LMFDB - Embedded newform 243.3.f.d.134.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,3,Mod(26,243)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(243, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("243.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	243.f (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.62127042396$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			134.5
Character	$\chi$	$=$	243.134
Dual form			243.3.f.d.107.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.26025 + 2.69367i) q^{2} +(-1.45250 + 8.23751i) q^{4} +(1.68497 + 4.62942i) q^{5} +(0.589325 + 3.34223i) q^{7} +(-13.2912 + 7.67367i) q^{8} +O(q^{10})$	\(q+(2.26025 + 2.69367i) q^{2} +(-1.45250 + 8.23751i) q^{4} +(1.68497 + 4.62942i) q^{5} +(0.589325 + 3.34223i) q^{7} +(-13.2912 + 7.67367i) q^{8} +(-8.66165 + 15.0024i) q^{10} +(5.43158 - 14.9231i) q^{11} +(-2.74092 - 2.29990i) q^{13} +(-7.67082 + 9.14172i) q^{14} +(-19.2712 - 7.01415i) q^{16} +(-9.99899 - 5.77292i) q^{17} +(9.59953 + 16.6269i) q^{19} +(-40.5823 + 7.15575i) q^{20} +(52.4747 - 19.0992i) q^{22} +(-15.2139 - 2.68263i) q^{23} +(0.558724 - 0.468825i) q^{25} -12.5815i q^{26} -28.3876 q^{28} +(7.19537 + 8.57510i) q^{29} +(-4.25648 + 24.1397i) q^{31} +(-3.66766 - 10.0768i) q^{32} +(-7.04994 - 39.9822i) q^{34} +(-14.4796 + 8.35978i) q^{35} +(21.2827 - 36.8628i) q^{37} +(-23.0899 + 63.4389i) q^{38} +(-57.9199 - 48.6006i) q^{40} +(-4.28956 + 5.11210i) q^{41} +(44.9789 + 16.3710i) q^{43} +(115.040 + 66.4185i) q^{44} +(-27.1612 - 47.0447i) q^{46} +(50.5542 - 8.91407i) q^{47} +(35.2218 - 12.8197i) q^{49} +(2.52572 + 0.445352i) q^{50} +(22.9267 - 19.2378i) q^{52} -61.1404i q^{53} +78.2375 q^{55} +(-33.4800 - 39.8999i) q^{56} +(-6.83511 + 38.7638i) q^{58} +(-15.3764 - 42.2463i) q^{59} +(-0.836678 - 4.74504i) q^{61} +(-74.6451 + 43.0964i) q^{62} +(-22.1622 + 38.3861i) q^{64} +(6.02885 - 16.5641i) q^{65} +(9.10899 + 7.64335i) q^{67} +(62.0780 - 73.9816i) q^{68} +(-55.2460 - 20.1079i) q^{70} +(-76.5190 - 44.1783i) q^{71} +(21.5726 + 37.3649i) q^{73} +(147.400 - 25.9907i) q^{74} +(-150.907 + 54.9258i) q^{76} +(53.0774 + 9.35899i) q^{77} +(-114.185 + 95.8125i) q^{79} -101.033i q^{80} -23.4658 q^{82} +(-50.9846 - 60.7610i) q^{83} +(9.87725 - 56.0167i) q^{85} +(57.5658 + 158.161i) q^{86} +(42.3231 + 240.026i) q^{88} +(69.3002 - 40.0105i) q^{89} +(6.07151 - 10.5162i) q^{91} +(44.1963 - 121.428i) q^{92} +(138.277 + 116.028i) q^{94} +(-60.7978 + 72.4560i) q^{95} +(173.019 + 62.9738i) q^{97} +(114.142 + 65.9000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8	$ 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29} - 87 q^{31} + 243 q^{32} - 153 q^{34} - 252 q^{35} - 3 q^{37} + 321 q^{38} - 168 q^{40} - 357 q^{41} - 87 q^{43} + 639 q^{44} - 3 q^{46} - 51 q^{47} - 69 q^{49} + 168 q^{50} - 36 q^{52} - 12 q^{55} - 177 q^{56} + 138 q^{58} + 48 q^{59} + 147 q^{61} - 900 q^{62} - 51 q^{64} + 624 q^{65} + 12 q^{67} - 477 q^{68} - 6 q^{70} + 315 q^{71} - 66 q^{73} - 480 q^{74} - 57 q^{76} + 453 q^{77} - 15 q^{79} - 12 q^{82} - 591 q^{83} + 243 q^{85} + 669 q^{86} + 591 q^{88} + 72 q^{89} + 96 q^{91} + 564 q^{92} + 957 q^{94} - 606 q^{95} + 696 q^{97} + 882 q^{98}+O(q^{100}) $ 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/243\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.26025	+	2.69367i	1.13013	+	1.34683i	0.930213	+	0.367020i	$0.119622\pi$
$2$	2.26025	+	2.69367i	1.13013	+	1.34683i	0.199914	+	0.979813i	$0.435934\pi$
$3$		0			0
$3$		0			0
$4$	−1.45250	+	8.23751i	−0.363124	+	2.05938i
$5$	1.68497	+	4.62942i	0.336994	+	0.925884i	0.986242	+	0.165307i	$0.0528615\pi$
$5$	1.68497	+	4.62942i	0.336994	+	0.925884i	−0.649248	+	0.760577i	$0.724916\pi$
$6$		0			0
$7$	0.589325	+	3.34223i	0.0841892	+	0.477461i	0.997529	+	0.0702616i	$0.0223834\pi$
$7$	0.589325	+	3.34223i	0.0841892	+	0.477461i	−0.913339	+	0.407199i	$0.866505\pi$
$8$	−13.2912	+	7.67367i	−1.66140	+	0.959209i
$9$		0			0
$10$	−8.66165	+	15.0024i	−0.866165	+	1.50024i
$11$	5.43158	−	14.9231i	0.493780	−	1.35665i	−0.403416	−	0.915016i	$-0.632177\pi$
$11$	5.43158	−	14.9231i	0.493780	−	1.35665i	0.897196	−	0.441632i	$-0.145600\pi$
$12$		0			0
$13$	−2.74092	−	2.29990i	−0.210840	−	0.176916i	0.531252	−	0.847214i	$-0.321722\pi$
$13$	−2.74092	−	2.29990i	−0.210840	−	0.176916i	−0.742092	+	0.670298i	$0.766166\pi$
$14$	−7.67082	+	9.14172i	−0.547915	+	0.652980i
$15$		0			0
$16$	−19.2712	−	7.01415i	−1.20445	−	0.438384i
$17$	−9.99899	−	5.77292i	−0.588176	−	0.339583i	0.176200	−	0.984354i	$-0.443619\pi$
$17$	−9.99899	−	5.77292i	−0.588176	−	0.339583i	−0.764376	+	0.644771i	$0.776953\pi$
$18$		0			0
$19$	9.59953	+	16.6269i	0.505238	+	0.875098i	0.999982	+	0.00605928i	$0.00192874\pi$
$19$	9.59953	+	16.6269i	0.505238	+	0.875098i	−0.494743	+	0.869039i	$0.664738\pi$
$20$	−40.5823	+	7.15575i	−2.02911	+	0.357788i
$21$		0			0
$22$	52.4747	−	19.0992i	2.38521	−	0.868147i
$23$	−15.2139	−	2.68263i	−0.661475	−	0.116636i	−0.167175	−	0.985927i	$-0.553464\pi$
$23$	−15.2139	−	2.68263i	−0.661475	−	0.116636i	−0.494300	+	0.869291i	$0.664576\pi$
$24$		0			0
$25$	0.558724	−	0.468825i	0.0223490	−	0.0187530i
$26$		−	12.5815i		−	0.483904i
$27$		0			0
$28$	−28.3876			−1.01384
$29$	7.19537	+	8.57510i	0.248116	+	0.295693i	0.875700	−	0.482856i	$-0.160400\pi$
$29$	7.19537	+	8.57510i	0.248116	+	0.295693i	−0.627584	+	0.778549i	$0.715956\pi$
$30$		0			0
$31$	−4.25648	+	24.1397i	−0.137306	+	0.778701i	0.835920	+	0.548851i	$0.184935\pi$
$31$	−4.25648	+	24.1397i	−0.137306	+	0.778701i	−0.973226	+	0.229850i	$0.926177\pi$
$32$	−3.66766	−	10.0768i	−0.114614	−	0.314901i
$33$		0			0
$34$	−7.04994	−	39.9822i	−0.207351	−	1.17595i
$35$	−14.4796	+	8.35978i	−0.413702	+	0.238851i
$36$		0			0
$37$	21.2827	−	36.8628i	0.575209	−	0.996292i	−0.420810	−	0.907149i	$-0.638254\pi$
$37$	21.2827	−	36.8628i	0.575209	−	0.996292i	0.996019	−	0.0891427i	$-0.0284127\pi$
$38$	−23.0899	+	63.4389i	−0.607628	+	1.66944i
$39$		0			0
$40$	−57.9199	−	48.6006i	−1.44800	−	1.21501i
$41$	−4.28956	+	5.11210i	−0.104624	+	0.124685i	−0.815815	−	0.578313i	$-0.803711\pi$
$41$	−4.28956	+	5.11210i	−0.104624	+	0.124685i	0.711192	+	0.702998i	$0.248156\pi$
$42$		0			0
$43$	44.9789	+	16.3710i	1.04602	+	0.380721i	0.807160	−	0.590333i	$-0.201003\pi$
$43$	44.9789	+	16.3710i	1.04602	+	0.380721i	0.238862	+	0.971054i	$0.423226\pi$
$44$	115.040	+	66.4185i	2.61455	+	1.50951i
$45$		0			0
$46$	−27.1612	−	47.0447i	−0.590462	−	1.02271i
$47$	50.5542	−	8.91407i	1.07562	−	0.189661i	0.392343	−	0.919819i	$-0.371665\pi$
$47$	50.5542	−	8.91407i	1.07562	−	0.189661i	0.683278	+	0.730158i	$0.260554\pi$
$48$		0			0
$49$	35.2218	−	12.8197i	0.718812	−	0.261626i
$50$	2.52572	+	0.445352i	0.0505143	+	0.00890704i
$51$		0			0
$52$	22.9267	−	19.2378i	0.440897	−	0.369957i
$53$		−	61.1404i		−	1.15359i	−0.816888	−	0.576797i	$-0.804303\pi$
$53$		−	61.1404i		−	1.15359i	0.816888	−	0.576797i	$-0.195697\pi$
$54$		0			0
$55$	78.2375			1.42250
$56$	−33.4800	−	39.8999i	−0.597856	−	0.712498i
$57$		0			0
$58$	−6.83511	+	38.7638i	−0.117847	+	0.668342i
$59$	−15.3764	−	42.2463i	−0.260617	−	0.716039i	−0.999126	−	0.0417955i	$-0.986692\pi$
$59$	−15.3764	−	42.2463i	−0.260617	−	0.716039i	0.738509	−	0.674243i	$-0.235530\pi$
$60$		0			0
$61$	−0.836678	−	4.74504i	−0.0137160	−	0.0777875i	0.977181	−	0.212406i	$-0.0681301\pi$
$61$	−0.836678	−	4.74504i	−0.0137160	−	0.0777875i	−0.990897	+	0.134619i	$0.957019\pi$
$62$	−74.6451	+	43.0964i	−1.20395	+	0.695103i
$63$		0			0
$64$	−22.1622	+	38.3861i	−0.346285	+	0.599783i
$65$	6.02885	−	16.5641i	0.0927516	−	0.254833i
$66$		0			0
$67$	9.10899	+	7.64335i	0.135955	+	0.114080i	0.708229	−	0.705982i	$-0.249494\pi$
$67$	9.10899	+	7.64335i	0.135955	+	0.114080i	−0.572274	+	0.820062i	$0.693939\pi$
$68$	62.0780	−	73.9816i	0.912911	−	1.08797i
$69$		0			0
$70$	−55.2460	−	20.1079i	−0.789228	−	0.287255i
$71$	−76.5190	−	44.1783i	−1.07773	−	0.622229i	−0.147448	−	0.989070i	$-0.547106\pi$
$71$	−76.5190	−	44.1783i	−1.07773	−	0.622229i	−0.930284	+	0.366841i	$0.880439\pi$
$72$		0			0
$73$	21.5726	+	37.3649i	0.295516	+	0.511848i	0.975105	−	0.221745i	$-0.0711752\pi$
$73$	21.5726	+	37.3649i	0.295516	+	0.511848i	−0.679589	+	0.733593i	$0.737842\pi$
$74$	147.400	−	25.9907i	1.99190	−	0.351225i
$75$		0			0
$76$	−150.907	+	54.9258i	−1.98562	+	0.722707i
$77$	53.0774	+	9.35899i	0.689317	+	0.121545i
$78$		0			0
$79$	−114.185	+	95.8125i	−1.44538	+	1.21282i	−0.509510	+	0.860465i	$0.670173\pi$
$79$	−114.185	+	95.8125i	−1.44538	+	1.21282i	−0.935868	+	0.352351i	$0.885382\pi$
$80$		−	101.033i		−	1.26291i
$81$		0			0
$82$	−23.4658			−0.286168
$83$	−50.9846	−	60.7610i	−0.614272	−	0.732061i	0.365802	−	0.930693i	$-0.380795\pi$
$83$	−50.9846	−	60.7610i	−0.614272	−	0.732061i	−0.980074	+	0.198632i	$0.936350\pi$
$84$		0			0
$85$	9.87725	−	56.0167i	0.116203	−	0.659020i
$86$	57.5658	+	158.161i	0.669370	+	1.83908i
$87$		0			0
$88$	42.3231	+	240.026i	0.480945	+	2.72757i
$89$	69.3002	−	40.0105i	0.778654	−	0.449556i	−0.0572990	−	0.998357i	$-0.518249\pi$
$89$	69.3002	−	40.0105i	0.778654	−	0.449556i	0.835953	+	0.548801i	$0.184916\pi$
$90$		0			0
$91$	6.07151	−	10.5162i	0.0667199	−	0.115562i
$92$	44.1963	−	121.428i	0.480395	−	1.31987i
$93$		0			0
$94$	138.277	+	116.028i	1.47103	+	1.23434i
$95$	−60.7978	+	72.4560i	−0.639977	+	0.762695i
$96$		0			0
$97$	173.019	+	62.9738i	1.78370	+	0.649215i	0.999591	+	0.0285947i	$0.00910323\pi$
$97$	173.019	+	62.9738i	1.78370	+	0.649215i	0.784112	+	0.620620i	$0.213119\pi$
$98$	114.142	+	65.9000i	1.16472	+	0.672449i
$99$		0			0
$100$	3.05041	+	5.28346i	0.0305041	+	0.0528346i
$101$	−100.724	+	17.7604i	−0.997270	+	0.175846i	−0.648379	−	0.761318i	$-0.724553\pi$
$101$	−100.724	+	17.7604i	−0.997270	+	0.175846i	−0.348891	+	0.937163i	$0.613442\pi$
$102$		0			0
$103$	−123.981	+	45.1252i	−1.20370	+	0.438109i	−0.864512	−	0.502611i	$-0.832373\pi$
$103$	−123.981	+	45.1252i	−1.20370	+	0.438109i	−0.339183	+	0.940721i	$0.610150\pi$
$104$	54.0788	+	9.53555i	0.519988	+	0.0916880i
$105$		0			0
$106$	164.692	−	138.193i	1.55370	−	1.30371i
$107$			21.6029i			0.201896i	0.994892	+	0.100948i	$0.0321876\pi$
$107$			21.6029i			0.201896i	−0.994892	+	0.100948i	$0.967812\pi$
$108$		0			0
$109$	−149.823			−1.37452			−0.687262	−	0.726410i	$-0.741187\pi$
$109$	−149.823			−1.37452			−0.687262	+	0.726410i	$0.741187\pi$
$110$	176.837	+	210.746i	1.60761	+	1.91587i
$111$		0			0
$112$	12.0859	−	68.5423i	0.107909	−	0.611985i
$113$	−31.7759	−	87.3036i	−0.281203	−	0.772598i	−0.997220	−	0.0745153i	$-0.976259\pi$
$113$	−31.7759	−	87.3036i	−0.281203	−	0.772598i	0.716017	−	0.698083i	$-0.245963\pi$
$114$		0			0
$115$	−13.2160	−	74.9518i	−0.114922	−	0.651755i
$116$	−81.0888	+	46.8166i	−0.699041	+	0.403592i
$117$		0			0
$118$	79.0428	−	136.906i	0.669855	−	1.16022i
$119$	13.4017	−	36.8210i	0.112620	−	0.309420i
$120$		0			0
$121$	−100.507	−	84.3350i	−0.830633	−	0.696984i
$122$	10.8904	−	12.9787i	0.0892659	−	0.106383i
$123$		0			0
$124$	−192.669	−	70.1257i	−1.55378	−	0.565530i
$125$	109.774	+	63.3782i	0.878194	+	0.507025i
$126$		0			0
$127$	−50.8221	−	88.0264i	−0.400174	−	0.693122i	0.593573	−	0.804780i	$-0.297717\pi$
$127$	−50.8221	−	88.0264i	−0.400174	−	0.693122i	−0.993747	+	0.111659i	$0.964384\pi$
$128$	−195.734	+	34.5132i	−1.52917	+	0.269634i
$129$		0			0
$130$	58.2450	−	21.1994i	0.448038	−	0.163073i
$131$	31.1428	+	5.49131i	0.237731	+	0.0419184i	0.291244	−	0.956649i	$-0.405931\pi$
$131$	31.1428	+	5.49131i	0.237731	+	0.0419184i	−0.0535131	+	0.998567i	$0.517042\pi$
$132$		0			0
$133$	−49.9135	+	41.8824i	−0.375290	+	0.314905i
$134$			41.8125i			0.312034i
$135$		0			0
$136$	177.198			1.30293
$137$	−17.9040	−	21.3371i	−0.130686	−	0.155745i	0.696733	−	0.717330i	$-0.254636\pi$
$137$	−17.9040	−	21.3371i	−0.130686	−	0.155745i	−0.827419	+	0.561585i	$0.810192\pi$
$138$		0			0
$139$	34.1355	−	193.592i	0.245579	−	1.39275i	−0.573565	−	0.819160i	$-0.694440\pi$
$139$	34.1355	−	193.592i	0.245579	−	1.39275i	0.819144	−	0.573588i	$-0.194449\pi$
$140$	−47.8323	−	131.418i	−0.341659	−	0.938701i
$141$		0			0
$142$	−53.9509	−	305.971i	−0.379936	−	2.15472i
$143$	−49.2093	+	28.4110i	−0.344121	+	0.198678i
$144$		0			0
$145$	−27.5738	+	47.7592i	−0.190164	+	0.329374i
$146$	−51.8890	+	142.564i	−0.355404	+	0.976464i
$147$		0			0
$148$	272.745	+	228.860i	1.84287	+	1.54635i
$149$	87.4949	−	104.272i	0.587214	−	0.699814i	−0.387854	−	0.921721i	$-0.626784\pi$
$149$	87.4949	−	104.272i	0.587214	−	0.699814i	0.975068	+	0.221906i	$0.0712280\pi$
$150$		0			0
$151$	−139.144	−	50.6442i	−0.921482	−	0.335392i	−0.162654	−	0.986683i	$-0.552005\pi$
$151$	−139.144	−	50.6442i	−0.921482	−	0.335392i	−0.758828	+	0.651291i	$0.774228\pi$
$152$	−255.178	−	147.327i	−1.67880	−	0.969258i
$153$		0			0
$154$	94.7585	+	164.127i	0.615315	+	1.06576i
$155$	−118.925	+	20.9697i	−0.767257	+	0.135288i
$156$		0			0
$157$	−33.0501	+	12.0292i	−0.210510	+	0.0766193i	−0.445123	−	0.895470i	$-0.646840\pi$
$157$	−33.0501	+	12.0292i	−0.210510	+	0.0766193i	0.234613	+	0.972089i	$0.424618\pi$
$158$	−516.174	−	91.0153i	−3.26692	−	0.576046i
$159$		0			0
$160$	40.4699	−	33.9583i	0.252937	−	0.212239i
$161$		−	52.4293i		−	0.325648i
$162$		0			0
$163$	147.146			0.902737			0.451368	−	0.892338i	$-0.350936\pi$
$163$	147.146			0.902737			0.451368	+	0.892338i	$0.350936\pi$
$164$	−35.8804	−	42.7606i	−0.218783	−	0.260736i
$165$		0			0
$166$	48.4319	−	274.671i	0.291758	−	1.65464i
$167$	−72.8658	−	200.197i	−0.436322	−	1.19879i	−0.941867	−	0.335985i	$-0.890931\pi$
$167$	−72.8658	−	200.197i	−0.436322	−	1.19879i	0.505545	−	0.862800i	$-0.331291\pi$
$168$		0			0
$169$	−27.1235	−	153.825i	−0.160494	−	0.910206i
$170$	173.215	−	100.006i	1.01891	−	0.588270i
$171$		0			0
$172$	−200.188	+	346.736i	−1.16388	+	2.01591i
$173$	−18.1001	+	49.7297i	−0.104625	+	0.287455i	−0.980948	−	0.194269i	$-0.937767\pi$
$173$	−18.1001	+	49.7297i	−0.104625	+	0.287455i	0.876323	+	0.481723i	$0.159989\pi$
$174$		0			0
$175$	1.89619	+	1.59109i	0.0108354	+	0.00909195i
$176$	−209.346	+	249.489i	−1.18947	+	1.41755i
$177$		0			0
$178$	264.411	+	96.2377i	1.48546	+	0.540661i
$179$	48.8286	+	28.1912i	0.272786	+	0.157493i	0.630153	−	0.776471i	$-0.282992\pi$
$179$	48.8286	+	28.1912i	0.272786	+	0.157493i	−0.357367	+	0.933964i	$0.616326\pi$
$180$		0			0
$181$	−92.1392	−	159.590i	−0.509056	−	0.881712i	−0.999945	−	0.0104893i	$-0.996661\pi$
$181$	−92.1392	−	159.590i	−0.509056	−	0.881712i	0.490888	−	0.871222i	$-0.336672\pi$
$182$	42.0502	−	7.41458i	0.231045	−	0.0407395i
$183$		0			0
$184$	222.797	−	81.0914i	1.21085	−	0.440714i
$185$	206.514	+	36.4140i	1.11629	+	0.196832i
$186$		0			0
$187$	−140.460	+	117.860i	−0.751125	+	0.630268i
$188$			429.388i			2.28398i
$189$		0			0
$190$	−332.591			−1.75048
$191$	−18.9549	−	22.5896i	−0.0992403	−	0.118270i	0.714138	−	0.700005i	$-0.246819\pi$
$191$	−18.9549	−	22.5896i	−0.0992403	−	0.118270i	−0.813379	+	0.581735i	$0.802374\pi$
$192$		0			0
$193$	−65.6683	+	372.424i	−0.340250	+	1.92966i	0.0272411	+	0.999629i	$0.491328\pi$
$193$	−65.6683	+	372.424i	−0.340250	+	1.92966i	−0.367491	+	0.930027i	$0.619783\pi$
$194$	221.437	+	608.393i	1.14143	+	3.13605i
$195$		0			0
$196$	54.4428	+	308.760i	0.277769	+	1.57531i
$197$	11.5940	−	6.69378i	0.0588526	−	0.0339786i	−0.470285	−	0.882515i	$-0.655849\pi$
$197$	11.5940	−	6.69378i	0.0588526	−	0.0339786i	0.529138	+	0.848536i	$0.322516\pi$
$198$		0			0
$199$	38.0531	−	65.9099i	0.191222	−	0.331205i	−0.754434	−	0.656376i	$-0.772088\pi$
$199$	38.0531	−	65.9099i	0.191222	−	0.331205i	0.945655	+	0.325171i	$0.105422\pi$
$200$	−3.82850	+	10.5187i	−0.0191425	+	0.0525935i
$201$		0			0
$202$	−275.503	−	231.175i	−1.36388	−	1.14443i
$203$	−24.4195	+	29.1021i	−0.120293	+	0.143360i
$204$		0			0
$205$	−30.8939	−	11.2444i	−0.150702	−	0.0548509i
$206$	−401.780	−	231.968i	−1.95039	−	1.12606i
$207$		0			0
$208$	36.6890	+	63.5471i	0.176389	+	0.305515i
$209$	300.266	−	52.9449i	1.43668	−	0.253325i
$210$		0			0
$211$	0.382496	−	0.139217i	0.00181278	−	0.000659797i	−0.341114	−	0.940022i	$-0.610804\pi$
$211$	0.382496	−	0.139217i	0.00181278	−	0.000659797i	0.342926	+	0.939362i	$0.388582\pi$
$212$	503.645	+	88.8062i	2.37568	+	0.418897i
$213$		0			0
$214$	−58.1910	+	48.8280i	−0.271920	+	0.228168i
$215$			235.811i			1.09680i
$216$		0			0
$217$	−83.1888			−0.383359
$218$	−338.638	−	403.573i	−1.55339	−	1.85125i
$219$		0			0
$220$	−113.640	+	644.482i	−0.516544	+	2.92946i
$221$	14.1293	+	38.8198i	0.0639333	+	0.175655i
$222$		0			0
$223$	−2.50974	−	14.2335i	−0.0112544	−	0.0638272i	0.978663	−	0.205471i	$-0.0658725\pi$
$223$	−2.50974	−	14.2335i	−0.0112544	−	0.0638272i	−0.989918	+	0.141643i	$0.954761\pi$
$224$	31.5176	−	18.1967i	0.140703	−	0.0812351i
$225$		0			0
$226$	163.345	−	282.922i	0.722766	−	1.25187i
$227$	−118.903	+	326.684i	−0.523803	+	1.43914i	0.342453	+	0.939535i	$0.388742\pi$
$227$	−118.903	+	326.684i	−0.523803	+	1.43914i	−0.866255	+	0.499601i	$0.833480\pi$
$228$		0			0
$229$	74.9545	+	62.8943i	0.327312	+	0.274648i	0.791604	−	0.611035i	$-0.209246\pi$
$229$	74.9545	+	62.8943i	0.327312	+	0.274648i	−0.464291	+	0.885683i	$0.653691\pi$
$230$	172.023	−	205.010i	0.747928	−	0.891346i
$231$		0			0
$232$	−161.437	−	58.7584i	−0.695851	−	0.253269i
$233$	−59.9442	−	34.6088i	−0.257271	−	0.148536i	0.365818	−	0.930686i	$-0.380789\pi$
$233$	−59.9442	−	34.6088i	−0.257271	−	0.148536i	−0.623089	+	0.782151i	$0.714123\pi$
$234$		0			0
$235$	126.449	+	219.017i	0.538082	+	0.931985i
$236$	370.338	−	65.3007i	1.56923	−	0.276698i
$237$		0			0
$238$	129.475	−	47.1250i	0.544012	−	0.198004i
$239$	−304.518	−	53.6947i	−1.27413	−	0.224664i	−0.504646	−	0.863326i	$-0.668377\pi$
$239$	−304.518	−	53.6947i	−1.27413	−	0.224664i	−0.769487	+	0.638663i	$0.779488\pi$
$240$		0			0
$241$	152.581	−	128.030i	0.633115	−	0.531247i	−0.268780	−	0.963202i	$-0.586620\pi$
$241$	152.581	−	128.030i	0.633115	−	0.531247i	0.901895	+	0.431955i	$0.142176\pi$
$242$		−	461.350i		−	1.90640i
$243$		0			0
$244$	40.3026			0.165175
$245$	118.695	+	141.456i	0.484471	+	0.577370i
$246$		0			0
$247$	11.9287	−	67.6509i	0.0482943	−	0.273890i
$248$	−128.667	−	353.508i	−0.518817	−	1.42544i
$249$		0			0
$250$	77.3980	+	438.946i	0.309592	+	1.75578i
$251$	−41.4853	+	23.9516i	−0.165280	+	0.0954245i	−0.580358	−	0.814361i	$-0.697088\pi$
$251$	−41.4853	+	23.9516i	−0.165280	+	0.0954245i	0.415078	+	0.909786i	$0.363754\pi$
$252$		0			0
$253$	−122.669	+	212.469i	−0.484857	+	0.839797i
$254$	122.243	−	335.860i	0.481272	−	1.32228i
$255$		0			0
$256$	−399.558	−	335.269i	−1.56077	−	1.30964i
$257$	−203.011	+	241.939i	−0.789925	+	0.941396i	−0.999336	−	0.0364321i	$-0.988401\pi$
$257$	−203.011	+	241.939i	−0.789925	+	0.941396i	0.209411	+	0.977828i	$0.432845\pi$
$258$		0			0
$259$	135.746	+	49.4076i	0.524117	+	0.190763i
$260$	127.690	+	73.7221i	0.491117	+	0.283546i
$261$		0			0
$262$	55.5988	+	96.3000i	0.212209	+	0.367557i
$263$	−147.360	+	25.9835i	−0.560302	+	0.0987964i	−0.446625	−	0.894721i	$-0.647374\pi$
$263$	−147.360	+	25.9835i	−0.560302	+	0.0987964i	−0.113677	+	0.993518i	$0.536263\pi$
$264$		0			0
$265$	283.045	−	103.020i	1.06809	−	0.388754i
$266$	−225.634	−	39.7854i	−0.848250	−	0.149569i
$267$		0			0
$268$	−76.1930	+	63.9335i	−0.284302	+	0.238558i
$269$			60.3653i			0.224406i	0.993685	+	0.112203i	$0.0357907\pi$
$269$			60.3653i			0.224406i	−0.993685	+	0.112203i	$0.964209\pi$
$270$		0			0
$271$	127.511			0.470522			0.235261	−	0.971932i	$-0.424406\pi$
$271$	127.511			0.470522			0.235261	+	0.971932i	$0.424406\pi$
$272$	152.200	+	181.385i	0.559560	+	0.666858i
$273$		0			0
$274$	17.0076	−	96.4546i	0.0620714	−	0.352024i
$275$	−3.96159	−	10.8844i	−0.0144058	−	0.0395795i
$276$		0			0
$277$	−30.8008	−	174.680i	−0.111194	−	0.630615i	−0.988564	−	0.150800i	$-0.951815\pi$
$277$	−30.8008	−	174.680i	−0.111194	−	0.630615i	0.877370	−	0.479815i	$-0.159296\pi$
$278$	598.627	−	345.618i	2.15334	−	1.24323i
$279$		0			0
$280$	128.300	−	222.223i	0.458216	−	0.793653i
$281$	173.406	−	476.429i	0.617103	−	1.69548i	−0.0968633	−	0.995298i	$-0.530881\pi$
$281$	173.406	−	476.429i	0.617103	−	1.69548i	0.713967	−	0.700180i	$-0.246897\pi$
$282$		0			0
$283$	−70.1486	−	58.8617i	−0.247875	−	0.207992i	0.510382	−	0.859948i	$-0.329504\pi$
$283$	−70.1486	−	58.8617i	−0.247875	−	0.207992i	−0.758257	+	0.651956i	$0.773949\pi$
$284$	475.062	−	566.157i	1.67275	−	1.99351i
$285$		0			0
$286$	−187.755	−	68.3373i	−0.656487	−	0.238942i
$287$	−19.6137	−	11.3240i	−0.0683406	−	0.0394565i
$288$		0			0
$289$	−77.8468	−	134.835i	−0.269366	−	0.466556i
$290$	−190.971	+	33.6733i	−0.658521	+	0.116115i
$291$		0			0
$292$	−339.128	+	123.433i	−1.16140	+	0.422714i
$293$	471.590	+	83.1540i	1.60952	+	0.283802i	0.904850	−	0.425732i	$-0.139983\pi$
$293$	471.590	+	83.1540i	1.60952	+	0.283802i	0.704672	+	0.709534i	$0.251094\pi$
$294$		0			0
$295$	169.667	−	142.367i	0.575142	−	0.482602i
$296$			653.267i			2.20698i
$297$		0			0
$298$	478.636			1.60616
$299$	35.5304	+	42.3434i	0.118831	+	0.141617i
$300$		0			0
$301$	−28.2084	+	159.978i	−0.0937155	+	0.531487i
$302$	−178.082	−	489.276i	−0.589675	−	1.62012i
$303$		0			0
$304$	−68.3712	−	387.752i	−0.224905	−	1.27550i
$305$	20.5570	−	11.8686i	0.0674000	−	0.0389134i
$306$		0			0
$307$	−24.1538	+	41.8357i	−0.0786770	+	0.136273i	−0.902679	−	0.430314i	$-0.858403\pi$
$307$	−24.1538	+	41.8357i	−0.0786770	+	0.136273i	0.824002	+	0.566586i	$0.191736\pi$
$308$	−154.190	+	423.632i	−0.500615	+	1.37543i
$309$		0			0
$310$	−325.286	−	272.947i	−1.04931	−	0.880475i
$311$	−276.535	+	329.562i	−0.889181	+	1.05968i	0.108665	+	0.994078i	$0.465342\pi$
$311$	−276.535	+	329.562i	−0.889181	+	1.05968i	−0.997846	+	0.0656058i	$0.979102\pi$
$312$		0			0
$313$	189.069	+	68.8156i	0.604056	+	0.219858i	0.625900	−	0.779903i	$-0.284732\pi$
$313$	189.069	+	68.8156i	0.604056	+	0.219858i	−0.0218446	+	0.999761i	$0.506954\pi$
$314$	−107.104	−	61.8367i	−0.341096	−	0.196932i
$315$		0			0
$316$	−623.403	−	1079.77i	−1.97280	−	3.41698i
$317$	−18.0917	+	3.19006i	−0.0570717	+	0.0100633i	−0.202111	−	0.979363i	$-0.564780\pi$
$317$	−18.0917	+	3.19006i	−0.0570717	+	0.0100633i	0.145039	+	0.989426i	$0.453669\pi$
$318$		0			0
$319$	167.050	−	60.8011i	0.523667	−	0.190599i
$320$	−215.048	−	37.9188i	−0.672025	−	0.118496i
$321$		0			0
$322$	141.227	−	118.504i	0.438593	−	0.368024i
$323$		−	221.669i		−	0.686282i
$324$		0			0
$325$	−2.60967			−0.00802976
$326$	332.588	+	396.363i	1.02021	+	1.21584i
$327$		0			0
$328$	17.7848	−	100.863i	0.0542220	−	0.307508i
$329$	59.5857	+	163.710i	0.181111	+	0.497599i
$330$		0			0
$331$	26.4006	+	149.725i	0.0797600	+	0.452341i	0.998365	+	0.0571640i	$0.0182058\pi$
$331$	26.4006	+	149.725i	0.0797600	+	0.452341i	−0.918605	+	0.395177i	$0.870683\pi$
$332$	574.574	−	331.731i	1.73065	−	0.999189i
$333$		0			0
$334$	374.569	−	648.773i	1.12146	−	1.94243i
$335$	−20.0359	+	55.0481i	−0.0598086	+	0.164323i
$336$		0			0
$337$	367.453	+	308.329i	1.09036	+	0.914924i	0.996740	−	0.0806837i	$-0.0257104\pi$
$337$	367.453	+	308.329i	1.09036	+	0.914924i	0.0936241	+	0.995608i	$0.470155\pi$
$338$	353.047	−	420.745i	1.04452	−	1.24481i
$339$		0			0
$340$	447.091	+	162.728i	1.31497	+	0.478612i
$341$	337.121	+	194.637i	0.988624	+	0.570782i
$342$		0			0
$343$	146.751	+	254.180i	0.427846	+	0.741050i
$344$	−723.449	+	127.564i	−2.10305	+	0.370824i
$345$		0			0
$346$	−174.866	+	63.6460i	−0.505393	+	0.183948i
$347$	403.200	+	71.0951i	1.16196	+	0.204885i	0.721192	−	0.692735i	$-0.243595\pi$
$347$	403.200	+	71.0951i	1.16196	+	0.204885i	0.440769	+	0.897621i	$0.354706\pi$
$348$		0			0
$349$	81.9686	−	68.7798i	0.234867	−	0.197077i	−0.517756	−	0.855528i	$-0.673233\pi$
$349$	81.9686	−	68.7798i	0.234867	−	0.197077i	0.752623	+	0.658451i	$0.228788\pi$
$350$			8.70397i			0.0248685i
$351$		0			0
$352$	−170.299			−0.483804
$353$	358.891	+	427.710i	1.01669	+	1.21164i	0.977178	+	0.212424i	$0.0681359\pi$
$353$	358.891	+	427.710i	1.01669	+	1.21164i	0.0395119	+	0.999219i	$0.487420\pi$
$354$		0			0
$355$	75.5874	−	428.677i	0.212922	−	1.20754i
$356$	228.929	+	628.976i	0.643058	+	1.76679i
$357$		0			0
$358$	34.4274	+	195.247i	0.0961659	+	0.545384i
$359$	−191.972	+	110.835i	−0.534740	+	0.308732i	−0.742944	−	0.669353i	$-0.766571\pi$
$359$	−191.972	+	110.835i	−0.534740	+	0.308732i	0.208205	+	0.978085i	$0.433238\pi$
$360$		0			0
$361$	−3.80187	+	6.58504i	−0.0105315	+	0.0182411i
$362$	221.624	−	608.906i	0.612220	−	1.68206i
$363$		0			0
$364$	77.8082	+	65.2888i	0.213759	+	0.179365i
$365$	−136.629	+	162.828i	−0.374325	+	0.446103i
$366$		0			0
$367$	−161.660	−	58.8394i	−0.440490	−	0.160325i	0.112248	−	0.993680i	$-0.464195\pi$
$367$	−161.660	−	58.8394i	−0.440490	−	0.160325i	−0.552738	+	0.833355i	$0.686417\pi$
$368$	274.374	+	158.410i	0.745583	+	0.430462i
$369$		0			0
$370$	368.687	+	638.585i	0.996452	+	1.72591i
$371$	204.345	−	36.0316i	0.550795	−	0.0971201i
$372$		0			0
$373$	−117.489	+	42.7624i	−0.314983	+	0.114645i	−0.494674	−	0.869079i	$-0.664713\pi$
$373$	−117.489	+	42.7624i	−0.314983	+	0.114645i	0.179691	+	0.983723i	$0.442490\pi$
$374$	−634.952	−	111.959i	−1.69773	−	0.299356i
$375$		0			0
$376$	−603.522	+	506.415i	−1.60511	+	1.34685i
$377$		−	40.0523i		−	0.106240i
$378$		0			0
$379$	−613.387			−1.61843			−0.809217	−	0.587510i	$-0.800108\pi$
$379$	−613.387			−1.61843			−0.809217	+	0.587510i	$0.800108\pi$
$380$	−508.549	−	606.065i	−1.33829	−	1.59491i
$381$		0			0
$382$	18.0059	−	102.116i	0.0471358	−	0.267320i
$383$	25.0342	+	68.7809i	0.0653635	+	0.179585i	0.968074	−	0.250663i	$-0.0806485\pi$
$383$	25.0342	+	68.7809i	0.0653635	+	0.179585i	−0.902711	+	0.430247i	$0.858426\pi$
$384$		0			0
$385$	46.1073	+	261.487i	0.119759	+	0.679188i
$386$	−1151.61	+	664.883i	−2.98345	+	1.72250i
$387$		0			0
$388$	−770.057	+	1333.78i	−1.98468	+	3.43757i
$389$	−5.85522	+	16.0871i	−0.0150520	+	0.0413550i	−0.946991	−	0.321260i	$-0.895894\pi$
$389$	−5.85522	+	16.0871i	−0.0150520	+	0.0413550i	0.931939	+	0.362615i	$0.118116\pi$
$390$		0			0
$391$	136.637	+	114.652i	0.349456	+	0.293228i
$392$	−369.765	+	440.669i	−0.943279	+	1.12416i
$393$		0			0
$394$	44.2361	+	16.1006i	0.112274	+	0.0408645i
$395$	−635.954	−	367.168i	−1.61001	−	0.929540i
$396$		0			0
$397$	82.5885	+	143.048i	0.208032	+	0.360321i	0.951094	−	0.308900i	$-0.0999610\pi$
$397$	82.5885	+	143.048i	0.208032	+	0.360321i	−0.743063	+	0.669222i	$0.766628\pi$
$398$	263.549	−	46.4708i	0.662183	−	0.116761i
$399$		0			0
$400$	−14.0557	+	5.11585i	−0.0351392	+	0.0127896i
$401$	111.754	+	19.7052i	0.278687	+	0.0491401i	0.311245	−	0.950330i	$-0.399254\pi$
$401$	111.754	+	19.7052i	0.278687	+	0.0491401i	−0.0325576	+	0.999470i	$0.510365\pi$
$402$		0			0
$403$	67.1857	−	56.3755i	0.166714	−	0.139890i
$404$		−	855.514i		−	2.11761i
$405$		0			0
$406$	−133.586			−0.329028
$407$	−434.510	−	517.828i	−1.06759	−	1.27231i
$408$		0			0
$409$	−95.4179	+	541.142i	−0.233296	+	1.32309i	0.612878	+	0.790178i	$0.290012\pi$
$409$	−95.4179	+	541.142i	−0.233296	+	1.32309i	−0.846173	+	0.532908i	$0.821099\pi$
$410$	−39.5392	−	108.633i	−0.0964371	−	0.264959i
$411$		0			0
$412$	−191.638	−	1086.84i	−0.465142	−	2.63795i
$413$	132.135	−	76.2881i	0.319939	−	0.184717i
$414$		0			0
$415$	195.381	−	338.409i	0.470797	−	0.815444i
$416$	−13.1230	+	36.0550i	−0.0315456	+	0.0866707i
$417$		0			0
$418$	821.293	+	689.146i	1.96481	+	1.64868i
$419$	−232.729	+	277.355i	−0.555439	+	0.661946i	−0.968575	−	0.248723i	$-0.919989\pi$
$419$	−232.729	+	277.355i	−0.555439	+	0.661946i	0.413136	+	0.910669i	$0.364434\pi$
$420$		0			0
$421$	−601.388	−	218.887i	−1.42848	−	0.519922i	−0.491981	−	0.870606i	$-0.663727\pi$
$421$	−601.388	−	218.887i	−1.42848	−	0.519922i	−0.936494	+	0.350683i	$0.885949\pi$
$422$	1.23954	+	0.715650i	0.00293731	+	0.00169585i
$423$		0			0
$424$	469.172	+	812.629i	1.10654	+	1.91658i
$425$	−8.29316	+	1.46231i	−0.0195133	+	0.00344073i
$426$		0			0
$427$	15.3659	−	5.59273i	0.0359857	−	0.0130977i
$428$	−177.954	−	31.3781i	−0.415780	−	0.0733133i
$429$		0			0
$430$	−635.196	+	532.993i	−1.47720	+	1.23952i
$431$		−	140.062i		−	0.324969i	−0.986711	−	0.162484i	$-0.948049\pi$
$431$		−	140.062i		−	0.324969i	0.986711	−	0.162484i	$-0.0519507\pi$
$432$		0			0
$433$	28.4373			0.0656750			0.0328375	−	0.999461i	$-0.489546\pi$
$433$	28.4373			0.0656750			0.0328375	+	0.999461i	$0.489546\pi$
$434$	−188.028	−	224.083i	−0.433244	−	0.516320i
$435$		0			0
$436$	217.617	−	1234.17i	0.499122	−	2.83066i
$437$	−101.443	−	278.712i	−0.232135	−	0.637785i
$438$		0			0
$439$	113.332	+	642.738i	0.258160	+	1.46410i	0.787830	+	0.615892i	$0.211204\pi$
$439$	113.332	+	642.738i	0.258160	+	1.46410i	−0.529671	+	0.848203i	$0.677684\pi$
$440$	−1039.87	+	600.369i	−2.36334	+	1.36447i
$441$		0			0
$442$	−72.6319	+	125.802i	−0.164326	+	0.284620i
$443$	−229.610	+	630.847i	−0.518306	+	1.42403i	0.354079	+	0.935216i	$0.384794\pi$
$443$	−229.610	+	630.847i	−0.518306	+	1.42403i	−0.872385	+	0.488819i	$0.837428\pi$
$444$		0			0
$445$	301.994	+	253.403i	0.678638	+	0.569445i
$446$	32.6675	−	38.9316i	0.0732456	−	0.0872907i
$447$		0			0
$448$	−141.356	−	51.4493i	−0.315526	−	0.114842i
$449$	−8.53167	−	4.92576i	−0.0190015	−	0.0109705i	0.490469	−	0.871459i	$-0.336825\pi$
$449$	−8.53167	−	4.92576i	−0.0190015	−	0.0109705i	−0.509471	+	0.860488i	$0.670159\pi$
$450$		0			0
$451$	52.9895	+	91.7805i	0.117493	+	0.203505i
$452$	765.318	−	134.946i	1.69318	−	0.298554i
$453$		0			0
$454$	−1148.73	+	418.103i	−2.53024	+	0.920932i
$455$	58.9140	+	10.3881i	0.129481	+	0.0228311i
$456$		0			0
$457$	590.330	−	495.346i	1.29175	−	1.08391i	0.300242	−	0.953863i	$-0.402933\pi$
$457$	590.330	−	495.346i	1.29175	−	1.08391i	0.991508	−	0.130044i	$-0.0415119\pi$
$458$			344.060i			0.751222i
$459$		0			0
$460$	636.612			1.38394
$461$	281.120	+	335.025i	0.609804	+	0.726736i	0.979282	−	0.202503i	$-0.0649077\pi$
$461$	281.120	+	335.025i	0.609804	+	0.726736i	−0.369477	+	0.929240i	$0.620463\pi$
$462$		0			0
$463$	36.4462	−	206.697i	0.0787176	−	0.446430i	−0.919819	−	0.392344i	$-0.871664\pi$
$463$	36.4462	−	206.697i	0.0787176	−	0.446430i	0.998536	−	0.0540859i	$-0.0172245\pi$
$464$	−78.5164	−	215.722i	−0.169216	−	0.464918i
$465$		0			0
$466$	−42.2646	−	239.694i	−0.0906966	−	0.514366i
$467$	−155.371	+	89.7038i	−0.332701	+	0.192085i	−0.657040	−	0.753856i	$-0.728192\pi$
$467$	−155.371	+	89.7038i	−0.332701	+	0.192085i	0.324338	+	0.945941i	$0.394858\pi$
$468$		0			0
$469$	−20.1776	+	34.9487i	−0.0430227	+	0.0745175i
$470$	−304.150	+	835.645i	−0.647128	+	1.77797i
$471$		0			0
$472$	528.555	+	443.510i	1.11982	+	0.939640i
$473$	488.613	−	582.306i	1.03301	−	1.23109i
$474$		0			0
$475$	13.1586	+	4.78933i	0.0277023	+	0.0100828i
$476$	283.847	+	163.879i	0.596318	+	0.344284i
$477$		0			0
$478$	−543.652	−	941.633i	−1.13735	−	1.96994i
$479$	95.0201	−	16.7546i	0.198372	−	0.0349783i	−0.0735793	−	0.997289i	$-0.523442\pi$
$479$	95.0201	−	16.7546i	0.198372	−	0.0349783i	0.271951	+	0.962311i	$0.412331\pi$
$480$		0			0
$481$	−143.115	+	52.0897i	−0.297537	+	0.108295i
$482$	689.743	+	121.620i	1.43100	+	0.252324i
$483$		0			0
$484$	840.696	−	705.428i	1.73698	−	1.45750i
$485$			907.087i			1.87028i
$486$		0			0
$487$	392.647			0.806257			0.403128	−	0.915143i	$-0.367923\pi$
$487$	392.647			0.806257			0.403128	+	0.915143i	$0.367923\pi$
$488$	47.5323	+	56.6468i	0.0974023	+	0.116080i
$489$		0			0
$490$	−112.752	+	639.451i	−0.230107	+	1.30500i
$491$	142.700	+	392.064i	0.290631	+	0.798501i	0.995975	+	0.0896358i	$0.0285703\pi$
$491$	142.700	+	392.064i	0.290631	+	0.798501i	−0.705344	+	0.708865i	$0.749207\pi$
$492$		0			0
$493$	−22.4430	−	127.281i	−0.0455233	−	0.258176i
$494$	209.191	−	120.776i	0.423463	−	0.244487i
$495$		0			0
$496$	251.347	−	435.346i	0.506748	−	0.877714i
$497$	102.559	−	281.779i	0.206356	−	0.566960i
$498$		0			0
$499$	−624.184	−	523.752i	−1.25087	−	1.04960i	−0.996593	−	0.0824719i	$-0.973719\pi$
$499$	−624.184	−	523.752i	−1.25087	−	1.04960i	−0.254276	−	0.967132i	$-0.581837\pi$
$500$	−681.525	+	812.210i	−1.36305	+	1.62442i
$501$		0			0
$502$	−158.285	−	57.6110i	−0.315309	−	0.114763i
$503$	507.223	+	292.845i	1.00840	+	0.582197i	0.910721	−	0.413021i	$-0.135526\pi$
$503$	507.223	+	292.845i	1.00840	+	0.582197i	0.0976739	+	0.995218i	$0.468860\pi$
$504$		0			0
$505$	−251.938	−	436.369i	−0.498887	−	0.864097i
$506$	−849.582	+	149.804i	−1.67902	+	0.296056i
$507$		0			0
$508$	798.938	−	290.790i	1.57271	−	0.572420i
$509$	−815.289	−	143.757i	−1.60175	−	0.282431i	−0.699819	−	0.714320i	$-0.746736\pi$
$509$	−815.289	−	143.757i	−1.60175	−	0.282431i	−0.901927	+	0.431889i	$0.857847\pi$
$510$		0			0
$511$	−112.169	+	94.1207i	−0.219508	+	0.184189i
$512$		−	1039.05i		−	2.02940i
$513$		0			0
$514$	−1110.56			−2.16062
$515$	−417.807	−	497.923i	−0.811276	−	0.966841i
$516$		0			0
$517$	141.563	−	802.845i	0.273817	−	1.55289i
$518$	173.733	+	477.329i	0.335393	+	0.921484i
$519$		0			0
$520$	46.9771	+	266.420i	0.0903406	+	0.512347i
$521$	568.718	−	328.350i	1.09159	−	0.630230i	0.157590	−	0.987505i	$-0.449627\pi$
$521$	568.718	−	328.350i	1.09159	−	0.630230i	0.933999	+	0.357275i	$0.116294\pi$
$522$		0			0
$523$	−260.887	+	451.869i	−0.498827	+	0.863995i	−0.999999	−	0.00135338i	$-0.999569\pi$
$523$	−260.887	+	451.869i	−0.498827	+	0.863995i	0.501172	+	0.865348i	$0.332903\pi$
$524$	−90.4695	+	248.563i	−0.172652	+	0.474357i
$525$		0			0
$526$	−403.061	−	338.208i	−0.766275	−	0.642981i
$527$	181.917	−	216.800i	0.345194	−	0.411386i
$528$		0			0
$529$	−272.830	−	99.3021i	−0.515747	−	0.187717i
$530$	917.254	+	529.577i	1.73067	+	0.999201i
$531$		0			0
$532$	−272.508	−	471.997i	−0.512232	−	0.887213i
$533$	23.5147	−	4.14628i	0.0441176	−	0.00777913i
$534$		0			0
$535$	−100.009	+	36.4002i	−0.186932	+	0.0680378i
$536$	−179.722	−	31.6898i	−0.335302	−	0.0591228i
$537$		0			0
$538$	−162.604	+	136.441i	−0.302238	+	0.253608i
$539$		−	595.250i		−	1.10436i
$540$		0			0
$541$	−10.3822			−0.0191908			−0.00959538	−	0.999954i	$-0.503054\pi$
$541$	−10.3822			−0.0191908			−0.00959538	+	0.999954i	$0.503054\pi$
$542$	288.208	+	343.473i	0.531749	+	0.633714i
$543$		0			0
$544$	−21.4997	+	121.931i	−0.0395216	+	0.224138i
$545$	−252.447	−	693.593i	−0.463206	−	1.27265i
$546$		0			0
$547$	42.2119	+	239.396i	0.0771698	+	0.437652i	0.998773	+	0.0495188i	$0.0157688\pi$
$547$	42.2119	+	239.396i	0.0771698	+	0.437652i	−0.921603	+	0.388133i	$0.873120\pi$
$548$	201.770	−	116.492i	0.368194	−	0.212577i
$549$		0			0
$550$	20.3647	−	35.2727i	0.0370267	−	0.0641321i
$551$	−73.5050	+	201.953i	−0.133403	+	0.366522i
$552$		0			0
$553$	−387.519	−	325.167i	−0.700757	−	0.588005i
$554$	400.913	−	477.789i	0.723669	−	0.862435i
$555$		0			0
$556$	1545.14	+	562.383i	2.77902	+	1.01148i
$557$	420.452	+	242.748i	0.754851	+	0.435813i	0.827444	−	0.561548i	$-0.189794\pi$
$557$	420.452	+	242.748i	0.754851	+	0.435813i	−0.0725930	+	0.997362i	$0.523127\pi$
$558$		0			0
$559$	−85.6319	−	148.319i	−0.153188	−	0.265329i
$560$	337.675	−	59.5413i	0.602992	−	0.106324i
$561$		0			0
$562$	1675.28	−	609.753i	2.98093	−	1.08497i
$563$	−436.711	−	77.0040i	−0.775686	−	0.136774i	−0.228228	−	0.973608i	$-0.573293\pi$
$563$	−436.711	−	77.0040i	−0.775686	−	0.136774i	−0.547458	+	0.836833i	$0.684404\pi$
$564$		0			0
$565$	350.623	−	294.208i	0.620572	−	0.520722i
$566$		−	321.999i		−	0.568904i
$567$		0			0
$568$	1356.04			2.38739
$569$	−147.724	−	176.051i	−0.259621	−	0.309404i	0.620451	−	0.784246i	$-0.286950\pi$
$569$	−147.724	−	176.051i	−0.259621	−	0.309404i	−0.880071	+	0.474842i	$0.842505\pi$
$570$		0			0
$571$	−51.8524	+	294.069i	−0.0908097	+	0.515008i	0.905141	+	0.425111i	$0.139765\pi$
$571$	−51.8524	+	294.069i	−0.0908097	+	0.515008i	−0.995951	+	0.0898968i	$0.971346\pi$
$572$	−162.560	−	446.629i	−0.284195	−	0.780820i
$573$		0			0
$574$	−13.8290	−	78.4280i	−0.0240923	−	0.136634i
$575$	−9.75807	+	5.63382i	−0.0169706	+	0.00979795i
$576$		0			0
$577$	319.742	−	553.809i	0.554145	−	0.959808i	−0.443824	−	0.896114i	$-0.646379\pi$
$577$	319.742	−	553.809i	0.554145	−	0.959808i	0.997969	−	0.0636938i	$-0.0202881\pi$
$578$	187.246	−	514.454i	0.323955	−	0.890059i
$579$		0			0
$580$	−353.366	−	296.509i	−0.609251	−	0.511223i
$581$	173.031	−	206.210i	0.297815	−	0.354922i
$582$		0			0
$583$	−912.407	−	332.089i	−1.56502	−	0.569621i
$584$	−573.452	−	331.083i	−0.981939	−	0.566923i
$585$		0			0
$586$	841.924	+	1458.25i	1.43673	+	2.48849i
$587$	−629.717	+	111.036i	−1.07277	+	0.189159i	−0.682017	−	0.731336i	$-0.738897\pi$
$587$	−629.717	+	111.036i	−1.07277	+	0.189159i	−0.390754	+	0.920495i	$0.627786\pi$
$588$		0			0
$589$	−442.228	+	160.958i	−0.750812	+	0.273273i
$590$	766.981	+	135.239i	1.29997	+	0.229219i
$591$		0			0
$592$	−668.705	+	561.110i	−1.12957	+	0.947821i
$593$		−	576.408i		−	0.972021i	−0.873953	−	0.486010i	$-0.838452\pi$
$593$		−	576.408i		−	0.972021i	0.873953	−	0.486010i	$-0.161548\pi$
$594$		0			0
$595$	193.041			0.324439
$596$	731.859	+	872.195i	1.22795	+	1.46341i
$597$		0			0
$598$	−33.7514	+	191.414i	−0.0564405	+	0.320090i
$599$	−214.710	−	589.910i	−0.358447	−	0.984824i	−0.979569	−	0.201110i	$-0.935545\pi$
$599$	−214.710	−	589.910i	−0.358447	−	0.984824i	0.621122	−	0.783714i	$-0.286677\pi$
$600$		0			0
$601$	−25.7319	−	145.933i	−0.0428151	−	0.242817i	0.955888	−	0.293732i	$-0.0948973\pi$
$601$	−25.7319	−	145.933i	−0.0428151	−	0.242817i	−0.998703	+	0.0509152i	$0.983786\pi$
$602$	−494.684	+	285.606i	−0.821735	+	0.474429i
$603$		0			0
$604$	619.288	−	1072.64i	1.02531	−	1.77589i
$605$	221.071	−	607.389i	0.365407	−	1.00395i
$606$		0			0
$607$	24.3699	+	20.4488i	0.0401482	+	0.0336883i	0.662641	−	0.748937i	$-0.269436\pi$
$607$	24.3699	+	20.4488i	0.0401482	+	0.0336883i	−0.622493	+	0.782626i	$0.713880\pi$
$608$	132.338	−	157.714i	0.217661	−	0.259399i
$609$		0			0
$610$	78.4340	+	28.5477i	0.128580	+	0.0467994i
$611$	−159.066	−	91.8371i	−0.260338	−	0.150306i
$612$		0			0
$613$	45.0079	+	77.9560i	0.0734223	+	0.127171i	0.900399	−	0.435065i	$-0.143275\pi$
$613$	45.0079	+	77.9560i	0.0734223	+	0.127171i	−0.826977	+	0.562236i	$0.809941\pi$
$614$	−167.285	+	29.4969i	−0.272452	+	0.0480406i
$615$		0			0
$616$	−777.280	+	282.907i	−1.26182	+	0.459264i
$617$	506.773	+	89.3577i	0.821349	+	0.144826i	0.568504	−	0.822681i	$-0.307522\pi$
$617$	506.773	+	89.3577i	0.821349	+	0.144826i	0.252845	+	0.967507i	$0.418634\pi$
$618$		0			0
$619$	−690.684	+	579.553i	−1.11581	+	0.936273i	−0.998385	−	0.0568096i	$-0.981907\pi$
$619$	−690.684	+	579.553i	−1.11581	+	0.936273i	−0.117421	+	0.993082i	$0.537463\pi$
$620$		−	1010.10i		−	1.62920i
$621$		0			0
$622$	−1512.77			−2.43211
$623$	174.564	+	208.038i	0.280200	+	0.333929i
$624$		0			0
$625$	−105.271	+	597.024i	−0.168434	+	0.955238i
$626$	241.979	+	664.831i	0.386547	+	1.06203i
$627$		0			0
$628$	−51.0859	−	289.723i	−0.0813470	−	0.461342i
$629$	−425.612	+	245.727i	−0.676648	+	0.390663i
$630$		0			0
$631$	−79.0534	+	136.925i	−0.125283	+	0.216996i	−0.921843	−	0.387562i	$-0.873317\pi$
$631$	−79.0534	+	136.925i	−0.125283	+	0.216996i	0.796561	+	0.604559i	$0.206650\pi$
$632$	782.419	−	2149.68i	1.23800	−	3.40139i
$633$		0			0
$634$	−49.4848	−	41.5227i	−0.0780518	−	0.0654932i
$635$	321.878	−	383.599i	0.506894	−	0.604092i
$636$		0			0
$637$	−126.024	−	45.8690i	−0.197840	−	0.0720079i
$638$	541.353	+	312.550i	0.848515	+	0.489890i
$639$		0			0
$640$	−489.582	−	847.982i	−0.764972	−	1.32497i
$641$	−758.630	+	133.767i	−1.18351	+	0.208685i	−0.730558	−	0.682850i	$-0.760740\pi$
$641$	−758.630	+	133.767i	−1.18351	+	0.208685i	−0.452952	+	0.891535i	$0.649629\pi$
$642$		0			0
$643$	−220.031	+	80.0846i	−0.342194	+	0.124548i	−0.507400	−	0.861711i	$-0.669393\pi$
$643$	−220.031	+	80.0846i	−0.342194	+	0.124548i	0.165206	+	0.986259i	$0.447171\pi$
$644$	431.887	+	76.1533i	0.670632	+	0.118251i
$645$		0			0
$646$	597.103	−	501.029i	0.924308	−	0.775586i
$647$			1162.87i			1.79733i	0.438638	+	0.898664i	$0.355461\pi$
$647$			1162.87i			1.79733i	−0.438638	+	0.898664i	$0.644539\pi$
$648$		0			0
$649$	−713.965			−1.10010
$650$	−5.89852	−	7.02958i	−0.00907465	−	0.0108147i
$651$		0			0
$652$	−213.729	+	1212.12i	−0.327805	+	1.85908i
$653$	307.012	+	843.509i	0.470157	+	1.29174i	0.917626	+	0.397445i	$0.130103\pi$
$653$	307.012	+	843.509i	0.470157	+	1.29174i	−0.447469	+	0.894299i	$0.647675\pi$
$654$		0			0
$655$	27.0531	+	153.426i	0.0413024	+	0.234238i
$656$	118.522	−	68.4288i	0.180674	−	0.104312i
$657$		0			0
$658$	−306.302	+	530.531i	−0.465505	+	0.806278i
$659$	69.7878	−	191.740i	0.105900	−	0.290957i	−0.875413	−	0.483375i	$-0.839411\pi$
$659$	69.7878	−	191.740i	0.105900	−	0.290957i	0.981313	+	0.192418i	$0.0616330\pi$
$660$		0			0
$661$	−495.984	−	416.180i	−0.750354	−	0.629621i	0.185243	−	0.982693i	$-0.440693\pi$
$661$	−495.984	−	416.180i	−0.750354	−	0.629621i	−0.935596	+	0.353071i	$0.885137\pi$
$662$	−343.637	+	409.531i	−0.519090	+	0.618627i
$663$		0			0
$664$	1143.91	+	416.347i	1.72275	+	0.627029i
$665$	−277.994	−	160.500i	−0.418036	−	0.241353i
$666$		0			0
$667$	−86.4660	−	149.763i	−0.129634	−	0.224533i
$668$	1754.96	−	309.448i	2.62719	−	0.463245i
$669$		0			0
$670$	−193.568	+	70.4528i	−0.288907	+	0.105153i
$671$	−75.3553	−	13.2872i	−0.112303	−	0.0198021i
$672$		0			0
$673$	−340.231	+	285.488i	−0.505544	+	0.424202i	−0.859558	−	0.511039i	$-0.829261\pi$
$673$	−340.231	+	285.488i	−0.505544	+	0.424202i	0.354014	+	0.935240i	$0.384816\pi$
$674$			1686.70i			2.50252i
$675$		0			0
$676$	1306.53			1.93274
$677$	175.642	+	209.321i	0.259441	+	0.309190i	0.880003	−	0.474967i	$-0.157540\pi$
$677$	175.642	+	209.321i	0.259441	+	0.309190i	−0.620562	+	0.784157i	$0.713096\pi$
$678$		0			0
$679$	−108.508	+	615.381i	−0.159806	+	0.906305i
$680$	298.573	+	820.323i	0.439078	+	1.20636i
$681$		0			0
$682$	237.692	+	1348.02i	0.348522	+	1.97657i
$683$	−207.206	+	119.631i	−0.303377	+	0.175155i	−0.643959	−	0.765060i	$-0.722709\pi$
$683$	−207.206	+	119.631i	−0.303377	+	0.175155i	0.340582	+	0.940215i	$0.389376\pi$
$684$		0			0
$685$	68.6108	−	118.837i	0.100162	−	0.173485i
$686$	−352.982	+	969.810i	−0.514551	+	1.41372i
$687$		0			0
$688$	−751.970	−	630.978i	−1.09298	−	0.917119i
$689$	−140.617	+	167.581i	−0.204089	+	0.243224i
$690$		0			0
$691$	872.828	+	317.683i	1.26314	+	0.459744i	0.884821	−	0.465932i	$-0.154281\pi$
$691$	872.828	+	317.683i	1.26314	+	0.459744i	0.378317	+	0.925676i	$0.376503\pi$
$692$	−383.358	−	221.332i	−0.553986	−	0.319844i
$693$		0			0
$694$	719.829	+	1246.78i	1.03722	+	1.79651i
$695$	953.736	−	168.169i	1.37228	−	0.241970i
$696$		0			0
$697$	72.4031	−	26.3526i	0.103878	−	0.0378085i
$698$	370.540	+	65.3362i	0.530859	+	0.0936048i
$699$		0			0
$700$	−15.8608	+	13.3088i	−0.0226583	+	0.0190126i
$701$		−	211.750i		−	0.302068i	−0.988529	−	0.151034i	$-0.951740\pi$
$701$		−	211.750i		−	0.302068i	0.988529	−	0.151034i	$-0.0482604\pi$
$702$		0			0
$703$	817.217			1.16247
$704$	452.465	+	539.227i	0.642707	+	0.765948i
$705$		0			0
$706$	−340.922	+	1933.47i	−0.482893	+	2.73862i
$707$	−118.719	−	326.177i	−0.167919	−	0.461353i
$708$		0			0
$709$	19.4720	+	110.431i	0.0274640	+	0.155756i	0.995456	−	0.0952264i	$-0.0303575\pi$
$709$	19.4720	+	110.431i	0.0274640	+	0.155756i	−0.967992	+	0.250982i	$0.919246\pi$
$710$	1325.56	−	765.313i	1.86699	−	1.07791i
$711$		0			0
$712$	−614.055	+	1063.57i	−0.862436	+	1.49378i
$713$	129.516	−	355.841i	0.181649	−	0.499076i
$714$		0			0
$715$	−214.443	−	179.939i	−0.299920	−	0.251663i
$716$	−303.149	+	361.279i	−0.423392	+	0.504579i
$717$		0			0
$718$	−732.457	−	266.592i	−1.02013	−	0.371299i
$719$	−590.067	−	340.675i	−0.820677	−	0.473818i	0.0299730	−	0.999551i	$-0.490458\pi$
$719$	−590.067	−	340.675i	−0.820677	−	0.473818i	−0.850650	+	0.525733i	$0.823791\pi$
$720$		0			0
$721$	−223.884	−	387.778i	−0.310518	−	0.537833i
$722$	−26.3311	+	4.64288i	−0.0364697	+	0.00643059i
$723$		0			0
$724$	1448.45	−	527.194i	2.00063	−	0.728169i
$725$	8.04045	+	1.41775i	0.0110903	+	0.00195551i
$726$		0			0
$727$	313.891	−	263.386i	0.431763	−	0.362292i	−0.400854	−	0.916142i	$-0.631286\pi$
$727$	313.891	−	263.386i	0.431763	−	0.362292i	0.832616	+	0.553850i	$0.186842\pi$
$728$			186.363i			0.255993i
$729$		0			0
$730$	−747.419			−1.02386
$731$	−355.235	−	423.353i	−0.485958	−	0.579142i
$732$		0			0
$733$	139.744	−	792.528i	0.190647	−	1.08121i	−0.727836	−	0.685751i	$-0.759474\pi$
$733$	139.744	−	792.528i	0.190647	−	1.08121i	0.918483	−	0.395460i	$-0.129415\pi$
$734$	−206.899	−	568.450i	−0.281879	−	0.774455i
$735$		0			0
$736$	28.7672	+	163.147i	0.0390859	+	0.221667i
$737$	163.539	−	94.4192i	0.221898	−	0.128113i
$738$		0			0
$739$	−13.7790	+	23.8659i	−0.0186455	+	0.0322949i	−0.875198	−	0.483766i	$-0.839269\pi$
$739$	−13.7790	+	23.8659i	−0.0186455	+	0.0322949i	0.856552	+	0.516061i	$0.172602\pi$
$740$	−599.922	+	1648.27i	−0.810705	+	2.22739i
$741$		0			0
$742$	558.929	+	468.997i	0.753273	+	0.632072i
$743$	168.116	−	200.353i	0.226266	−	0.269654i	−0.640953	−	0.767580i	$-0.721461\pi$
$743$	168.116	−	200.353i	0.226266	−	0.269654i	0.867219	+	0.497927i	$0.165905\pi$
$744$		0			0
$745$	630.147	+	229.355i	0.845834	+	0.307859i
$746$	−380.742	−	219.822i	−0.510378	−	0.294667i
$747$		0			0
$748$	−766.857	−	1328.23i	−1.02521	−	1.77571i
$749$	−72.2017	+	12.7311i	−0.0963975	+	0.0169975i
$750$		0			0
$751$	611.773	−	222.667i	0.814611	−	0.296494i	0.0990841	−	0.995079i	$-0.468409\pi$
$751$	611.773	−	222.667i	0.814611	−	0.296494i	0.715527	+	0.698585i	$0.246187\pi$
$752$	−1036.76	−	182.810i	−1.37868	−	0.243098i
$753$		0			0
$754$	107.888	−	90.5285i	0.143087	−	0.120064i
$755$		−	729.489i		−	0.966210i
$756$		0			0
$757$	636.818			0.841240			0.420620	−	0.907237i	$-0.361813\pi$
$757$	636.818			0.841240			0.420620	+	0.907237i	$0.361813\pi$
$758$	−1386.41	−	1652.26i	−1.82904	−	2.17976i
$759$		0			0
$760$	252.072	−	1429.57i	0.331673	−	1.88101i
$761$	−302.174	−	830.215i	−0.397074	−	1.09095i	−0.963702	−	0.266979i	$-0.913975\pi$
$761$	−302.174	−	830.215i	−0.397074	−	1.09095i	0.566628	−	0.823974i	$-0.308248\pi$
$762$		0			0
$763$	−88.2944	−	500.742i	−0.115720	−	0.656281i
$764$	213.614	−	123.330i	0.279599	−	0.161427i
$765$		0			0
$766$	−128.689	+	222.896i	−0.168002	+	0.290987i
$767$	−55.0170	+	151.158i	−0.0717301	+	0.197077i
$768$		0			0
$769$	416.564	+	349.539i	0.541696	+	0.454537i	0.872117	−	0.489297i	$-0.162746\pi$
$769$	416.564	+	349.539i	0.541696	+	0.454537i	−0.330422	+	0.943833i	$0.607191\pi$
$770$	−600.145	+	715.225i	−0.779410	+	0.928864i
$771$		0			0
$772$	−2972.46	−	1081.89i	−3.85034	−	1.40141i
$773$	−1004.48	−	579.936i	−1.29945	−	0.750241i	−0.319145	−	0.947706i	$-0.603396\pi$
$773$	−1004.48	−	579.936i	−1.29945	−	0.750241i	−0.980310	+	0.197465i	$0.936729\pi$
$774$		0			0
$775$	8.93911	+	15.4830i	0.0115343	+	0.0199780i
$776$	−2782.87	+	490.695i	−3.58617	+	0.632339i
$777$		0			0
$778$	−56.5675	+	20.5889i	−0.0727089	+	0.0264639i
$779$	−126.176	−	22.2482i	−0.161972	−	0.0285600i
$780$		0			0
$781$	−1074.90	+	901.945i	−1.37631	+	1.15486i
$782$			627.199i			0.802044i
$783$		0			0
$784$	−768.685			−0.980466
$785$	−111.377	−	132.734i	−0.141881	−	0.169087i
$786$		0			0
$787$	29.3521	−	166.464i	0.0372961	−	0.211517i	−0.960465	−	0.278402i	$-0.910195\pi$
$787$	29.3521	−	166.464i	0.0372961	−	0.211517i	0.997761	+	0.0668855i	$0.0213062\pi$
$788$	38.2999	+	105.228i	0.0486039	+	0.133538i
$789$		0			0
$790$	−448.389	−	2542.94i	−0.567581	−	3.21891i
$791$	273.062	−	157.652i	0.345211	−	0.199308i
$792$		0			0
$793$	−8.61987	+	14.9300i	−0.0108699	+	0.0188273i
$794$	−198.651	+	545.790i	−0.250191	+	0.687393i
$795$		0			0
$796$	487.662	+	409.197i	0.612640	+	0.514066i
$797$	4.74959	−	5.66034i	0.00595933	−	0.00710205i	−0.763057	−	0.646332i	$-0.776302\pi$
$797$	4.74959	−	5.66034i	0.00595933	−	0.00710205i	0.769016	+	0.639230i	$0.220747\pi$
$798$		0			0
$799$	−556.951	−	202.714i	−0.697060	−	0.253709i
$800$	−6.77348	−	3.91067i	−0.00846685	−	0.00488834i
$801$		0			0
$802$	199.512	+	345.565i	0.248768	+	0.430880i
$803$	674.775	−	118.981i	0.840318	−	0.148171i
$804$		0			0
$805$	242.717	−	88.3418i	0.301512	−	0.109741i
$806$	303.714	+	53.5529i	0.376816	+	0.0664428i
$807$		0			0
$808$	1202.46	−	1008.98i	1.48819	−	1.24874i
$809$		−	1006.43i		−	1.24404i	−0.783001	−	0.622021i	$-0.786312\pi$
$809$		−	1006.43i		−	1.24404i	0.783001	−	0.622021i	$-0.213688\pi$
$810$		0			0
$811$	662.217			0.816543			0.408272	−	0.912861i	$-0.366132\pi$
$811$	662.217			0.816543			0.408272	+	0.912861i	$0.366132\pi$
$812$	−204.259	−	243.427i	−0.251551	−	0.299787i
$813$		0			0
$814$	412.755	−	2340.85i	0.507070	−	2.87573i
$815$	247.937	+	681.201i	0.304217	+	0.835829i
$816$		0			0
$817$	159.578	+	905.013i	0.195322	+	1.10773i
$818$	−1673.32	+	966.095i	−2.04563	+	1.18104i
$819$		0			0
$820$	137.499	−	238.156i	0.167682	−	0.290434i
$821$	−238.954	+	656.520i	−0.291052	+	0.799659i	0.704861	+	0.709345i	$0.251009\pi$
$821$	−238.954	+	656.520i	−0.291052	+	0.799659i	−0.995913	+	0.0903136i	$0.971213\pi$
$822$		0			0
$823$	−365.555	−	306.737i	−0.444174	−	0.372707i	0.393094	−	0.919498i	$-0.371405\pi$
$823$	−365.555	−	306.737i	−0.444174	−	0.372707i	−0.837269	+	0.546792i	$0.815849\pi$
$824$	1301.57	−	1551.15i	1.57958	−	1.88247i
$825$		0			0
$826$	504.153	+	183.497i	0.610355	+	0.222151i
$827$	1393.63	+	804.614i	1.68517	+	0.972931i	0.958131	+	0.286330i	$0.0924355\pi$
$827$	1393.63	+	804.614i	1.68517	+	0.972931i	0.727035	+	0.686601i	$0.240898\pi$
$828$		0			0
$829$	712.510	+	1234.10i	0.859481	+	1.48867i	0.872424	+	0.488749i	$0.162547\pi$
$829$	712.510	+	1234.10i	0.859481	+	1.48867i	−0.0129428	+	0.999916i	$0.504120\pi$
$830$	1353.17	−	238.601i	1.63033	−	0.287471i
$831$		0			0
$832$	149.029	−	54.2422i	0.179122	−	0.0651950i
$833$	−426.189	−	75.1486i	−0.511631	−	0.0902144i
$834$		0			0
$835$	804.020	−	674.653i	0.962898	−	0.807967i
$836$			2550.34i			3.05065i
$837$		0			0
$838$	−1273.13			−1.51925
$839$	−387.049	−	461.267i	−0.461322	−	0.549782i	0.484363	−	0.874867i	$-0.339052\pi$
$839$	−387.049	−	461.267i	−0.461322	−	0.549782i	−0.945685	+	0.325085i	$0.894607\pi$
$840$		0			0
$841$	124.279	−	704.821i	0.147775	−	0.838075i
$842$	−769.681	−	2114.68i	−0.914110	−	2.51150i
$843$		0			0
$844$	0.591229	+	3.35303i	0.000700509	+	0.00397278i
$845$	666.417	−	384.756i	0.788659	−	0.455333i
$846$		0			0
$847$	222.636	−	385.616i	0.262852	−	0.455273i
$848$	−428.848	+	1178.25i	−0.505717	+	1.38945i
$849$		0			0
$850$	−22.6836	−	19.0338i	−0.0266866	−	0.0223927i
$851$	−422.683	+	503.734i	−0.496690	+	0.591932i
$852$		0			0
$853$	1312.02	+	477.538i	1.53813	+	0.559833i	0.965596	−	0.260048i	$-0.0837383\pi$
$853$	1312.02	+	477.538i	1.53813	+	0.559833i	0.572534	+	0.819881i	$0.305961\pi$
$854$	49.7958	+	28.7496i	0.0583089	+	0.0336647i
$855$		0			0
$856$	−165.773	−	287.128i	−0.193661	−	0.335430i
$857$	−830.529	+	146.445i	−0.969112	+	0.170881i	−0.635730	−	0.771911i	$-0.719301\pi$
$857$	−830.529	+	146.445i	−0.969112	+	0.170881i	−0.333382	+	0.942792i	$0.608190\pi$
$858$		0			0
$859$	623.731	−	227.020i	0.726113	−	0.264284i	0.0475944	−	0.998867i	$-0.484845\pi$
$859$	623.731	−	227.020i	0.726113	−	0.264284i	0.678519	+	0.734583i	$0.262622\pi$
$860$	−1942.50	−	342.514i	−2.25872	−	0.398273i
$861$		0			0
$862$	377.279	−	316.575i	0.437679	−	0.367256i
$863$		−	437.898i		−	0.507414i	−0.967281	−	0.253707i	$-0.918350\pi$
$863$		−	437.898i		−	0.507414i	0.967281	−	0.253707i	$-0.0816499\pi$
$864$		0			0
$865$	−260.717			−0.301408
$866$	64.2755	+	76.6006i	0.0742211	+	0.0884533i
$867$		0			0
$868$	120.831	−	685.269i	0.139207	−	0.789480i
$869$	809.619	+	2224.41i	0.931667	+	2.55973i
$870$		0			0
$871$	−7.38803	−	41.8996i	−0.00848224	−	0.0481052i
$872$	1991.33	−	1149.69i	2.28363	−	1.31845i
$873$		0			0
$874$	521.470	−	903.213i	0.596648	−	1.03342i
$875$	−147.131	+	404.240i	−0.168150	+	0.461989i
$876$		0			0
$877$	1135.52	+	952.812i	1.29477	+	1.08644i	0.991023	+	0.133693i	$0.0426837\pi$
$877$	1135.52	+	952.812i	1.29477	+	1.08644i	0.303751	+	0.952751i	$0.401761\pi$
$878$	−1475.16	+	1758.03i	−1.68014	+	2.00231i
$879$		0			0
$880$	−1507.73	−	548.769i	−1.71333	−	0.623601i
$881$	311.715	+	179.969i	0.353820	+	0.204278i	0.666366	−	0.745625i	$-0.267849\pi$
$881$	311.715	+	179.969i	0.353820	+	0.204278i	−0.312547	+	0.949902i	$0.601182\pi$
$882$		0			0
$883$	−262.307	−	454.329i	−0.297064	−	0.514529i	0.678399	−	0.734693i	$-0.262674\pi$
$883$	−262.307	−	454.329i	−0.297064	−	0.514529i	−0.975463	+	0.220164i	$0.929341\pi$
$884$	−340.301	+	60.0043i	−0.384956	+	0.0678782i
$885$		0			0
$886$	−2218.27	+	807.384i	−2.50369	+	0.911268i
$887$	−1189.72	−	209.780i	−1.34129	−	0.236505i	−0.543483	−	0.839420i	$-0.682895\pi$
$887$	−1189.72	−	209.780i	−1.34129	−	0.236505i	−0.797806	+	0.602915i	$0.794006\pi$
$888$		0			0
$889$	264.254	−	221.735i	0.297248	−	0.249421i
$890$			1386.23i			1.55756i
$891$		0			0
$892$	120.894			0.135531
$893$	633.509	+	754.987i	0.709417	+	0.845450i
$894$		0			0
$895$	−48.2342	+	273.550i	−0.0538929	+	0.305642i
$896$	−230.702	−	633.848i	−0.257480	−	0.707420i
$897$		0			0
$898$	−6.01538	−	34.1149i	−0.00669865	−	0.0379899i
$899$	−237.628	+	137.194i	−0.264324	+	0.152608i
$900$		0			0
$901$	−352.959	+	611.342i	−0.391741	+	0.678515i
$902$	−127.456	+	350.183i	−0.141304	+	0.388230i
$903$		0			0
$904$	1092.28	+	916.530i	1.20827	+	1.01386i
$905$	583.556	−	695.455i	0.644813	−	0.768459i
$906$		0			0
$907$	1321.09	+	480.839i	1.45655	+	0.530142i	0.944414	−	0.328759i	$-0.106630\pi$
$907$	1321.09	+	480.839i	1.45655	+	0.530142i	0.512141	+	0.858902i	$0.328853\pi$
$908$	−2518.36	−	1453.97i	−2.77352	−	1.60129i
$909$		0			0
$910$	105.179	+	182.175i	0.115581	+	0.200192i
$911$	1531.52	−	270.048i	1.68114	−	0.296430i	0.750093	−	0.661332i	$-0.230009\pi$
$911$	1531.52	−	270.048i	1.68114	−	0.296430i	0.931046	+	0.364902i	$0.118897\pi$
$912$		0			0
$913$	−1183.67	+	430.821i	−1.29646	+	0.471874i
$914$	2668.59	+	470.545i	2.91968	+	0.514819i
$915$		0			0
$916$	−626.964	+	526.085i	−0.684458	+	0.574329i
$917$			107.322i			0.117036i
$918$		0			0
$919$	−1361.80			−1.48183			−0.740916	−	0.671597i	$-0.765609\pi$
$919$	−1361.80			−1.48183			−0.740916	+	0.671597i	$0.765609\pi$
$920$	750.812	+	894.783i	0.816100	+	0.972590i
$921$		0			0
$922$	−267.045	+	1514.49i	−0.289636	+	1.64261i
$923$	108.127	+	297.075i	0.117147	+	0.321858i
$924$		0			0
$925$	−5.39102	−	30.5740i	−0.00582813	−	0.0330530i
$926$	639.150	−	369.014i	0.690227	−	0.398503i
$927$		0			0
$928$	60.0196	−	103.957i	0.0646763	−	0.112023i
$929$	530.745	−	1458.21i	0.571308	−	1.56966i	−0.231131	−	0.972923i	$-0.574243\pi$
$929$	530.745	−	1458.21i	0.571308	−	1.56966i	0.802440	−	0.596733i	$-0.203535\pi$
$930$		0			0
$931$	551.263	+	462.565i	0.592120	+	0.496847i
$932$	372.159	−	443.522i	0.399312	−	0.475882i
$933$		0			0
$934$	−592.811	−	215.766i	−0.634701	−	0.231012i
$935$	−782.296	−	451.659i	−0.836680	−	0.483057i
$936$		0			0
$937$	109.572	+	189.785i	0.116939	+	0.202545i	0.918553	−	0.395297i	$-0.129358\pi$
$937$	109.572	+	189.785i	0.116939	+	0.202545i	−0.801614	+	0.597842i	$0.796025\pi$
$938$	−139.747	+	24.6411i	−0.148984	+	0.0262699i
$939$		0			0
$940$	−1987.82	+	723.507i	−2.11470	+	0.769688i
$941$	−92.2315	−	16.2629i	−0.0980144	−	0.0172826i	0.124426	−	0.992229i	$-0.460291\pi$
$941$	−92.2315	−	16.2629i	−0.0980144	−	0.0172826i	−0.222440	+	0.974946i	$0.571402\pi$
$942$		0			0
$943$	78.9750	−	66.2679i	0.0837487	−	0.0702735i
$944$			921.989i			0.976683i
$945$		0			0
$946$	2672.93			2.82551
$947$	321.631	+	383.305i	0.339632	+	0.404757i	0.908644	−	0.417572i	$-0.137119\pi$
$947$	321.631	+	383.305i	0.339632	+	0.404757i	−0.569012	+	0.822329i	$0.692674\pi$
$948$		0			0
$949$	26.8069	−	152.029i	0.0282475	−	0.160199i
$950$	16.8409	+	46.2699i	0.0177272	+	0.0487052i
$951$		0			0
$952$	104.427	+	592.235i	0.109692	+	0.622096i
$953$	−1162.81	+	671.350i	−1.22016	+	0.704459i	−0.964952	−	0.262427i	$-0.915477\pi$
$953$	−1162.81	+	671.350i	−1.22016	+	0.704459i	−0.255208	+	0.966886i	$0.582144\pi$
$954$		0			0
$955$	72.6381	−	125.813i	0.0760609	−	0.131741i
$956$	884.621	−	2430.48i	0.925336	−	2.54234i
$957$		0			0
$958$	259.901	+	218.083i	0.271295	+	0.227644i
$959$	60.7622	−	72.4136i	0.0633600	−	0.0755095i
$960$		0			0
$961$	338.436	+	123.181i	0.352171	+	0.128180i
$962$	−463.789	−	267.769i	−0.482109	−	0.278346i
$963$		0			0
$964$	833.030	+	1442.85i	0.864139	+	1.49673i
$965$	−1834.75	+	323.517i	−1.90130	+	0.335250i
$966$		0			0
$967$	−674.832	+	245.619i	−0.697861	+	0.254001i	−0.666497	−	0.745507i	$-0.732207\pi$
$967$	−674.832	+	245.619i	−0.697861	+	0.254001i	−0.0313638	+	0.999508i	$0.509985\pi$
$968$	1983.01	+	349.658i	2.04856	+	0.361217i
$969$		0			0
$970$	−2443.39	+	2050.25i	−2.51896	+	2.11366i
$971$			1118.48i			1.15189i	0.817489	+	0.575944i	$0.195365\pi$
$971$			1118.48i			1.15189i	−0.817489	+	0.575944i	$0.804635\pi$
$972$		0			0
$973$	667.145			0.685658
$974$	887.482	+	1057.66i	0.911173	+	1.08589i
$975$		0			0
$976$	−17.1586	+	97.3112i	−0.0175805	+	0.0997041i
$977$	220.157	+	604.877i	0.225340	+	0.619117i	0.999911	−	0.0133707i	$-0.00425616\pi$
$977$	220.157	+	604.877i	0.225340	+	0.619117i	−0.774571	+	0.632488i	$0.782034\pi$
$978$		0			0
$979$	−220.673	−	1251.50i	−0.225406	−	1.27834i
$980$	−1337.65	+	772.290i	−1.36494	+	0.788051i
$981$		0			0
$982$	−733.552	+	1270.55i	−0.746998	+	1.29384i
$983$	118.541	−	325.687i	0.120591	−	0.331320i	−0.864680	−	0.502323i	$-0.832479\pi$
$983$	118.541	−	325.687i	0.120591	−	0.331320i	0.985270	+	0.171004i	$0.0547009\pi$
$984$		0			0
$985$	50.5238	+	42.3945i	0.0512932	+	0.0430401i
$986$	292.125	−	348.141i	0.296272	−	0.353084i
$987$		0			0
$988$	539.949	+	196.525i	0.546507	+	0.198912i
$989$	−640.389	−	369.729i	−0.647512	−	0.373841i
$990$		0			0
$991$	−204.099	−	353.510i	−0.205953	−	0.356720i	0.744483	−	0.667641i	$-0.232696\pi$
$991$	−204.099	−	353.510i	−0.205953	−	0.356720i	−0.950436	+	0.310921i	$0.899363\pi$
$992$	258.863	−	45.6445i	0.260951	−	0.0460126i
$993$		0			0
$994$	990.828	−	360.632i	0.996809	−	0.362809i
$995$	369.243	+	65.1075i	0.371098	+	0.0654346i
$996$		0			0
$997$	−670.506	+	562.621i	−0.672523	+	0.564314i	−0.913811	−	0.406140i	$-0.866875\pi$
$997$	−670.506	+	562.621i	−0.672523	+	0.564314i	0.241288	+	0.970454i	$0.422430\pi$
$998$		−	2865.16i		−	2.87090i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	243.3.f.d.134.5		30
3.2	odd	2		243.3.f.a.134.1		30
9.2	odd	6		243.3.f.b.53.1		30
9.4	even	3		27.3.f.a.14.1	yes	30
9.5	odd	6		81.3.f.a.71.5		30
9.7	even	3		243.3.f.c.53.5		30
27.2	odd	18		243.3.f.c.188.5		30
27.4	even	9		729.3.b.a.728.29		30
27.7	even	9		81.3.f.a.8.5		30
27.11	odd	18	inner	243.3.f.d.107.5		30
27.16	even	9		243.3.f.a.107.1		30
27.20	odd	18		27.3.f.a.2.1	✓	30
27.23	odd	18		729.3.b.a.728.2		30
27.25	even	9		243.3.f.b.188.1		30
36.31	odd	6		432.3.bc.a.257.2		30
108.47	even	18		432.3.bc.a.353.2		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.f.a.2.1	✓	30	27.20	odd	18
27.3.f.a.14.1	yes	30	9.4	even	3
81.3.f.a.8.5		30	27.7	even	9
81.3.f.a.71.5		30	9.5	odd	6
243.3.f.a.107.1		30	27.16	even	9
243.3.f.a.134.1		30	3.2	odd	2
243.3.f.b.53.1		30	9.2	odd	6
243.3.f.b.188.1		30	27.25	even	9
243.3.f.c.53.5		30	9.7	even	3
243.3.f.c.188.5		30	27.2	odd	18
243.3.f.d.107.5		30	27.11	odd	18	inner
243.3.f.d.134.5		30	1.1	even	1	trivial
432.3.bc.a.257.2		30	36.31	odd	6
432.3.bc.a.353.2		30	108.47	even	18
729.3.b.a.728.2		30	27.23	odd	18
729.3.b.a.728.29		30	27.4	even	9

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 243 = 3^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	243.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.26025 + 2.69367i) q^{2} +(-1.45250 + 8.23751i) q^{4} +(1.68497 + 4.62942i) q^{5} +(0.589325 + 3.34223i) q^{7} +(-13.2912 + 7.67367i) q^{8} +O(q^{10})\)	\(q+(2.26025 + 2.69367i) q^{2} +(-1.45250 + 8.23751i) q^{4} +(1.68497 + 4.62942i) q^{5} +(0.589325 + 3.34223i) q^{7} +(-13.2912 + 7.67367i) q^{8} +(-8.66165 + 15.0024i) q^{10} +(5.43158 - 14.9231i) q^{11} +(-2.74092 - 2.29990i) q^{13} +(-7.67082 + 9.14172i) q^{14} +(-19.2712 - 7.01415i) q^{16} +(-9.99899 - 5.77292i) q^{17} +(9.59953 + 16.6269i) q^{19} +(-40.5823 + 7.15575i) q^{20} +(52.4747 - 19.0992i) q^{22} +(-15.2139 - 2.68263i) q^{23} +(0.558724 - 0.468825i) q^{25} -12.5815i q^{26} -28.3876 q^{28} +(7.19537 + 8.57510i) q^{29} +(-4.25648 + 24.1397i) q^{31} +(-3.66766 - 10.0768i) q^{32} +(-7.04994 - 39.9822i) q^{34} +(-14.4796 + 8.35978i) q^{35} +(21.2827 - 36.8628i) q^{37} +(-23.0899 + 63.4389i) q^{38} +(-57.9199 - 48.6006i) q^{40} +(-4.28956 + 5.11210i) q^{41} +(44.9789 + 16.3710i) q^{43} +(115.040 + 66.4185i) q^{44} +(-27.1612 - 47.0447i) q^{46} +(50.5542 - 8.91407i) q^{47} +(35.2218 - 12.8197i) q^{49} +(2.52572 + 0.445352i) q^{50} +(22.9267 - 19.2378i) q^{52} -61.1404i q^{53} +78.2375 q^{55} +(-33.4800 - 39.8999i) q^{56} +(-6.83511 + 38.7638i) q^{58} +(-15.3764 - 42.2463i) q^{59} +(-0.836678 - 4.74504i) q^{61} +(-74.6451 + 43.0964i) q^{62} +(-22.1622 + 38.3861i) q^{64} +(6.02885 - 16.5641i) q^{65} +(9.10899 + 7.64335i) q^{67} +(62.0780 - 73.9816i) q^{68} +(-55.2460 - 20.1079i) q^{70} +(-76.5190 - 44.1783i) q^{71} +(21.5726 + 37.3649i) q^{73} +(147.400 - 25.9907i) q^{74} +(-150.907 + 54.9258i) q^{76} +(53.0774 + 9.35899i) q^{77} +(-114.185 + 95.8125i) q^{79} -101.033i q^{80} -23.4658 q^{82} +(-50.9846 - 60.7610i) q^{83} +(9.87725 - 56.0167i) q^{85} +(57.5658 + 158.161i) q^{86} +(42.3231 + 240.026i) q^{88} +(69.3002 - 40.0105i) q^{89} +(6.07151 - 10.5162i) q^{91} +(44.1963 - 121.428i) q^{92} +(138.277 + 116.028i) q^{94} +(-60.7978 + 72.4560i) q^{95} +(173.019 + 62.9738i) q^{97} +(114.142 + 65.9000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8	\( 30 q + 3 q^{2} + 3 q^{4} + 21 q^{5} + 3 q^{7} - 9 q^{8} - 3 q^{10} + 57 q^{11} + 3 q^{13} - 114 q^{14} + 27 q^{16} - 9 q^{17} - 3 q^{19} - 183 q^{20} + 75 q^{22} + 48 q^{23} + 21 q^{25} - 12 q^{28} - 78 q^{29} - 87 q^{31} + 243 q^{32} - 153 q^{34} - 252 q^{35} - 3 q^{37} + 321 q^{38} - 168 q^{40} - 357 q^{41} - 87 q^{43} + 639 q^{44} - 3 q^{46} - 51 q^{47} - 69 q^{49} + 168 q^{50} - 36 q^{52} - 12 q^{55} - 177 q^{56} + 138 q^{58} + 48 q^{59} + 147 q^{61} - 900 q^{62} - 51 q^{64} + 624 q^{65} + 12 q^{67} - 477 q^{68} - 6 q^{70} + 315 q^{71} - 66 q^{73} - 480 q^{74} - 57 q^{76} + 453 q^{77} - 15 q^{79} - 12 q^{82} - 591 q^{83} + 243 q^{85} + 669 q^{86} + 591 q^{88} + 72 q^{89} + 96 q^{91} + 564 q^{92} + 957 q^{94} - 606 q^{95} + 696 q^{97} + 882 q^{98}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^4 + 21 * q^5 + 3 * q^7 - 9 * q^8 - 3 * q^10 + 57 * q^11 + 3 * q^13 - 114 * q^14 + 27 * q^16 - 9 * q^17 - 3 * q^19 - 183 * q^20 + 75 * q^22 + 48 * q^23 + 21 * q^25 - 12 * q^28 - 78 * q^29 - 87 * q^31 + 243 * q^32 - 153 * q^34 - 252 * q^35 - 3 * q^37 + 321 * q^38 - 168 * q^40 - 357 * q^41 - 87 * q^43 + 639 * q^44 - 3 * q^46 - 51 * q^47 - 69 * q^49 + 168 * q^50 - 36 * q^52 - 12 * q^55 - 177 * q^56 + 138 * q^58 + 48 * q^59 + 147 * q^61 - 900 * q^62 - 51 * q^64 + 624 * q^65 + 12 * q^67 - 477 * q^68 - 6 * q^70 + 315 * q^71 - 66 * q^73 - 480 * q^74 - 57 * q^76 + 453 * q^77 - 15 * q^79 - 12 * q^82 - 591 * q^83 + 243 * q^85 + 669 * q^86 + 591 * q^88 + 72 * q^89 + 96 * q^91 + 564 * q^92 + 957 * q^94 - 606 * q^95 + 696 * q^97 + 882 * q^98

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