a
1
=
18.7634u
49
+ 19.8851u
48
+ ··· − 48.5576u + 9.06249
−16.6950u
49
− 16.8858u
48
+ ··· + 41.3570u − 7.89452
a
4
=
−u
u
a
2
=
17.6370u
49
+ 18.2744u
48
+ ··· − 47.4202u + 9.99346
−15.5686u
49
− 15.2750u
48
+ ··· + 40.2196u − 8.82549
a
6
=
21.0483u
49
− 10.5923u
48
+ ··· − 127.437u + 67.3379
−12.4036u
49
+ 10.1549u
48
+ ··· + 73.6768u − 43.7186
a
7
=
−60.9798u
49
− 45.6514u
48
+ ··· + 182.212u − 46.5606
39.1711u
49
+ 33.8004u
48
+ ··· − 95.6716u + 16.8798
a
12
=
24.9094u
49
+ 23.6681u
48
+ ··· − 72.2730u + 18.0788
−19.9736u
49
− 19.6660u
48
+ ··· + 49.8661u − 10.2575
a
10
=
22.7887u
49
+ 14.0600u
48
+ ··· − 58.8778u + 17.1876
−4.76674u
49
− 11.2406u
48
+ ··· − 1.30878u + 9.26784
a
11
=
−41.0336u
49
− 47.5575u
48
+ ··· + 99.1207u − 20.2116
39.3074u
49
+ 44.7248u
48
+ ··· − 77.7751u + 14.1418
a
3
=
−49.3553u
49
− 5.70787u
48
+ ··· + 169.775u − 83.7004
21.4885u
49
− 4.89438u
48
+ ··· − 64.3359u + 39.9719
(ii) Obstruction class = 1
(iii) Cusp Shapes = 300.545u
49
+ 408.122u
48
+ ··· − 390.330u − 108.565
26
(iv) u-Polynomials at the component
27
Crossings u-Polynomials at each crossing
c
1
u
50
− 15u
49
+ ··· − 5u + 1
c
2
u
50
+ 2u
49
+ ··· + 8u + 1
c
3
u
50
+ 2u
49
+ ··· + 152u + 9
c
4
u
50
− u
49
+ ··· + u + 1
c
5
u
50
+ 3u
49
+ ··· + 62u + 3
c
6
u
50
+ 4u
49
+ ··· − 7u + 1
c
7
u
50
+ 5u
49
+ ··· − 79u + 21
c
8
u
50
+ u
49
+ ··· − u + 1
c
9
u
50
+ 9u
49
+ ··· + 14u + 1
c
10
u
50
+ 2u
49
+ ··· + 2u + 1
c
11
u
50
+ u
49
+ ··· − 385u + 73
c
12
u
50
− 9u
49
+ ··· − 14u + 1
28
29
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
50
+ 13y
49
+ ··· + 59y + 1
c
2
y
50
+ 28y
49
+ ··· + 4y + 1
c
3
y
50
+ 18y
49
+ ··· + 2726y + 81
c
4
, c
8
y
50
− 23y
49
+ ··· − 11y + 1
c
5
y
50
− 9y
49
+ ··· − 856y + 9
c
6
y
50
− 8y
49
+ ··· − 25y + 1
c
7
y
50
+ 11y
49
+ ··· + 731y + 441
c
9
, c
12
y
50
+ 49y
49
+ ··· − 36y + 1
c
10
y
50
+ 14y
49
+ ··· − 42y
2
+ 1
c
11
y
50
+ 11y
49
+ ··· − 116105y + 5329
30
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.979533 + 0.244417I
a = −1.15576 + 1.36277I
b = 0.334192 + 0.357473I
−2.08791 − 6.16379I 14.4561 + 12.0834I
u = −0.979533 − 0.244417I
a = −1.15576 − 1.36277I
b = 0.334192 − 0.357473I
−2.08791 + 6.16379I 14.4561 − 12.0834I
u = −0.930274 + 0.414483I
a = −2.16981 + 0.73984I
b = 0.444472 − 1.213660I
−3.44482 − 3.43958I 4.00000 + 8.45629I
u = −0.930274 − 0.414483I
a = −2.16981 − 0.73984I
b = 0.444472 + 1.213660I
−3.44482 + 3.43958I 4.00000 − 8.45629I
u = −0.891005 + 0.552623I
a = 0.749148 + 1.174700I
b = −1.169030 + 0.055784I
3.82773 + 2.65583I 0
u = −0.891005 − 0.552623I
a = 0.749148 − 1.174700I
b = −1.169030 − 0.055784I
3.82773 − 2.65583I 0
u = −0.320844 + 1.014670I
a = −0.121594 + 0.517807I
b = −0.865007 − 0.883880I
−3.18409 + 5.82509I 0
u = −0.320844 − 1.014670I
a = −0.121594 − 0.517807I
b = −0.865007 + 0.883880I
−3.18409 − 5.82509I 0
u = 0.863144 + 0.135298I
a = 4.24251 − 0.08863I
b = −2.99886 + 0.05850I
−1.99227 + 0.40754I −17.2715 + 30.5408I
u = 0.863144 − 0.135298I
a = 4.24251 + 0.08863I
b = −2.99886 − 0.05850I
−1.99227 − 0.40754I −17.2715 − 30.5408I
31
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.852285 + 0.145871I
a = 2.15634 − 1.55914I
b = −0.513968 − 0.363710I
−2.77353 + 4.38322I 7.7174 − 15.4863I
u = −0.852285 − 0.145871I
a = 2.15634 + 1.55914I
b = −0.513968 + 0.363710I
−2.77353 − 4.38322I 7.7174 + 15.4863I
u = 0.835751 + 0.075628I
a = −0.87541 + 3.17909I
b = 0.80591 − 3.40883I
−1.82901 + 2.93990I −102.7223 + 67.6745I
u = 0.835751 − 0.075628I
a = −0.87541 − 3.17909I
b = 0.80591 + 3.40883I
−1.82901 − 2.93990I −102.7223 − 67.6745I
u = 1.124130 + 0.330433I
a = 0.541999 + 0.475533I
b = −0.477600 − 0.868843I
2.46153 + 0.79337I 0
u = 1.124130 − 0.330433I
a = 0.541999 − 0.475533I
b = −0.477600 + 0.868843I
2.46153 − 0.79337I 0
u = −0.042798 + 0.813062I
a = 0.157036 − 0.397943I
b = −0.779129 − 0.258410I
0.98115 + 1.10321I 5.69144 − 3.12152I
u = −0.042798 − 0.813062I
a = 0.157036 + 0.397943I
b = −0.779129 + 0.258410I
0.98115 − 1.10321I 5.69144 + 3.12152I
u = 0.762951 + 0.261217I
a = −0.728367 − 1.006170I
b = −0.071789 − 0.862288I
−1.09268 + 4.57589I 2.69298 − 8.67577I
u = 0.762951 − 0.261217I
a = −0.728367 + 1.006170I
b = −0.071789 + 0.862288I
−1.09268 − 4.57589I 2.69298 + 8.67577I
32
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −1.110440 + 0.507988I
a = −0.978996 − 0.550252I
b = 1.252380 − 0.583962I
4.81206 − 7.13900I 0
u = −1.110440 − 0.507988I
a = −0.978996 + 0.550252I
b = 1.252380 + 0.583962I
4.81206 + 7.13900I 0
u = 0.072325 + 1.238530I
a = 0.051342 + 0.553946I
b = 0.224356 − 0.387627I
−6.39220 + 3.89351I 0
u = 0.072325 − 1.238530I
a = 0.051342 − 0.553946I
b = 0.224356 + 0.387627I
−6.39220 − 3.89351I 0
u = −0.651822 + 0.334525I
a = −1.300010 − 0.041308I
b = 0.09557 − 1.74427I
−4.39851 + 0.01341I −3.15892 − 0.50193I
u = −0.651822 − 0.334525I
a = −1.300010 + 0.041308I
b = 0.09557 + 1.74427I
−4.39851 − 0.01341I −3.15892 + 0.50193I
u = −0.661288 + 0.091994I
a = 2.55973 + 1.41302I
b = −0.88278 − 1.50493I
−2.44047 − 10.11450I 3.00451 + 7.11704I
u = −0.661288 − 0.091994I
a = 2.55973 − 1.41302I
b = −0.88278 + 1.50493I
−2.44047 + 10.11450I 3.00451 − 7.11704I
u = −1.281190 + 0.457487I
a = −1.303890 − 0.405846I
b = 0.903764 − 0.558190I
4.84403 − 5.90050I 0
u = −1.281190 − 0.457487I
a = −1.303890 + 0.405846I
b = 0.903764 + 0.558190I
4.84403 + 5.90050I 0
33
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.024720 + 0.931142I
a = 0.700225 − 0.603200I
b = −1.105090 − 0.377866I
1.61624 + 6.51721I 0
u = 1.024720 − 0.931142I
a = 0.700225 + 0.603200I
b = −1.105090 + 0.377866I
1.61624 − 6.51721I 0
u = −1.243890 + 0.638367I
a = −1.57324 − 0.09706I
b = 1.40678 − 1.01888I
−0.30705 − 11.83690I 0
u = −1.243890 − 0.638367I
a = −1.57324 + 0.09706I
b = 1.40678 + 1.01888I
−0.30705 + 11.83690I 0
u = −1.352630 + 0.353921I
a = 0.960018 − 0.721319I
b = −0.494262 + 1.233310I
1.25896 − 10.95850I 0
u = −1.352630 − 0.353921I
a = 0.960018 + 0.721319I
b = −0.494262 − 1.233310I
1.25896 + 10.95850I 0
u = 0.568599 + 0.176853I
a = 3.13400 − 0.06086I
b = −0.700753 − 0.130350I
−2.37685 − 0.16806I 5.77176 − 3.53520I
u = 0.568599 − 0.176853I
a = 3.13400 + 0.06086I
b = −0.700753 + 0.130350I
−2.37685 + 0.16806I 5.77176 + 3.53520I
u = 1.46036 + 0.11890I
a = −0.312873 + 0.275406I
b = 0.408066 + 0.300516I
2.83601 − 1.40399I 0
u = 1.46036 − 0.11890I
a = −0.312873 − 0.275406I
b = 0.408066 − 0.300516I
2.83601 + 1.40399I 0
34
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 1.38021 + 0.52670I
a = −0.982369 + 0.183391I
b = 0.782722 + 0.194544I
4.26216 + 4.21941I 0
u = 1.38021 − 0.52670I
a = −0.982369 − 0.183391I
b = 0.782722 − 0.194544I
4.26216 − 4.21941I 0
u = 0.164530 + 0.475429I
a = 1.48315 − 0.25949I
b = 0.11170 − 1.44128I
−4.67411 + 0.67670I −2.68411 − 0.53298I
u = 0.164530 − 0.475429I
a = 1.48315 + 0.25949I
b = 0.11170 + 1.44128I
−4.67411 − 0.67670I −2.68411 + 0.53298I
u = 1.40783 + 0.68571I
a = −0.771817 + 0.032734I
b = 1.060630 + 0.542293I
3.05472 + 0.93938I 0
u = 1.40783 − 0.68571I
a = −0.771817 − 0.032734I
b = 1.060630 − 0.542293I
3.05472 − 0.93938I 0
u = 0.169150 + 0.355045I
a = 1.01935 − 2.23933I
b = −0.478660 + 0.941272I
−3.05580 − 3.13859I 0.71817 + 6.65696I
u = 0.169150 − 0.355045I
a = 1.01935 + 2.23933I
b = −0.478660 − 0.941272I
−3.05580 + 3.13859I 0.71817 − 6.65696I
u = −0.01570 + 1.64014I
a = 0.019301 − 0.191847I
b = 0.206382 + 0.313760I
−4.70972 + 4.72747I 0
u = −0.01570 − 1.64014I
a = 0.019301 + 0.191847I
b = 0.206382 − 0.313760I
−4.70972 − 4.72747I 0
35
III. I
u
3
= h2b − 3, 2a + 5, u − 1i
(i) Arc colorings
a
5
=
0
1
a
8
=
1
0
a
9
=
1
−1
a
1
=
−2.5
1.5
a
4
=
−1
1
a
2
=
−1.5
0.5
a
6
=
−2.25
1.75
a
7
=
−2.75
2.25
a
12
=
−1.5
0.5
a
10
=
−0.5
−0.5
a
11
=
4
−4
a
3
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 26.0625
36
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
u + 1
c
2
, c
8
, c
12
u − 1
c
3
u
c
5
, c
7
2(2u − 3)
c
6
2(2u + 1)
c
10
, c
11
u + 2
37
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
8
, c
9
, c
12
y −1
c
3
y
c
5
, c
7
4(4y −9)
c
6
4(4y −1)
c
10
, c
11
y −4
38
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −2.50000
b = 1.50000
3.28987 26.0630
39
IV. I
u
4
= hb, a + 1, u − 1i
(i) Arc colorings
a
5
=
0
1
a
8
=
1
0
a
9
=
1
−1
a
1
=
−1
0
a
4
=
−1
1
a
2
=
0
−1
a
6
=
0
1
a
7
=
1
0
a
12
=
0
−1
a
10
=
1
−2
a
11
=
1
−1
a
3
=
−1
1
(ii) Obstruction class = 1
(iii) Cusp Shapes = 12
40
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
4
, c
9
u + 1
c
2
, c
6
, c
8
c
10
, c
11
, c
12
u − 1
c
3
, c
5
, c
7
u
41
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
4
c
6
, c
8
, c
9
c
10
, c
11
, c
12
y −1
c
3
, c
5
, c
7
y
42
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = −1.00000
b = 0
3.28987 12.0000
43
V. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u + 1)
2
)(u
50
− 15u
49
+ ··· − 5u + 1)
· (u
203
+ 10u
202
+ ··· − 1413591u + 4819)
c
2
((u − 1)
2
)(u
50
+ 2u
49
+ ··· + 8u + 1)(u
203
+ 3u
202
+ ··· + 62u + 1)
c
3
u
2
(u
50
+ 2u
49
+ ··· + 152u + 9)(u
203
+ u
202
+ ··· − 274u + 16)
c
4
((u + 1)
2
)(u
50
− u
49
+ ··· + u + 1)(u
203
− 2u
202
+ ··· − 80511u + 7321)
c
5
4(u)(2u − 3)(u
50
+ 3u
49
+ ··· + 62u + 3)
· (2u
203
+ u
202
+ ··· − 82268703170u + 4618463170)
c
6
4(u − 1)(2u + 1)(u
50
+ 4u
49
+ ··· − 7u + 1)(2u
203
− 7u
202
+ ··· + 4u + 11)
c
7
4(u)(2u − 3)(u
50
+ 5u
49
+ ··· − 79u + 21)
· (2u
203
+ 5u
202
+ ··· + 2459520u + 382966)
c
8
((u − 1)
2
)(u
50
+ u
49
+ ··· − u + 1)(u
203
− 2u
202
+ ··· − 80511u + 7321)
c
9
((u + 1)
2
)(u
50
+ 9u
49
+ ··· + 14u + 1)
· (u
203
− 8u
202
+ ··· − 1110488u + 1091189)
c
10
(u − 1)(u + 2)(u
50
+ 2u
49
+ ··· + 2u + 1)
· (u
203
− 4u
201
+ ··· − 1855u + 158)
c
11
(u − 1)(u + 2)(u
50
+ u
49
+ ··· − 385u + 73)
· (u
203
+ 3u
202
+ ··· + 6685893u + 3717382)
c
12
((u − 1)
2
)(u
50
− 9u
49
+ ··· − 14u + 1)
· (u
203
− 8u
202
+ ··· − 1110488u + 1091189)
44
VI. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y −1)
2
)(y
50
+ 13y
49
+ ··· + 59y + 1)
· (y
203
+ 42y
202
+ ··· + 1989941534611y −23222761)
c
2
((y −1)
2
)(y
50
+ 28y
49
+ ··· + 4y + 1)(y
203
+ 25y
202
+ ··· + 194y −1)
c
3
y
2
(y
50
+ 18y
49
+ ··· + 2726y + 81)(y
203
+ 9y
202
+ ··· + 36740y −256)
c
4
, c
8
((y −1)
2
)(y
50
− 23y
49
+ ··· − 11y + 1)
· (y
203
− 110y
202
+ ··· + 5254435841y −53597041)
c
5
16(y)(4y −9)(y
50
− 9y
49
+ ··· − 856y + 9)
· (4y
203
− 225y
202
+ ··· − 1.20 × 10
21
y −2.13 × 10
19
)
c
6
16(y −1)(4y −1)(y
50
− 8y
49
+ ··· − 25y + 1)
· (4y
203
− 89y
202
+ ··· + 3822y −121)
c
7
16(y)(4y −9)(y
50
+ 11y
49
+ ··· + 731y + 441)
· (4y
203
− 49y
202
+ ··· + 2413527165508y −146662957156)
c
9
, c
12
((y −1)
2
)(y
50
+ 49y
49
+ ··· − 36y + 1)
· (y
203
+ 142y
202
+ ··· − 192816319316354y −1190693433721)
c
10
(y −4)(y −1)(y
50
+ 14y
49
+ ··· − 42y
2
+ 1)
· (y
203
− 8y
202
+ ··· + 2071797y −24964)
c
11
(y −4)(y −1)(y
50
+ 11y
49
+ ··· − 116105y + 5329)
· (y
203
− 19y
202
+ ··· + 1958373122289601y −13818928933924)
45
