12a
0325
(K12a
0325
)
A knot diagram
1
Linearized knot diagam
3 6 8 11 2 10 1 12 5 7 9 4
Solving Sequence
2,6 3,10
7 11 1 8 5 4 9 12
c
2
c
6
c
10
c
1
c
7
c
5
c
4
c
9
c
12
c
3
, c
8
, c
11
Ideals for irreducible components
2
of X
par
I
u
1
= h2.44329 × 10
482
u
152
− 7.61384 × 10
482
u
151
+ ··· + 5.78608 × 10
483
b − 1.24996 × 10
485
,
− 2.64221 × 10
485
u
152
+ 9.59872 × 10
485
u
151
+ ··· + 4.66358 × 10
486
a − 5.87365 × 10
487
,
u
153
− 4u
152
+ ··· − 1308u + 403i
I
u
2
= h−151829464u
34
− 651172393u
33
+ ··· + 1552697b + 149127254,
− 32108261u
34
− 103994396u
33
+ ··· + 1552697a − 12080656, u
35
+ 5u
34
+ ··· − 4u − 1i
I
u
3
= hb − 2a − 1, a
2
+ a + 1, u + 1i
I
u
4
= h−a
3
b − a
3
+ b
2
− 2ba + 3a
2
+ a − 2, a
4
− a
2
+ 1, u − 1i
I
u
5
= h−u
8
+ 2u
7
− 2u
4
+ b + u, −u
8
+ 2u
7
+ u
6
− 2u
5
− 3u
4
+ 2u
3
+ 2u
2
+ a − 1,
u
9
− 2u
8
− u
7
+ 2u
6
+ 3u
5
− 2u
4
− 2u
3
+ u + 1i
* 5 irreducible components of dim
C
= 0, with total 207 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
= h2.44 × 10
482
u
152
− 7.61 × 10
482
u
151
+ · · · + 5.79 × 10
483
b − 1.25 ×
10
485
, −2.64 × 10
485
u
152
+ 9.60 × 10
485
u
151
+ · · · + 4.66 × 10
486
a − 5.87 ×
10
487
, u
153
− 4u
152
+ · · · − 1308u + 403i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
0.0566562u
152
− 0.205823u
151
+ ··· − 38.0727u + 12.5947
−0.0422271u
152
+ 0.131589u
151
+ ··· − 54.6888u + 21.6029
a
7
=
0.00265909u
152
− 0.00685318u
151
+ ··· − 17.1575u + 4.86894
0.00422906u
152
+ 0.00397335u
151
+ ··· + 9.07092u − 3.66335
a
11
=
−0.0405739u
152
+ 0.158089u
151
+ ··· + 92.2622u − 8.25737
−0.0194224u
152
+ 0.0553301u
151
+ ··· + 12.8460u − 10.3832
a
1
=
−u
2
+ 1
−u
4
a
8
=
−0.0307886u
152
+ 0.0997291u
151
+ ··· − 40.0301u + 9.22919
−0.0327039u
152
+ 0.116997u
151
+ ··· − 26.8406u + 10.0730
a
5
=
u
u
a
4
=
−0.0341103u
152
+ 0.146828u
151
+ ··· + 72.8214u + 10.7106
−0.0262821u
152
+ 0.106569u
151
+ ··· − 17.8242u + 20.3022
a
9
=
0.107309u
152
− 0.383646u
151
+ ··· − 1.89981u − 10.8282
0.00842534u
152
− 0.0462346u
151
+ ··· − 18.5159u − 1.82006
a
12
=
−0.00158834u
152
+ 0.0137909u
151
+ ··· + 82.2526u − 20.2425
0.0437817u
152
− 0.135616u
151
+ ··· + 54.3146u − 23.0555
(ii) Obstruction class = −1
(iii) Cusp Shapes = 0.179165u
152
− 0.633170u
151
+ ··· + 417.974u − 142.860
2
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
153
+ 56u
152
+ ··· + 5203262u + 162409
c
2
, c
5
u
153
+ 4u
152
+ ··· − 1308u − 403
c
3
u
153
+ 4u
152
+ ··· + 3298135u + 149921
c
4
u
153
+ 2u
152
+ ··· − 590459u + 127561
c
6
, c
10
u
153
+ 4u
152
+ ··· − 32672u − 1744
c
7
u
153
− 4u
152
+ ··· − 54959u − 3812
c
8
, c
11
u
153
− 11u
152
+ ··· + 444u − 9
c
9
u
153
− 36u
151
+ ··· − 415921821u − 28550563
c
12
u
153
+ 12u
152
+ ··· − 183u + 11
3
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
153
+ 88y
152
+ ··· + 4445192262174y −26376683281
c
2
, c
5
y
153
− 56y
152
+ ··· + 5203262y −162409
c
3
y
153
− 58y
152
+ ··· + 6128533920791y −22476306241
c
4
y
153
− 22y
152
+ ··· + 398065340131y −16271808721
c
6
, c
10
y
153
− 96y
152
+ ··· + 45684864y −3041536
c
7
y
153
− 4y
152
+ ··· + 642535585y −14531344
c
8
, c
11
y
153
+ 127y
152
+ ··· + 10368y −81
c
9
y
153
− 72y
152
+ ··· + 144574949507127535y −815134647616969
c
12
y
153
− 16y
152
+ ··· + 16637y −121
4
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.675420 + 0.737717I
a = 1.31203 + 0.65867I
b = 0.192324 − 0.026203I
3.56258 − 1.68630I 0
u = −0.675420 − 0.737717I
a = 1.31203 − 0.65867I
b = 0.192324 + 0.026203I
3.56258 + 1.68630I 0
u = 0.712633 + 0.692997I
a = −0.853056 − 0.873264I
b = −0.267587 − 1.229830I
−0.06386 + 2.09461I 0
u = 0.712633 − 0.692997I
a = −0.853056 + 0.873264I
b = −0.267587 + 1.229830I
−0.06386 − 2.09461I 0
u = 0.833577 + 0.529608I
a = −0.808363 + 0.906087I
b = 0.30919 + 1.83699I
1.92792 − 4.14574I 0
u = 0.833577 − 0.529608I
a = −0.808363 − 0.906087I
b = 0.30919 − 1.83699I
1.92792 + 4.14574I 0
u = 0.726189 + 0.712147I
a = 1.234100 − 0.684681I
b = −0.500158 + 0.082418I
9.74457 + 4.78074I 0
u = 0.726189 − 0.712147I
a = 1.234100 + 0.684681I
b = −0.500158 − 0.082418I
9.74457 − 4.78074I 0
u = −0.848864 + 0.565331I
a = 1.117470 − 0.856923I
b = 0.43012 − 1.41259I
−0.424170 − 0.231230I 0
u = −0.848864 − 0.565331I
a = 1.117470 + 0.856923I
b = 0.43012 + 1.41259I
−0.424170 + 0.231230I 0
5
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.637354 + 0.807506I
a = 0.866602 + 0.671451I
b = −0.126080 + 1.155340I
5.44000 + 7.90600I 0
u = 0.637354 − 0.807506I
a = 0.866602 − 0.671451I
b = −0.126080 − 1.155340I
5.44000 − 7.90600I 0
u = −0.750041 + 0.616302I
a = −1.241710 + 0.108581I
b = −0.256077 + 1.381250I
2.67326 − 0.74208I 0
u = −0.750041 − 0.616302I
a = −1.241710 − 0.108581I
b = −0.256077 − 1.381250I
2.67326 + 0.74208I 0
u = −0.658054 + 0.804069I
a = −0.608800 + 0.419900I
b = 0.433604 + 0.871465I
6.01531 + 0.24800I 0
u = −0.658054 − 0.804069I
a = −0.608800 − 0.419900I
b = 0.433604 − 0.871465I
6.01531 − 0.24800I 0
u = 0.797105 + 0.686679I
a = −1.26136 + 0.71763I
b = 0.022369 + 0.437942I
5.44169 − 1.59304I 0
u = 0.797105 − 0.686679I
a = −1.26136 − 0.71763I
b = 0.022369 − 0.437942I
5.44169 + 1.59304I 0
u = −0.911731 + 0.552948I
a = −0.477581 + 1.096580I
b = 0.07984 + 1.80339I
−0.60988 + 4.66390I 0
u = −0.911731 − 0.552948I
a = −0.477581 − 1.096580I
b = 0.07984 − 1.80339I
−0.60988 − 4.66390I 0
6
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.044140 + 0.221555I
a = 0.234186 + 0.137129I
b = 0.900973 − 0.502033I
−0.419188 + 0.000601I 0
u = 1.044140 − 0.221555I
a = 0.234186 − 0.137129I
b = 0.900973 + 0.502033I
−0.419188 − 0.000601I 0
u = 0.223508 + 0.900376I
a = 0.048702 − 1.141970I
b = −0.098374 − 0.290094I
1.69039 − 3.74324I 0
u = 0.223508 − 0.900376I
a = 0.048702 + 1.141970I
b = −0.098374 + 0.290094I
1.69039 + 3.74324I 0
u = 1.046970 + 0.275240I
a = −0.612920 + 0.491990I
b = −1.94412 + 0.94083I
−2.13134 − 2.48634I 0
u = 1.046970 − 0.275240I
a = −0.612920 − 0.491990I
b = −1.94412 − 0.94083I
−2.13134 + 2.48634I 0
u = 0.855023 + 0.329474I
a = −0.44008 + 1.38498I
b = 0.14747 + 1.64774I
−1.65566 − 4.20561I 0
u = 0.855023 − 0.329474I
a = −0.44008 − 1.38498I
b = 0.14747 − 1.64774I
−1.65566 + 4.20561I 0
u = −0.908445 + 0.098730I
a = −1.211430 − 0.055199I
b = −2.53684 + 0.64359I
5.43502 − 5.17729I 0
u = −0.908445 − 0.098730I
a = −1.211430 + 0.055199I
b = −2.53684 − 0.64359I
5.43502 + 5.17729I 0
7
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.042560 + 0.314422I
a = 0.005034 − 0.658412I
b = −0.629969 − 1.128490I
−1.84749 − 0.93407I 0
u = 1.042560 − 0.314422I
a = 0.005034 + 0.658412I
b = −0.629969 + 1.128490I
−1.84749 + 0.93407I 0
u = 0.771627 + 0.775380I
a = 0.299982 + 0.523125I
b = 0.14897 + 1.55115I
4.97087 − 5.83091I 0
u = 0.771627 − 0.775380I
a = 0.299982 − 0.523125I
b = 0.14897 − 1.55115I
4.97087 + 5.83091I 0
u = 0.891588 + 0.126622I
a = −1.008690 − 0.627616I
b = −1.53323 − 0.42808I
−1.37826 + 1.95591I 0
u = 0.891588 − 0.126622I
a = −1.008690 + 0.627616I
b = −1.53323 + 0.42808I
−1.37826 − 1.95591I 0
u = 0.870067 + 0.203606I
a = −1.137610 − 0.247333I
b = 0.18143 − 1.88250I
−1.52748 + 1.01810I 0
u = 0.870067 − 0.203606I
a = −1.137610 + 0.247333I
b = 0.18143 + 1.88250I
−1.52748 − 1.01810I 0
u = 1.060790 + 0.318839I
a = 0.250423 − 0.244541I
b = −0.060557 − 0.528126I
−1.90791 − 1.30264I 0
u = 1.060790 − 0.318839I
a = 0.250423 + 0.244541I
b = −0.060557 + 0.528126I
−1.90791 + 1.30264I 0
8
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.850090 + 0.712175I
a = 1.32657 − 0.67283I
b = 0.424380 − 0.107176I
10.17410 − 7.33774I 0
u = 0.850090 − 0.712175I
a = 1.32657 + 0.67283I
b = 0.424380 + 0.107176I
10.17410 + 7.33774I 0
u = −0.432157 + 0.775321I
a = −1.20345 − 1.22917I
b = −0.025196 − 0.180087I
6.52645 − 5.80569I 0
u = −0.432157 − 0.775321I
a = −1.20345 + 1.22917I
b = −0.025196 + 0.180087I
6.52645 + 5.80569I 0
u = −0.626201 + 0.625096I
a = −0.838410 − 0.678997I
b = 1.01490 − 1.77224I
4.32590 − 5.42619I 0
u = −0.626201 − 0.625096I
a = −0.838410 + 0.678997I
b = 1.01490 + 1.77224I
4.32590 + 5.42619I 0
u = −0.570543 + 0.959668I
a = −0.800270 − 0.848486I
b = 0.200774 − 0.268302I
6.27187 − 2.95983I 0
u = −0.570543 − 0.959668I
a = −0.800270 + 0.848486I
b = 0.200774 + 0.268302I
6.27187 + 2.95983I 0
u = −1.113800 + 0.077620I
a = 0.446702 − 0.639826I
b = −0.32574 − 1.61736I
−0.77901 + 7.21951I 0
u = −1.113800 − 0.077620I
a = 0.446702 + 0.639826I
b = −0.32574 + 1.61736I
−0.77901 − 7.21951I 0
9
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.657255 + 0.909275I
a = 1.088970 − 0.712066I
b = −0.123532 − 0.187303I
4.36186 + 7.97183I 0
u = 0.657255 − 0.909275I
a = 1.088970 + 0.712066I
b = −0.123532 + 0.187303I
4.36186 − 7.97183I 0
u = −0.914797 + 0.660919I
a = 0.739234 + 0.676124I
b = −0.83643 + 1.47876I
1.29894 + 5.17544I 0
u = −0.914797 − 0.660919I
a = 0.739234 − 0.676124I
b = −0.83643 − 1.47876I
1.29894 − 5.17544I 0
u = −0.760740 + 0.416967I
a = 1.241350 − 0.136865I
b = 0.608290 − 1.115850I
1.246610 − 0.582741I 0
u = −0.760740 − 0.416967I
a = 1.241350 + 0.136865I
b = 0.608290 + 1.115850I
1.246610 + 0.582741I 0
u = 0.874822 + 0.719721I
a = 0.716781 − 1.155820I
b = 1.23055 − 1.78049I
10.10190 + 1.87017I 0
u = 0.874822 − 0.719721I
a = 0.716781 + 1.155820I
b = 1.23055 + 1.78049I
10.10190 − 1.87017I 0
u = 0.913453 + 0.670384I
a = −0.777747 + 1.015990I
b = −1.04270 + 2.14454I
5.08027 − 3.64584I 0
u = 0.913453 − 0.670384I
a = −0.777747 − 1.015990I
b = −1.04270 − 2.14454I
5.08027 + 3.64584I 0
10
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.959519 + 0.620623I
a = −0.010563 − 0.987263I
b = −1.10142 − 1.57540I
1.99753 + 5.62196I 0
u = −0.959519 − 0.620623I
a = −0.010563 + 0.987263I
b = −1.10142 + 1.57540I
1.99753 − 5.62196I 0
u = −0.997511 + 0.567853I
a = −0.106511 + 0.731704I
b = 0.52936 + 1.36991I
0.03637 + 4.78899I 0
u = −0.997511 − 0.567853I
a = −0.106511 − 0.731704I
b = 0.52936 − 1.36991I
0.03637 − 4.78899I 0
u = −0.753439 + 0.893258I
a = −0.685128 − 0.757617I
b = 0.190907 − 0.138520I
8.96953 + 2.45341I 0
u = −0.753439 − 0.893258I
a = −0.685128 + 0.757617I
b = 0.190907 + 0.138520I
8.96953 − 2.45341I 0
u = 0.921136 + 0.724216I
a = −0.687688 − 0.470788I
b = 0.132010 − 0.733189I
4.54242 + 0.18184I 0
u = 0.921136 − 0.724216I
a = −0.687688 + 0.470788I
b = 0.132010 + 0.733189I
4.54242 − 0.18184I 0
u = −0.771547 + 0.297595I
a = 0.096710 + 1.336130I
b = 0.27809 + 1.99610I
−0.90498 + 4.15963I 0
u = −0.771547 − 0.297595I
a = 0.096710 − 1.336130I
b = 0.27809 − 1.99610I
−0.90498 − 4.15963I 0
11
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.971620 + 0.669648I
a = 0.673407 − 0.924552I
b = 1.48002 − 2.39998I
8.98690 − 10.09910I 0
u = 0.971620 − 0.669648I
a = 0.673407 + 0.924552I
b = 1.48002 + 2.39998I
8.98690 + 10.09910I 0
u = −0.262704 + 0.773616I
a = 0.264280 − 0.778739I
b = −0.633860 + 0.099427I
3.78491 − 3.02009I 0
u = −0.262704 − 0.773616I
a = 0.264280 + 0.778739I
b = −0.633860 − 0.099427I
3.78491 + 3.02009I 0
u = −0.556761 + 1.045740I
a = 0.793384 + 0.769810I
b = −0.455631 − 0.074561I
9.95442 − 3.96437I 0
u = −0.556761 − 1.045740I
a = 0.793384 − 0.769810I
b = −0.455631 + 0.074561I
9.95442 + 3.96437I 0
u = 0.976610 + 0.673104I
a = 0.748537 + 0.817036I
b = 0.29436 + 1.49763I
−0.86937 − 7.38752I 0
u = 0.976610 − 0.673104I
a = 0.748537 − 0.817036I
b = 0.29436 − 1.49763I
−0.86937 + 7.38752I 0
u = 0.620597 + 1.012920I
a = −0.982464 + 0.744526I
b = 0.218852 − 0.018938I
9.7647 + 13.7165I 0
u = 0.620597 − 1.012920I
a = −0.982464 − 0.744526I
b = 0.218852 + 0.018938I
9.7647 − 13.7165I 0
12
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.842678 + 0.838630I
a = −1.243570 + 0.434373I
b = −0.447992 + 0.181524I
7.42495 + 0.18404I 0
u = 0.842678 − 0.838630I
a = −1.243570 − 0.434373I
b = −0.447992 − 0.181524I
7.42495 − 0.18404I 0
u = 1.172770 + 0.203097I
a = 0.818682 + 0.261927I
b = 0.44461 + 1.88302I
0.16800 + 3.52115I 0
u = 1.172770 − 0.203097I
a = 0.818682 − 0.261927I
b = 0.44461 − 1.88302I
0.16800 − 3.52115I 0
u = −1.068460 + 0.528251I
a = 0.495743 + 0.300993I
b = 1.58281 + 0.40351I
−0.49224 + 4.40585I 0
u = −1.068460 − 0.528251I
a = 0.495743 − 0.300993I
b = 1.58281 − 0.40351I
−0.49224 − 4.40585I 0
u = −0.602031 + 1.038280I
a = 0.679717 + 0.937809I
b = 0.215654 + 0.315550I
10.29690 − 2.97111I 0
u = −0.602031 − 1.038280I
a = 0.679717 − 0.937809I
b = 0.215654 − 0.315550I
10.29690 + 2.97111I 0
u = −1.185720 + 0.192296I
a = −0.781517 − 0.576114I
b = −1.27731 − 1.23026I
−3.19590 + 7.16430I 0
u = −1.185720 − 0.192296I
a = −0.781517 + 0.576114I
b = −1.27731 + 1.23026I
−3.19590 − 7.16430I 0
13
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.774891 + 0.186761I
a = 0.87427 + 1.21071I
b = 1.01288 + 1.25442I
0.96095 + 3.03835I 0
u = −0.774891 − 0.186761I
a = 0.87427 − 1.21071I
b = 1.01288 − 1.25442I
0.96095 − 3.03835I 0
u = −0.994423 + 0.677816I
a = 0.588656 + 1.117510I
b = 1.11154 + 2.02086I
2.60492 + 7.09908I 0
u = −0.994423 − 0.677816I
a = 0.588656 − 1.117510I
b = 1.11154 − 2.02086I
2.60492 − 7.09908I 0
u = −1.026250 + 0.630511I
a = −0.667338 − 0.661116I
b = 0.08517 − 2.29893I
3.08999 + 10.43030I 0
u = −1.026250 − 0.630511I
a = −0.667338 + 0.661116I
b = 0.08517 + 2.29893I
3.08999 − 10.43030I 0
u = 1.173520 + 0.273220I
a = 0.455407 − 0.360654I
b = 1.19123 − 1.48870I
−0.655419 − 0.092291I 0
u = 1.173520 − 0.273220I
a = 0.455407 + 0.360654I
b = 1.19123 + 1.48870I
−0.655419 + 0.092291I 0
u = 0.971208 + 0.743223I
a = 0.528657 − 0.589456I
b = 0.099570 − 1.279170I
−0.68184 − 2.97639I 0
u = 0.971208 − 0.743223I
a = 0.528657 + 0.589456I
b = 0.099570 + 1.279170I
−0.68184 + 2.97639I 0
14
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −0.889665 + 0.850196I
a = −0.332897 − 0.961223I
b = −0.95870 − 1.65805I
8.81685 + 4.75994I 0
u = −0.889665 − 0.850196I
a = −0.332897 + 0.961223I
b = −0.95870 + 1.65805I
8.81685 − 4.75994I 0
u = 0.949153 + 0.798991I
a = −0.452701 + 1.187980I
b = −0.64662 + 1.92882I
7.08944 − 6.30071I 0
u = 0.949153 − 0.798991I
a = −0.452701 − 1.187980I
b = −0.64662 − 1.92882I
7.08944 + 6.30071I 0
u = −1.024250 + 0.702796I
a = 0.496948 − 0.481525I
b = −0.05463 − 1.50732I
4.90542 + 5.42536I 0
u = −1.024250 − 0.702796I
a = 0.496948 + 0.481525I
b = −0.05463 + 1.50732I
4.90542 − 5.42536I 0
u = −0.890819 + 0.867981I
a = −0.916706 − 0.391285I
b = −0.007710 + 0.270069I
8.83253 + 1.56785I 0
u = −0.890819 − 0.867981I
a = −0.916706 + 0.391285I
b = −0.007710 − 0.270069I
8.83253 − 1.56785I 0
u = 1.035090 + 0.701633I
a = −0.657342 − 0.766281I
b = −0.08280 − 1.68582I
4.2403 − 13.5881I 0
u = 1.035090 − 0.701633I
a = −0.657342 + 0.766281I
b = −0.08280 + 1.68582I
4.2403 + 13.5881I 0
15
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.128870 + 0.540160I
a = −0.496476 + 0.060059I
b = −1.13466 + 0.89487I
1.24165 + 7.88041I 0
u = −1.128870 − 0.540160I
a = −0.496476 − 0.060059I
b = −1.13466 − 0.89487I
1.24165 − 7.88041I 0
u = 0.695099 + 1.046860I
a = −0.187252 + 0.517983I
b = 0.065553 + 1.209850I
5.02145 − 5.56410I 0
u = 0.695099 − 1.046860I
a = −0.187252 − 0.517983I
b = 0.065553 − 1.209850I
5.02145 + 5.56410I 0
u = 0.590454 + 0.448407I
a = 0.206533 + 0.075884I
b = −0.260318 − 0.895000I
−0.75181 − 1.75911I 0
u = 0.590454 − 0.448407I
a = 0.206533 − 0.075884I
b = −0.260318 + 0.895000I
−0.75181 + 1.75911I 0
u = 1.214290 + 0.331544I
a = 0.533415 − 0.214242I
b = 0.592306 − 0.489412I
−1.83287 − 1.28802I 0
u = 1.214290 − 0.331544I
a = 0.533415 + 0.214242I
b = 0.592306 + 0.489412I
−1.83287 + 1.28802I 0
u = 0.592865 + 0.435887I
a = 0.84521 − 1.19939I
b = −1.010780 − 0.969887I
1.69596 − 2.80767I 0
u = 0.592865 − 0.435887I
a = 0.84521 + 1.19939I
b = −1.010780 + 0.969887I
1.69596 + 2.80767I 0
16
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 1.258530 + 0.129668I
a = 0.949986 + 0.211044I
b = 1.67338 + 0.32332I
1.03334 + 3.15335I 0
u = 1.258530 − 0.129668I
a = 0.949986 − 0.211044I
b = 1.67338 − 0.32332I
1.03334 − 3.15335I 0
u = −1.090750 + 0.644844I
a = −0.777817 − 0.993349I
b = −1.35180 − 1.98578I
4.66317 + 11.17020I 0
u = −1.090750 − 0.644844I
a = −0.777817 + 0.993349I
b = −1.35180 + 1.98578I
4.66317 − 11.17020I 0
u = −0.501854 + 0.494679I
a = 0.850357 + 0.182406I
b = 0.333900 − 0.518337I
1.344830 − 0.367303I 0
u = −0.501854 − 0.494679I
a = 0.850357 − 0.182406I
b = 0.333900 + 0.518337I
1.344830 + 0.367303I 0
u = −1.012260 + 0.813521I
a = −0.557837 − 0.579479I
b = −0.98432 − 1.39711I
8.19560 + 3.84853I 0
u = −1.012260 − 0.813521I
a = −0.557837 + 0.579479I
b = −0.98432 + 1.39711I
8.19560 − 3.84853I 0
u = 1.066020 + 0.748565I
a = 0.595459 − 1.003130I
b = 0.98924 − 2.15417I
3.0936 − 14.0941I 0
u = 1.066020 − 0.748565I
a = 0.595459 + 1.003130I
b = 0.98924 + 2.15417I
3.0936 + 14.0941I 0
17
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.108540 + 0.725067I
a = −0.642614 − 0.802010I
b = −0.99655 − 1.87804I
4.60037 + 9.10371I 0
u = −1.108540 − 0.725067I
a = −0.642614 + 0.802010I
b = −0.99655 + 1.87804I
4.60037 − 9.10371I 0
u = 0.200810 + 1.311100I
a = 0.001357 + 0.844155I
b = −0.206213 + 0.177742I
7.11502 − 6.59112I 0
u = 0.200810 − 1.311100I
a = 0.001357 − 0.844155I
b = −0.206213 − 0.177742I
7.11502 + 6.59112I 0
u = 1.122210 + 0.767503I
a = −0.574907 + 0.953747I
b = −1.18822 + 2.15176I
8.1750 − 20.1811I 0
u = 1.122210 − 0.767503I
a = −0.574907 − 0.953747I
b = −1.18822 − 2.15176I
8.1750 + 20.1811I 0
u = −1.130570 + 0.780366I
a = 0.736243 + 0.766101I
b = 1.08578 + 1.30249I
8.64198 + 9.53082I 0
u = −1.130570 − 0.780366I
a = 0.736243 − 0.766101I
b = 1.08578 − 1.30249I
8.64198 − 9.53082I 0
u = −1.354970 + 0.238706I
a = 0.723068 + 0.454325I
b = 1.37125 + 1.17547I
1.23384 + 11.69350I 0
u = −1.354970 − 0.238706I
a = 0.723068 − 0.454325I
b = 1.37125 − 1.17547I
1.23384 − 11.69350I 0
18
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = −1.154050 + 0.758715I
a = 0.530945 + 0.803697I
b = 1.26385 + 2.11724I
8.08457 + 10.46880I 0
u = −1.154050 − 0.758715I
a = 0.530945 − 0.803697I
b = 1.26385 − 2.11724I
8.08457 − 10.46880I 0
u = 1.41426 + 0.24865I
a = −0.593767 + 0.264467I
b = −0.602795 + 1.179350I
1.57961 − 0.90971I 0
u = 1.41426 − 0.24865I
a = −0.593767 − 0.264467I
b = −0.602795 − 1.179350I
1.57961 + 0.90971I 0
u = −0.510501
a = 2.73379
b = 0.514162
2.62224 −10.7210
u = −0.474905 + 0.105090I
a = −3.10488 − 0.39152I
b = −0.006293 − 0.407151I
7.06383 − 5.40730I −2.10146 + 3.84042I
u = −0.474905 − 0.105090I
a = −3.10488 + 0.39152I
b = −0.006293 + 0.407151I
7.06383 + 5.40730I −2.10146 − 3.84042I
u = 0.424562 + 0.075928I
a = −1.03913 − 1.15125I
b = −1.156600 + 0.188778I
−1.03654 + 1.97369I −3.23403 − 3.94535I
u = 0.424562 − 0.075928I
a = −1.03913 + 1.15125I
b = −1.156600 − 0.188778I
−1.03654 − 1.97369I −3.23403 + 3.94535I
u = 0.126420 + 0.370317I
a = −0.46542 − 1.59180I
b = 1.84958 + 0.05960I
3.79450 − 5.96104I 5.56144 + 10.98017I
19
Solutions to I
u
1
√
−1(vol +
√
−1CS) Cusp shape
u = 0.126420 − 0.370317I
a = −0.46542 + 1.59180I
b = 1.84958 − 0.05960I
3.79450 + 5.96104I 5.56144 − 10.98017I
u = −0.007858 + 0.366859I
a = 1.77418 + 0.79931I
b = 0.197596 − 0.346161I
0.77391 − 1.80327I 3.26429 + 3.38985I
u = −0.007858 − 0.366859I
a = 1.77418 − 0.79931I
b = 0.197596 + 0.346161I
0.77391 + 1.80327I 3.26429 − 3.38985I
20
II.
I
u
2
= h−1.52 × 10
8
u
34
− 6.51 × 10
8
u
33
+ · · · + 1.55 × 10
6
b + 1.49 × 10
8
, −3.21 ×
10
7
u
34
−1.04×10
8
u
33
+· · · +1.55×10
6
a−1.21×10
7
, u
35
+5u
34
+· · · − 4u −1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
20.6790u
34
+ 66.9766u
33
+ ··· − 9.40460u + 7.78043
97.7843u
34
+ 419.381u
33
+ ··· − 331.791u − 96.0440
a
7
=
50.9369u
34
+ 186.635u
33
+ ··· − 86.4751u − 16.3830
68.3050u
34
+ 285.435u
33
+ ··· − 203.901u − 63.1350
a
11
=
−41.0631u
34
− 176.365u
33
+ ··· + 139.525u + 45.6170
−4.60138u
34
− 22.1666u
33
+ ··· + 24.3394u + 15.4841
a
1
=
−u
2
+ 1
−u
4
a
8
=
78.9053u
34
+ 291.003u
33
+ ··· − 143.193u − 30.7292
87.6712u
34
+ 351.410u
33
+ ··· − 230.910u − 65.8919
a
5
=
u
u
a
4
=
39.8584u
34
+ 165.801u
33
+ ··· − 103.368u − 24.9750
15.1794u
34
+ 79.8247u
33
+ ··· − 67.9637u − 19.7554
a
9
=
32.3951u
34
+ 80.8831u
33
+ ··· + 45.9770u + 40.9022
109.500u
34
+ 433.288u
33
+ ··· − 276.409u − 62.9223
a
12
=
−24.4144u
34
− 105.711u
33
+ ··· + 81.8965u + 25.0201
16.0473u
34
+ 68.4873u
33
+ ··· − 58.2890u − 22.1127
(ii) Obstruction class = 1
(iii) Cusp Shapes =
278558292
1552697
u
34
+
1156360262
1552697
u
33
+ ··· −
23488223
50087
u −
208700972
1552697
21
(iv) u-Polynomials at the component
22
Crossings u-Polynomials at each crossing
c
1
u
35
− 15u
34
+ ··· + 12u − 1
c
2
u
35
+ 5u
34
+ ··· − 4u − 1
c
3
u
35
− 6u
33
+ ··· + 6u
2
− 1
c
4
u
35
− 4u
33
+ ··· + 5u
3
− 1
c
5
u
35
− 5u
34
+ ··· − 4u + 1
c
6
u
35
+ 3u
34
+ ··· − u + 1
c
7
u
35
− 4u
34
+ ··· − 2u + 1
c
8
u
35
− 4u
34
+ ··· − 16u + 1
c
9
u
35
− 2u
33
+ ··· − 17u
2
− 1
c
10
u
35
− 3u
34
+ ··· − u − 1
c
11
u
35
+ 4u
34
+ ··· − 16u − 1
c
12
u
35
− 4u
33
+ ··· + 4u + 1
23
24
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
y
35
+ 9y
34
+ ··· + 12y −1
c
2
, c
5
y
35
− 15y
34
+ ··· + 12y −1
c
3
y
35
− 12y
34
+ ··· + 12y −1
c
4
y
35
− 8y
34
+ ··· − 12y
2
− 1
c
6
, c
10
y
35
− 19y
34
+ ··· + 27y −1
c
7
y
35
+ 20y
33
+ ··· − 2y −1
c
8
, c
11
y
35
+ 28y
34
+ ··· + 2y −1
c
9
y
35
− 4y
34
+ ··· − 34y −1
c
12
y
35
− 8y
34
+ ··· − 12y −1
25
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.952324 + 0.369350I
a = 0.654714 + 0.663740I
b = 0.801199 + 0.888255I
−1.87460 + 0.57113I −5.17275 − 1.58863I
u = 0.952324 − 0.369350I
a = 0.654714 − 0.663740I
b = 0.801199 − 0.888255I
−1.87460 − 0.57113I −5.17275 + 1.58863I
u = −0.763074 + 0.572132I
a = −1.165640 + 0.560134I
b = −0.60988 + 1.30359I
0.005916 − 1.049110I 2.95322 + 2.05623I
u = −0.763074 − 0.572132I
a = −1.165640 − 0.560134I
b = −0.60988 − 1.30359I
0.005916 + 1.049110I 2.95322 − 2.05623I
u = 0.710870 + 0.631310I
a = 0.640178 − 0.901706I
b = −0.561482 − 1.244580I
0.46747 − 3.07344I 2.02904 + 5.41703I
u = 0.710870 − 0.631310I
a = 0.640178 + 0.901706I
b = −0.561482 + 1.244580I
0.46747 + 3.07344I 2.02904 − 5.41703I
u = −0.940591 + 0.571888I
a = 0.190979 − 1.133390I
b = −0.41658 − 1.68997I
−0.57376 + 5.61276I −0.20505 − 10.95929I
u = −0.940591 − 0.571888I
a = 0.190979 + 1.133390I
b = −0.41658 + 1.68997I
−0.57376 − 5.61276I −0.20505 + 10.95929I
u = −1.004130 + 0.512194I
a = −0.300402 − 0.478538I
b = −1.53489 − 0.28906I
−1.01057 + 4.86471I −2.41225 − 8.49143I
u = −1.004130 − 0.512194I
a = −0.300402 + 0.478538I
b = −1.53489 + 0.28906I
−1.01057 − 4.86471I −2.41225 + 8.49143I
26
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.715012 + 0.494155I
a = −0.985754 + 0.042073I
b = −0.59448 + 1.61405I
0.006296 − 0.742006I 0.280768 + 0.453523I
u = −0.715012 − 0.494155I
a = −0.985754 − 0.042073I
b = −0.59448 − 1.61405I
0.006296 + 0.742006I 0.280768 − 0.453523I
u = 0.556860 + 1.046160I
a = −0.228651 + 0.632619I
b = 0.293159 + 1.285910I
5.40416 − 5.73662I 14.5171 + 10.1664I
u = 0.556860 − 1.046160I
a = −0.228651 − 0.632619I
b = 0.293159 − 1.285910I
5.40416 + 5.73662I 14.5171 − 10.1664I
u = −1.100590 + 0.460700I
a = 0.387508 + 0.177224I
b = 0.672862 − 1.006260I
1.49510 + 8.67317I 4.48341 − 10.04345I
u = −1.100590 − 0.460700I
a = 0.387508 − 0.177224I
b = 0.672862 + 1.006260I
1.49510 − 8.67317I 4.48341 + 10.04345I
u = −0.833944 + 0.861183I
a = −1.114360 − 0.451541I
b = −0.295447 − 0.177981I
7.18663 − 0.09516I −2.23336 − 2.40298I
u = −0.833944 − 0.861183I
a = −1.114360 + 0.451541I
b = −0.295447 + 0.177981I
7.18663 + 0.09516I −2.23336 + 2.40298I
u = 1.130950 + 0.407668I
a = 0.597695 − 0.260622I
b = 1.121610 − 0.802185I
−1.37185 − 1.60234I 3.69800 + 4.97364I
u = 1.130950 − 0.407668I
a = 0.597695 + 0.260622I
b = 1.121610 + 0.802185I
−1.37185 + 1.60234I 3.69800 − 4.97364I
27
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = 0.704634 + 0.351829I
a = 0.14118 − 1.42247I
b = −0.14689 − 1.73746I
−1.00331 − 3.62857I −0.299753 + 0.113090I
u = 0.704634 − 0.351829I
a = 0.14118 + 1.42247I
b = −0.14689 + 1.73746I
−1.00331 + 3.62857I −0.299753 − 0.113090I
u = −0.962687 + 0.818475I
a = −0.391871 − 1.059390I
b = −0.60653 − 1.82164I
6.78931 + 6.33721I 0. − 9.64738I
u = −0.962687 − 0.818475I
a = −0.391871 + 1.059390I
b = −0.60653 + 1.82164I
6.78931 − 6.33721I 0. + 9.64738I
u = −0.400764 + 0.616466I
a = 1.26826 + 1.46524I
b = −0.443571 + 0.343597I
7.77251 − 5.32661I 10.87504 + 3.22243I
u = −0.400764 − 0.616466I
a = 1.26826 − 1.46524I
b = −0.443571 − 0.343597I
7.77251 + 5.32661I 10.87504 − 3.22243I
u = 0.132863 + 0.700344I
a = −0.22196 + 1.85127I
b = −0.442969 + 0.087579I
7.78742 − 5.47056I 11.30668 + 5.00480I
u = 0.132863 − 0.700344I
a = −0.22196 − 1.85127I
b = −0.442969 − 0.087579I
7.78742 + 5.47056I 11.30668 − 5.00480I
u = −1.112870 + 0.647724I
a = 0.754171 + 0.807475I
b = 1.21984 + 2.00058I
5.72869 + 10.57970I 7.53102 − 8.63101I
u = −1.112870 − 0.647724I
a = 0.754171 − 0.807475I
b = 1.21984 − 2.00058I
5.72869 − 10.57970I 7.53102 + 8.63101I
28
Solutions to I
u
2
√
−1(vol +
√
−1CS) Cusp shape
u = −0.629011 + 0.299001I
a = 0.778076 + 0.100265I
b = 2.28291 − 1.38325I
3.38154 − 5.29286I −1.11480 + 2.37174I
u = −0.629011 − 0.299001I
a = 0.778076 − 0.100265I
b = 2.28291 + 1.38325I
3.38154 + 5.29286I −1.11480 − 2.37174I
u = 0.451080
a = 3.09738
b = 0.855377
2.84524 26.9720
u = 1.54864 + 0.21635I
a = −0.552813 + 0.192199I
b = −0.666552 + 0.765646I
1.15471 − 0.87139I 0
u = 1.54864 − 0.21635I
a = −0.552813 − 0.192199I
b = −0.666552 − 0.765646I
1.15471 + 0.87139I 0
29
III. I
u
3
= hb − 2a − 1, a
2
+ a + 1, u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
−1
a
3
=
1
1
a
10
=
a
2a + 1
a
7
=
a + 1
a + 1
a
11
=
a − 1
2a
a
1
=
0
−1
a
8
=
a + 1
0
a
5
=
−1
−1
a
4
=
a + 1
1
a
9
=
−1
a
a
12
=
a
a
(ii) Obstruction class = −1
(iii) Cusp Shapes = −4a − 8
30
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
8
, c
11
(u + 1)
2
c
2
, c
5
(u − 1)
2
c
3
u
2
− u + 1
c
4
, c
6
, c
7
c
9
, c
10
, c
12
u
2
+ u + 1
31
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
c
8
, c
11
(y −1)
2
c
3
, c
4
, c
6
c
7
, c
9
, c
10
c
12
y
2
+ y + 1
32
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
3
√
−1(vol +
√
−1CS) Cusp shape
u = −1.00000
a = −0.500000 + 0.866025I
b = 1.73205I
−4.93480 + 2.02988I −6.00000 − 3.46410I
u = −1.00000
a = −0.500000 − 0.866025I
b = − 1.73205I
−4.93480 − 2.02988I −6.00000 + 3.46410I
33
IV. I
u
4
= h−a
3
b − a
3
+ b
2
− 2ba + 3a
2
+ a − 2, a
4
− a
2
+ 1, u − 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
1
a
3
=
1
1
a
10
=
a
b
a
7
=
a
2
ba + 1
a
11
=
−a
3
+ a
−a
2
b + b − a
a
1
=
0
−1
a
8
=
a
2
ba − a
2
+ 1
a
5
=
1
1
a
4
=
−a
3
b + a
2
− 1
−ba + 2a
2
+ a − 1
a
9
=
−b + 2a
a
a
12
=
−a
3
b − a
3
+ 2a
2
+ a − 2
−a
2
b + a
2
+ b − a − 1
(ii) Obstruction class = 1
(iii) Cusp Shapes = −4a
2
+ 4
34
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
, c
2
(u − 1)
8
c
3
u
8
− 2u
7
− u
6
+ 4u
5
− 6u
3
+ 3u
2
+ 4u + 1
c
4
u
8
+ 3u
6
+ 2u
5
+ 4u
4
+ 7u
2
− 2u + 1
c
5
(u + 1)
8
c
6
, c
10
(u
4
− u
2
+ 1)
2
c
7
(u
2
+ u + 1)
4
c
8
, c
11
(u
2
+ 1)
4
c
9
u
8
− 2u
5
+ u
4
− 6u
3
+ 4u
2
+ 2u + 1
c
12
u
8
− 4u
7
+ 8u
6
− 10u
5
+ 9u
4
− 6u
3
+ 2u + 1
35
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
2
, c
5
(y −1)
8
c
3
y
8
− 6y
7
+ 17y
6
− 34y
5
+ 60y
4
− 70y
3
+ 57y
2
− 10y + 1
c
4
y
8
+ 6y
7
+ 17y
6
+ 34y
5
+ 60y
4
+ 70y
3
+ 57y
2
+ 10y + 1
c
6
, c
10
(y
2
− y + 1)
4
c
7
(y
2
+ y + 1)
4
c
8
, c
11
(y + 1)
8
c
9
y
8
+ 2y
6
+ 4y
5
− 21y
4
− 20y
3
+ 42y
2
+ 4y + 1
c
12
y
8
+ 2y
6
− 4y
5
− 21y
4
+ 20y
3
+ 42y
2
− 4y + 1
36
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
4
√
−1(vol +
√
−1CS) Cusp shape
u = 1.00000
a = 0.866025 + 0.500000I
b = 1.090230 + 0.183732I
2.02988I 2.00000 − 3.46410I
u = 1.00000
a = 0.866025 + 0.500000I
b = 0.64182 + 1.81627I
2.02988I 2.00000 − 3.46410I
u = 1.00000
a = 0.866025 − 0.500000I
b = 1.090230 − 0.183732I
− 2.02988I 2.00000 + 3.46410I
u = 1.00000
a = 0.866025 − 0.500000I
b = 0.64182 − 1.81627I
− 2.02988I 2.00000 + 3.46410I
u = 1.00000
a = −0.866025 + 0.500000I
b = 0.33397 + 1.56918I
− 2.02988I 2.00000 + 3.46410I
u = 1.00000
a = −0.866025 + 0.500000I
b = −2.06602 + 0.43082I
− 2.02988I 2.00000 + 3.46410I
u = 1.00000
a = −0.866025 − 0.500000I
b = 0.33397 − 1.56918I
2.02988I 2.00000 − 3.46410I
u = 1.00000
a = −0.866025 − 0.500000I
b = −2.06602 − 0.43082I
2.02988I 2.00000 − 3.46410I
37
V. I
u
5
= h−u
8
+ 2u
7
− 2u
4
+ b + u, −u
8
+ 2u
7
+ · · · + a − 1, u
9
− 2u
8
− u
7
+
2u
6
+ 3u
5
− 2u
4
− 2u
3
+ u + 1i
(i) Arc colorings
a
2
=
1
0
a
6
=
0
u
a
3
=
1
u
2
a
10
=
u
8
− 2u
7
− u
6
+ 2u
5
+ 3u
4
− 2u
3
− 2u
2
+ 1
u
8
− 2u
7
+ 2u
4
− u
a
7
=
−u
8
+ 2u
7
+ u
6
− 2u
5
− 3u
4
+ 2u
3
+ 2u
2
− 1
−u
8
+ 2u
7
− 2u
4
+ 2u
a
11
=
0
u
a
1
=
−u
2
+ 1
−u
4
a
8
=
u
5
− 2u
4
+ u
2
+ u − 1
u
7
− 2u
6
+ u
5
− u
2
+ u
a
5
=
u
u
a
4
=
u
u
3
+ u
a
9
=
u
4
− u
3
− u
2
+ 1
u
6
− 2u
5
+ u
3
+ u
2
− u
a
12
=
1
u
2
(ii) Obstruction class = −1
(iii) Cusp Shapes = 6
38
(iv) u-Polynomials at the component
Crossings u-Polynomials at each crossing
c
1
u
9
+ 6u
8
+ 15u
7
+ 22u
6
+ 23u
5
+ 14u
4
+ 6u
3
+ u + 1
c
2
, c
5
, c
12
u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u − 1
c
3
, c
8
, c
11
u
9
+ u
7
− u
5
+ u − 1
c
4
u
9
− 6u
8
+ 15u
7
− 22u
6
+ 23u
5
− 14u
4
+ 6u
3
+ u − 1
c
6
, c
10
(u − 1)
9
c
7
u
9
− u
7
− 3u
6
+ 7u
5
− 10u
4
+ 4u
3
− 3u
2
+ 3u − 1
c
9
u
9
+ 3u
7
− 4u
6
+ u
5
− 6u
4
− 2u
3
+ 4u
2
+ 5u + 1
39
(v) Riley Polynomials at the component
Crossings Riley Polynomials at each crossing
c
1
, c
4
y
9
− 6y
8
+ 7y
7
+ 50y
6
+ 95y
5
+ 98y
4
+ 38y
3
− 16y
2
+ y − 1
c
2
, c
5
, c
12
y
9
− 6y
8
+ 15y
7
− 22y
6
+ 23y
5
− 14y
4
+ 6y
3
+ y − 1
c
3
, c
8
, c
11
y
9
+ 2y
8
− y
7
− 2y
6
+ 3y
5
+ 2y
4
− 2y
3
+ y − 1
c
6
, c
10
(y − 1)
9
c
7
y
9
− 2y
8
+ 15y
7
− 15y
6
− 13y
5
− 68y
4
− 8y
3
− 5y
2
+ 3y − 1
c
9
y
9
+ 6y
8
+ 11y
7
− 14y
6
− 49y
5
+ 22y
4
+ 70y
3
− 24y
2
+ 17y − 1
40
(vi) Complex Volumes and Cusp Shapes
Solutions to I
u
5
√
−1(vol +
√
−1CS) Cusp shape
u = −0.804809 + 0.675390I
a = 0.729080 + 0.611838I
b = 0.14426 + 2.22883I
1.64493 6.00000
u = −0.804809 − 0.675390I
a = 0.729080 − 0.611838I
b = 0.14426 − 2.22883I
1.64493 6.00000
u = 0.938584 + 0.497255I
a = −0.831928 + 0.440750I
b = −0.11581 + 1.56743I
1.64493 6.00000
u = 0.938584 − 0.497255I
a = −0.831928 − 0.440750I
b = −0.11581 − 1.56743I
1.64493 6.00000
u = −0.741936
a = 1.34783
b = 1.68729
1.64493 6.00000
u = −0.269653 + 0.627398I
a = 0.57823 + 1.34536I
b = 0.158673 − 0.330377I
1.64493 6.00000
u = −0.269653 − 0.627398I
a = 0.57823 − 1.34536I
b = 0.158673 + 0.330377I
1.64493 6.00000
u = 1.50685 + 0.22394I
a = −0.649297 + 0.096495I
b = −1.030760 − 0.107997I
1.64493 6.00000
u = 1.50685 − 0.22394I
a = −0.649297 − 0.096495I
b = −1.030760 + 0.107997I
1.64493 6.00000
41
VI. u-Polynomials
Crossings u-Polynomials at each crossing
c
1
((u − 1)
8
)(u + 1)
2
(u
9
+ 6u
8
+ ··· + u + 1)
· (u
35
− 15u
34
+ ··· + 12u − 1)
· (u
153
+ 56u
152
+ ··· + 5203262u + 162409)
c
2
(u − 1)
10
(u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u − 1)
· (u
35
+ 5u
34
+ ··· − 4u − 1)(u
153
+ 4u
152
+ ··· − 1308u − 403)
c
3
(u
2
− u + 1)(u
8
− 2u
7
− u
6
+ 4u
5
− 6u
3
+ 3u
2
+ 4u + 1)
· (u
9
+ u
7
− u
5
+ u − 1)(u
35
− 6u
33
+ ··· + 6u
2
− 1)
· (u
153
+ 4u
152
+ ··· + 3298135u + 149921)
c
4
(u
2
+ u + 1)(u
8
+ 3u
6
+ 2u
5
+ 4u
4
+ 7u
2
− 2u + 1)
· (u
9
− 6u
8
+ 15u
7
− 22u
6
+ 23u
5
− 14u
4
+ 6u
3
+ u − 1)
· (u
35
− 4u
33
+ ··· + 5u
3
− 1)(u
153
+ 2u
152
+ ··· − 590459u + 127561)
c
5
(u − 1)
2
(u + 1)
8
(u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u − 1)
· (u
35
− 5u
34
+ ··· − 4u + 1)(u
153
+ 4u
152
+ ··· − 1308u − 403)
c
6
((u − 1)
9
)(u
2
+ u + 1)(u
4
− u
2
+ 1)
2
(u
35
+ 3u
34
+ ··· − u + 1)
· (u
153
+ 4u
152
+ ··· − 32672u − 1744)
c
7
(u
2
+ u + 1)
5
(u
9
− u
7
− 3u
6
+ 7u
5
− 10u
4
+ 4u
3
− 3u
2
+ 3u − 1)
· (u
35
− 4u
34
+ ··· − 2u + 1)(u
153
− 4u
152
+ ··· − 54959u − 3812)
c
8
((u + 1)
2
)(u
2
+ 1)
4
(u
9
+ u
7
+ ··· + u − 1)(u
35
− 4u
34
+ ··· − 16u + 1)
· (u
153
− 11u
152
+ ··· + 444u − 9)
c
9
(u
2
+ u + 1)(u
8
− 2u
5
+ u
4
− 6u
3
+ 4u
2
+ 2u + 1)
· (u
9
+ 3u
7
− 4u
6
+ u
5
− 6u
4
− 2u
3
+ 4u
2
+ 5u + 1)
· (u
35
− 2u
33
+ ··· − 17u
2
− 1)
· (u
153
− 36u
151
+ ··· − 415921821u − 28550563)
c
10
((u − 1)
9
)(u
2
+ u + 1)(u
4
− u
2
+ 1)
2
(u
35
− 3u
34
+ ··· − u − 1)
· (u
153
+ 4u
152
+ ··· − 32672u − 1744)
c
11
((u + 1)
2
)(u
2
+ 1)
4
(u
9
+ u
7
+ ··· + u − 1)(u
35
+ 4u
34
+ ··· − 16u − 1)
· (u
153
− 11u
152
+ ··· + 444u − 9)
c
12
(u
2
+ u + 1)(u
8
− 4u
7
+ 8u
6
− 10u
5
+ 9u
4
− 6u
3
+ 2u + 1)
· (u
9
+ 2u
8
− u
7
− 2u
6
+ 3u
5
+ 2u
4
− 2u
3
+ u − 1)
· (u
35
− 4u
33
+ ··· + 4u + 1)(u
153
+ 12u
152
+ ··· − 183u + 11)
42
VII. Riley Polynomials
Crossings Riley Polynomials at each crossing
c
1
((y − 1)
10
)(y
9
− 6y
8
+ ··· + y − 1)
· (y
35
+ 9y
34
+ ··· + 12y − 1)
· (y
153
+ 88y
152
+ ··· + 4445192262174y − 26376683281)
c
2
, c
5
(y − 1)
10
(y
9
− 6y
8
+ 15y
7
− 22y
6
+ 23y
5
− 14y
4
+ 6y
3
+ y − 1)
· (y
35
− 15y
34
+ ··· + 12y − 1)
· (y
153
− 56y
152
+ ··· + 5203262y − 162409)
c
3
(y
2
+ y + 1)(y
8
− 6y
7
+ ··· − 10y + 1)
· (y
9
+ 2y
8
− y
7
− 2y
6
+ 3y
5
+ 2y
4
− 2y
3
+ y − 1)
· (y
35
− 12y
34
+ ··· + 12y − 1)
· (y
153
− 58y
152
+ ··· + 6128533920791y − 22476306241)
c
4
(y
2
+ y + 1)(y
8
+ 6y
7
+ ··· + 10y + 1)
· (y
9
− 6y
8
+ 7y
7
+ 50y
6
+ 95y
5
+ 98y
4
+ 38y
3
− 16y
2
+ y − 1)
· (y
35
− 8y
34
+ ··· − 12y
2
− 1)
· (y
153
− 22y
152
+ ··· + 398065340131y − 16271808721)
c
6
, c
10
((y − 1)
9
)(y
2
− y + 1)
4
(y
2
+ y + 1)(y
35
− 19y
34
+ ··· + 27y − 1)
· (y
153
− 96y
152
+ ··· + 45684864y − 3041536)
c
7
(y
2
+ y + 1)
5
· (y
9
− 2y
8
+ 15y
7
− 15y
6
− 13y
5
− 68y
4
− 8y
3
− 5y
2
+ 3y − 1)
· (y
35
+ 20y
33
+ ··· − 2y − 1)
· (y
153
− 4y
152
+ ··· + 642535585y − 14531344)
c
8
, c
11
(y − 1)
2
(y + 1)
8
(y
9
+ 2y
8
− y
7
− 2y
6
+ 3y
5
+ 2y
4
− 2y
3
+ y − 1)
· (y
35
+ 28y
34
+ ··· + 2y − 1)(y
153
+ 127y
152
+ ··· + 10368y − 81)
c
9
(y
2
+ y + 1)(y
8
+ 2y
6
+ 4y
5
− 21y
4
− 20y
3
+ 42y
2
+ 4y + 1)
· (y
9
+ 6y
8
+ 11y
7
− 14y
6
− 49y
5
+ 22y
4
+ 70y
3
− 24y
2
+ 17y − 1)
· (y
35
− 4y
34
+ ··· − 34y − 1)
· (y
153
− 72y
152
+ ··· + 144574949507127535y − 815134647616969)
c
12
(y
2
+ y + 1)(y
8
+ 2y
6
− 4y
5
− 21y
4
+ 20y
3
+ 42y
2
− 4y + 1)
· (y
9
− 6y
8
+ 15y
7
− 22y
6
+ 23y
5
− 14y
4
+ 6y
3
+ y − 1)
· (y
35
− 8y
34
+ ··· − 12y − 1)(y
153
− 16y
152
+ ··· + 16637y − 121)
43
