LMFDB - Embedded newform 243.2.e.c.55.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [243,2,Mod(28,243)]

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([8]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("243.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 243 = 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	243.e (of order $9$, 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:	$1.94036476912$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Root			$0.500000 + 2.22827i$ of defining polynomial
Character	$\chi$	$=$	243.55
Dual form			243.2.e.c.190.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +O(q^{10})$	\(q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-2.83955 - 4.91825i) q^{10} +(-0.0550295 + 0.312088i) q^{11} +(1.42272 + 0.517829i) q^{13} +(1.93395 + 0.703898i) q^{14} +(-0.487835 + 2.76665i) q^{16} +(-0.587342 - 1.01731i) q^{17} +(-3.11040 + 5.38737i) q^{19} +(-5.09751 - 4.27732i) q^{20} +(0.116477 + 0.660572i) q^{22} +(1.65676 - 1.39018i) q^{23} +(-2.06640 + 0.752107i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(4.13926 - 1.50657i) q^{29} +(-6.64408 + 5.57504i) q^{31} +(1.38548 + 7.85742i) q^{32} +(-1.90466 - 1.59820i) q^{34} +(1.30443 - 2.25934i) q^{35} +(2.23332 + 3.86823i) q^{37} +(-2.28644 + 12.9671i) q^{38} +(-2.56206 - 0.932515i) q^{40} +(-5.49268 - 1.99917i) q^{41} +(0.970865 - 5.50605i) q^{43} +(0.392973 + 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(-1.89678 - 1.59159i) q^{47} +(-1.05136 - 5.96259i) q^{49} +(-3.56554 + 2.99184i) q^{50} +(3.52848 - 1.28426i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.928471 - 0.337936i) q^{56} +(7.14224 - 5.99305i) q^{58} +(-0.299406 - 1.69802i) q^{59} +(0.777365 + 0.652287i) q^{61} +(-9.17898 + 15.8985i) q^{62} +(5.63455 + 9.75933i) q^{64} +(0.705410 - 4.00058i) q^{65} +(-0.804895 - 0.292958i) q^{67} +(-2.73763 - 0.996416i) q^{68} +(0.958882 - 5.43809i) q^{70} +(4.79788 + 8.31018i) q^{71} +(7.62091 - 13.1998i) q^{73} +(7.24234 + 6.07705i) q^{74} +(2.67907 + 15.1938i) q^{76} +(-0.236045 + 0.198065i) q^{77} +(10.5375 - 3.83533i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-4.40239 + 1.60234i) q^{83} +(-2.41441 + 2.02593i) q^{85} +(-2.05496 - 11.6542i) q^{86} +(0.246687 + 0.206995i) q^{88} +(7.74976 - 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(0.931414 - 5.28231i) q^{92} +(-4.92484 - 1.79249i) q^{94} +(15.6844 + 5.70867i) q^{95} +(-0.963658 + 5.46518i) q^{97} +(-6.40762 - 11.0983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8	$ 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 3 q^{13} + 6 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} - 21 q^{20} - 15 q^{22} + 24 q^{23} - 15 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 15 q^{31} - 27 q^{32} - 9 q^{34} + 12 q^{35} - 3 q^{37} - 12 q^{38} - 6 q^{40} - 21 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{46} + 3 q^{47} + 21 q^{49} + 12 q^{50} + 36 q^{52} - 18 q^{53} - 12 q^{55} + 3 q^{56} + 30 q^{58} + 15 q^{59} + 21 q^{61} - 12 q^{62} + 12 q^{64} - 24 q^{65} + 21 q^{67} - 18 q^{68} + 30 q^{70} + 27 q^{71} + 6 q^{73} - 12 q^{74} + 42 q^{76} - 3 q^{77} + 21 q^{79} + 42 q^{80} - 12 q^{82} - 33 q^{83} - 9 q^{85} - 30 q^{86} - 12 q^{88} + 9 q^{89} + 6 q^{91} + 42 q^{92} - 33 q^{94} + 30 q^{95} - 42 q^{97} - 45 q^{98}+O(q^{100}) $ 12 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 3 * q^13 + 6 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 - 21 * q^20 - 15 * q^22 + 24 * q^23 - 15 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 15 * q^31 - 27 * q^32 - 9 * q^34 + 12 * q^35 - 3 * q^37 - 12 * q^38 - 6 * q^40 - 21 * q^41 + 12 * q^43 + 3 * q^44 - 3 * q^46 + 3 * q^47 + 21 * q^49 + 12 * q^50 + 36 * q^52 - 18 * q^53 - 12 * q^55 + 3 * q^56 + 30 * q^58 + 15 * q^59 + 21 * q^61 - 12 * q^62 + 12 * q^64 - 24 * q^65 + 21 * q^67 - 18 * q^68 + 30 * q^70 + 27 * q^71 + 6 * q^73 - 12 * q^74 + 42 * q^76 - 3 * q^77 + 21 * q^79 + 42 * q^80 - 12 * q^82 - 33 * q^83 - 9 * q^85 - 30 * q^86 - 12 * q^88 + 9 * q^89 + 6 * q^91 + 42 * q^92 - 33 * q^94 + 30 * q^95 - 42 * q^97 - 45 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

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 $

$2$	1.98897	−	0.723928i	1.40642	−	0.511894i	0.476341	−	0.879261i	$-0.341963\pi$
$2$	1.98897	−	0.723928i	1.40642	−	0.511894i	0.930076	+	0.367366i	$0.119740\pi$
$3$		0			0
$3$		0			0
$4$	1.89986	−	1.59417i	0.949930	−	0.797086i
$5$	−0.465915	−	2.64234i	−0.208364	−	1.18169i	−0.892058	−	0.451920i	$-0.850739\pi$
$5$	−0.465915	−	2.64234i	−0.208364	−	1.18169i	0.683695	−	0.729768i	$-0.260372\pi$
$6$		0			0
$7$	0.744850	+	0.625003i	0.281527	+	0.236229i	0.772606	−	0.634886i	$-0.218953\pi$
$7$	0.744850	+	0.625003i	0.281527	+	0.236229i	−0.491079	+	0.871115i	$0.663397\pi$
$8$	0.508086	−	0.880031i	0.179636	−	0.311138i
$9$		0			0
$10$	−2.83955	−	4.91825i	−0.897945	−	1.55529i
$11$	−0.0550295	+	0.312088i	−0.0165920	+	0.0940980i	−0.991979	−	0.126401i	$-0.959657\pi$
$11$	−0.0550295	+	0.312088i	−0.0165920	+	0.0940980i	0.975387	+	0.220499i	$0.0707685\pi$
$12$		0			0
$13$	1.42272	+	0.517829i	0.394592	+	0.143620i	0.531693	−	0.846937i	$-0.321556\pi$
$13$	1.42272	+	0.517829i	0.394592	+	0.143620i	−0.137100	+	0.990557i	$0.543778\pi$
$14$	1.93395	+	0.703898i	0.516869	+	0.188125i
$15$		0			0
$16$	−0.487835	+	2.76665i	−0.121959	+	0.691662i
$17$	−0.587342	−	1.01731i	−0.142451	−	0.246733i	0.785968	−	0.618267i	$-0.212165\pi$
$17$	−0.587342	−	1.01731i	−0.142451	−	0.246733i	−0.928419	+	0.371534i	$0.878832\pi$
$18$		0			0
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	0.249931	+	0.968264i	$0.419592\pi$
$19$	−3.11040	+	5.38737i	−0.713575	+	1.23595i	−0.963507	+	0.267685i	$0.913741\pi$
$20$	−5.09751	−	4.27732i	−1.13984	−	0.956438i
$21$		0			0
$22$	0.116477	+	0.660572i	0.0248329	+	0.140834i
$23$	1.65676	−	1.39018i	0.345458	−	0.289873i	−0.453505	−	0.891254i	$-0.649827\pi$
$23$	1.65676	−	1.39018i	0.345458	−	0.289873i	0.798963	+	0.601380i	$0.205382\pi$
$24$		0			0
$25$	−2.06640	+	0.752107i	−0.413280	+	0.150421i
$26$	3.20463			0.628480
$27$		0			0
$28$	2.41147			0.455726
$29$	4.13926	−	1.50657i	0.768642	−	0.279763i	0.0722135	−	0.997389i	$-0.476994\pi$
$29$	4.13926	−	1.50657i	0.768642	−	0.279763i	0.696428	+	0.717627i	$0.254771\pi$
$30$		0			0
$31$	−6.64408	+	5.57504i	−1.19331	+	1.00131i	−0.193516	+	0.981097i	$0.561989\pi$
$31$	−6.64408	+	5.57504i	−1.19331	+	1.00131i	−0.999796	+	0.0202102i	$0.993566\pi$
$32$	1.38548	+	7.85742i	0.244920	+	1.38901i
$33$		0			0
$34$	−1.90466	−	1.59820i	−0.326647	−	0.274090i
$35$	1.30443	−	2.25934i	0.220489	−	0.381899i
$36$		0			0
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	0.989120	−	0.147113i	$-0.0469982\pi$
$37$	2.23332	+	3.86823i	0.367156	+	0.635933i	−0.621964	+	0.783046i	$0.713665\pi$
$38$	−2.28644	+	12.9671i	−0.370910	+	2.10353i
$39$		0			0
$40$	−2.56206	−	0.932515i	−0.405098	−	0.147443i
$41$	−5.49268	−	1.99917i	−0.857812	−	0.312218i	−0.124591	−	0.992208i	$-0.539762\pi$
$41$	−5.49268	−	1.99917i	−0.857812	−	0.312218i	−0.733221	+	0.679990i	$0.761984\pi$
$42$		0			0
$43$	0.970865	−	5.50605i	0.148056	−	0.839665i	−0.816807	−	0.576911i	$-0.804258\pi$
$43$	0.970865	−	5.50605i	0.148056	−	0.839665i	0.964863	−	0.262754i	$-0.0846308\pi$
$44$	0.392973	+	0.680649i	0.0592429	+	0.102612i
$45$		0			0
$46$	2.28885	−	3.96441i	0.337473	−	0.584521i
$47$	−1.89678	−	1.59159i	−0.276674	−	0.232157i	0.493883	−	0.869528i	$-0.335577\pi$
$47$	−1.89678	−	1.59159i	−0.276674	−	0.232157i	−0.770556	+	0.637372i	$0.780022\pi$
$48$		0			0
$49$	−1.05136	−	5.96259i	−0.150195	−	0.851798i
$50$	−3.56554	+	2.99184i	−0.504244	+	0.423111i
$51$		0			0
$52$	3.52848	−	1.28426i	0.489313	−	0.178095i
$53$	−10.8920			−1.49613			−0.748063	−	0.663628i	$-0.769016\pi$
$53$	−10.8920			−1.49613			−0.748063	+	0.663628i	$0.769016\pi$
$54$		0			0
$55$	0.850279			0.114652
$56$	0.928471	−	0.337936i	0.124072	−	0.0451586i
$57$		0			0
$58$	7.14224	−	5.99305i	0.937822	−	0.786926i
$59$	−0.299406	−	1.69802i	−0.0389793	−	0.221063i	0.959096	−	0.283082i	$-0.0913570\pi$
$59$	−0.299406	−	1.69802i	−0.0389793	−	0.221063i	−0.998075	+	0.0620196i	$0.980246\pi$
$60$		0			0
$61$	0.777365	+	0.652287i	0.0995314	+	0.0835168i	0.691195	−	0.722668i	$-0.257084\pi$
$61$	0.777365	+	0.652287i	0.0995314	+	0.0835168i	−0.591664	+	0.806185i	$0.701529\pi$
$62$	−9.17898	+	15.8985i	−1.16573	+	2.01911i
$63$		0			0
$64$	5.63455	+	9.75933i	0.704319	+	1.21992i
$65$	0.705410	−	4.00058i	0.0874953	−	0.496210i
$66$		0			0
$67$	−0.804895	−	0.292958i	−0.0983335	−	0.0357905i	0.292385	−	0.956301i	$-0.405551\pi$
$67$	−0.804895	−	0.292958i	−0.0983335	−	0.0357905i	−0.390718	+	0.920510i	$0.627773\pi$
$68$	−2.73763	−	0.996416i	−0.331986	−	0.120833i
$69$		0			0
$70$	0.958882	−	5.43809i	0.114608	−	0.649976i
$71$	4.79788	+	8.31018i	0.569404	+	0.986237i	0.996625	+	0.0820894i	$0.0261593\pi$
$71$	4.79788	+	8.31018i	0.569404	+	0.986237i	−0.427221	+	0.904147i	$0.640507\pi$
$72$		0			0
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.0544385	−	0.998517i	$-0.482663\pi$
$73$	7.62091	−	13.1998i	0.891960	−	1.54492i	0.837522	−	0.546404i	$-0.184004\pi$
$74$	7.24234	+	6.07705i	0.841905	+	0.706442i
$75$		0			0
$76$	2.67907	+	15.1938i	0.307311	+	1.74285i
$77$	−0.236045	+	0.198065i	−0.0268998	+	0.0225716i
$78$		0			0
$79$	10.5375	−	3.83533i	1.18556	−	0.431509i	0.327398	−	0.944887i	$-0.393828\pi$
$79$	10.5375	−	3.83533i	1.18556	−	0.431509i	0.858163	+	0.513378i	$0.171606\pi$
$80$	7.53771			0.842741
$81$		0			0
$82$	−12.3721			−1.36626
$83$	−4.40239	+	1.60234i	−0.483226	+	0.175880i	−0.572134	−	0.820160i	$-0.693884\pi$
$83$	−4.40239	+	1.60234i	−0.483226	+	0.175880i	0.0889086	+	0.996040i	$0.471662\pi$
$84$		0			0
$85$	−2.41441	+	2.02593i	−0.261880	+	0.219743i
$86$	−2.05496	−	11.6542i	−0.221592	−	1.25671i
$87$		0			0
$88$	0.246687	+	0.206995i	0.0262969	+	0.0220657i
$89$	7.74976	−	13.4230i	0.821473	−	1.42283i	−0.0831130	−	0.996540i	$-0.526486\pi$
$89$	7.74976	−	13.4230i	0.821473	−	1.42283i	0.904586	−	0.426292i	$-0.140180\pi$
$90$		0			0
$91$	0.736071	+	1.27491i	0.0771612	+	0.133647i
$92$	0.931414	−	5.28231i	0.0971066	−	0.550719i
$93$		0			0
$94$	−4.92484	−	1.79249i	−0.507958	−	0.184882i
$95$	15.6844	+	5.70867i	1.60919	+	0.585697i
$96$		0			0
$97$	−0.963658	+	5.46518i	−0.0978446	+	0.554905i	0.895994	+	0.444066i	$0.146465\pi$
$97$	−0.963658	+	5.46518i	−0.0978446	+	0.554905i	−0.993838	+	0.110838i	$0.964647\pi$
$98$	−6.40762	−	11.0983i	−0.647267	−	1.12110i
$99$		0			0
$100$	−2.72688	+	4.72309i	−0.272688	+	0.472309i
$101$	−7.76696	−	6.51725i	−0.772841	−	0.648491i	0.168594	−	0.985686i	$-0.446077\pi$
$101$	−7.76696	−	6.51725i	−0.772841	−	0.648491i	−0.941435	+	0.337195i	$0.890522\pi$
$102$		0			0
$103$	−1.71101	−	9.70360i	−0.168590	−	0.956124i	−0.945285	−	0.326246i	$-0.894216\pi$
$103$	−1.71101	−	9.70360i	−0.168590	−	0.956124i	0.776694	−	0.629878i	$-0.216895\pi$
$104$	1.17857	−	0.988939i	0.115568	−	0.0969734i
$105$		0			0
$106$	−21.6638	+	7.88499i	−2.10418	+	0.765858i
$107$	5.17080			0.499880			0.249940	−	0.968261i	$-0.419589\pi$
$107$	5.17080			0.499880			0.249940	+	0.968261i	$0.419589\pi$
$108$		0			0
$109$	−7.31065			−0.700234			−0.350117	−	0.936706i	$-0.613858\pi$
$109$	−7.31065			−0.700234			−0.350117	+	0.936706i	$0.613858\pi$
$110$	1.69118	−	0.615541i	0.161248	−	0.0586895i
$111$		0			0
$112$	−2.09253	+	1.75584i	−0.197725	+	0.165911i
$113$	1.80171	+	10.2180i	0.169491	+	0.961230i	0.944313	+	0.329050i	$0.106728\pi$
$113$	1.80171	+	10.2180i	0.169491	+	0.961230i	−0.774822	+	0.632180i	$0.782160\pi$
$114$		0			0
$115$	−4.44524	−	3.73000i	−0.414521	−	0.347824i
$116$	5.46229	−	9.46096i	0.507161	−	0.878428i
$117$		0			0
$118$	−1.82475	−	3.16056i	−0.167982	−	0.290953i
$119$	0.198338	−	1.12483i	0.0181816	−	0.103113i
$120$		0			0
$121$	10.2422	+	3.72787i	0.931113	+	0.338898i
$122$	2.01837	+	0.734626i	0.182734	+	0.0665099i
$123$		0			0
$124$	−3.73524	+	21.1836i	−0.335435	+	1.90234i
$125$	−3.75766	−	6.50846i	−0.336095	−	0.582134i
$126$		0			0
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	−0.958376	−	0.285509i	$-0.907837\pi$
$127$	−2.61372	+	4.52709i	−0.231930	+	0.401714i	0.726446	+	0.687223i	$0.241171\pi$
$128$	6.04805	+	5.07491i	0.534577	+	0.448563i
$129$		0			0
$130$	−1.49309	−	8.46771i	−0.130952	−	0.742667i
$131$	−5.54180	+	4.65012i	−0.484189	+	0.406283i	−0.851938	−	0.523642i	$-0.824573\pi$
$131$	−5.54180	+	4.65012i	−0.484189	+	0.406283i	0.367749	+	0.929925i	$0.380128\pi$
$132$		0			0
$133$	−5.68391	+	2.06877i	−0.492858	+	0.179385i
$134$	−1.81300			−0.156619
$135$		0			0
$136$	−1.19368			−0.102357
$137$	−10.5709	+	3.84749i	−0.903133	+	0.328714i	−0.751508	−	0.659724i	$-0.770673\pi$
$137$	−10.5709	+	3.84749i	−0.903133	+	0.328714i	−0.151626	+	0.988438i	$0.548451\pi$
$138$		0			0
$139$	7.18562	−	6.02945i	0.609477	−	0.511412i	−0.284999	−	0.958528i	$-0.591993\pi$
$139$	7.18562	−	6.02945i	0.609477	−	0.511412i	0.894476	+	0.447116i	$0.147549\pi$
$140$	−1.12354	−	6.37192i	−0.0949566	−	0.538526i
$141$		0			0
$142$	15.5588	+	13.0554i	1.30567	+	1.09559i
$143$	−0.239900	+	0.415518i	−0.0200614	+	0.0347474i
$144$		0			0
$145$	−5.90940	−	10.2354i	−0.490749	−	0.850003i
$146$	5.60210	−	31.7711i	0.463633	−	2.62939i
$147$		0			0
$148$	10.4096	+	3.78879i	0.855666	+	0.311437i
$149$	−17.9023	−	6.51591i	−1.46661	−	0.533804i	−0.519436	−	0.854509i	$-0.673858\pi$
$149$	−17.9023	−	6.51591i	−1.46661	−	0.533804i	−0.947179	+	0.320705i	$0.896080\pi$
$150$		0			0
$151$	0.697024	−	3.95302i	0.0567230	−	0.321692i	−0.943222	−	0.332163i	$-0.892222\pi$
$151$	0.697024	−	3.95302i	0.0567230	−	0.321692i	0.999945	+	0.0104703i	$0.00333286\pi$
$152$	3.16070	+	5.47450i	0.256367	+	0.444041i
$153$		0			0
$154$	−0.326102	+	0.564825i	−0.0262780	+	0.0455149i
$155$	17.8267	+	14.9584i	1.43188	+	1.20149i
$156$		0			0
$157$	1.26345	+	7.16538i	0.100834	+	0.571860i	0.992803	+	0.119762i	$0.0382131\pi$
$157$	1.26345	+	7.16538i	0.100834	+	0.571860i	−0.891968	+	0.452098i	$0.850676\pi$
$158$	18.1823	−	15.2568i	1.44651	−	1.21376i
$159$		0			0
$160$	20.1164	−	7.32178i	1.59034	−	0.578838i
$161$	2.10290			0.165732
$162$		0			0
$163$	12.4492			0.975094			0.487547	−	0.873097i	$-0.337892\pi$
$163$	12.4492			0.975094			0.487547	+	0.873097i	$0.337892\pi$
$164$	−13.6223	+	4.95813i	−1.06373	+	0.387165i
$165$		0			0
$166$	−7.59627	+	6.37403i	−0.589585	+	0.494721i
$167$	−0.404928	−	2.29646i	−0.0313343	−	0.177705i	0.965124	−	0.261793i	$-0.0843137\pi$
$167$	−0.404928	−	2.29646i	−0.0313343	−	0.177705i	−0.996458	+	0.0840872i	$0.973203\pi$
$168$		0			0
$169$	−8.20258	−	6.88278i	−0.630968	−	0.529445i
$170$	−3.33558	+	5.77739i	−0.255827	+	0.443106i
$171$		0			0
$172$	−6.93308	−	12.0085i	−0.528643	−	0.915636i
$173$	−0.622055	+	3.52785i	−0.0472939	+	0.268217i	−0.999281	−	0.0379219i	$-0.987926\pi$
$173$	−0.622055	+	3.52785i	−0.0472939	+	0.268217i	0.951987	+	0.306139i	$0.0990373\pi$
$174$		0			0
$175$	−2.00923	−	0.731298i	−0.151883	−	0.0552810i
$176$	−0.836592	−	0.304494i	−0.0630605	−	0.0229521i
$177$		0			0
$178$	5.69681	−	32.3082i	0.426994	−	2.42160i
$179$	9.99785	+	17.3168i	0.747275	+	1.29432i	0.949124	+	0.314901i	$0.101971\pi$
$179$	9.99785	+	17.3168i	0.747275	+	1.29432i	−0.201850	+	0.979416i	$0.564695\pi$
$180$		0			0
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	−0.988241	−	0.152907i	$-0.951136\pi$
$181$	−4.86616	+	8.42844i	−0.361699	+	0.626481i	0.626542	+	0.779388i	$0.284470\pi$
$182$	2.38697	+	2.00291i	0.176934	+	0.148465i
$183$		0			0
$184$	−0.381630	−	2.16433i	−0.0281341	−	0.159557i
$185$	9.18062	−	7.70346i	0.674973	−	0.566369i
$186$		0			0
$187$	0.349810	−	0.127320i	0.0255806	−	0.00931059i
$188$	−6.14088			−0.447869
$189$		0			0
$190$	35.3286			2.56301
$191$	16.6857	−	6.07309i	1.20733	−	0.439433i	0.341555	−	0.939862i	$-0.389046\pi$
$191$	16.6857	−	6.07309i	1.20733	−	0.439433i	0.865778	+	0.500428i	$0.166824\pi$
$192$		0			0
$193$	8.10807	−	6.80348i	0.583632	−	0.489725i	−0.302506	−	0.953148i	$-0.597823\pi$
$193$	8.10807	−	6.80348i	0.583632	−	0.489725i	0.886138	+	0.463422i	$0.153379\pi$
$194$	2.03970	+	11.5677i	0.146442	+	0.830514i
$195$		0			0
$196$	−11.5028	−	9.65202i	−0.821631	−	0.689430i
$197$	−7.07945	+	12.2620i	−0.504390	+	0.873628i	0.495597	+	0.868552i	$0.334949\pi$
$197$	−7.07945	+	12.2620i	−0.504390	+	0.873628i	−0.999987	+	0.00507615i	$0.998384\pi$
$198$		0			0
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	0.700897	−	0.713263i	$-0.252783\pi$
$199$	−3.77010	−	6.53000i	−0.267255	−	0.462899i	−0.968152	+	0.250363i	$0.919450\pi$
$200$	−0.388030	+	2.20063i	−0.0274379	+	0.155608i
$201$		0			0
$202$	−20.1663	−	7.33993i	−1.41890	−	0.516436i
$203$	4.02474	+	1.46489i	0.282481	+	0.102815i
$204$		0			0
$205$	−2.72336	+	15.4449i	−0.190208	+	1.07872i
$206$	−10.4278	−	18.0616i	−0.726543	−	1.25841i
$207$		0			0
$208$	−2.12670	+	3.68356i	−0.147460	+	0.255409i
$209$	−1.51017	−	1.26718i	−0.104461	−	0.0876528i
$210$		0			0
$211$	0.905339	+	5.13443i	0.0623261	+	0.353469i	0.999983	+	0.00590544i	$0.00187977\pi$
$211$	0.905339	+	5.13443i	0.0623261	+	0.353469i	−0.937656	+	0.347563i	$0.887009\pi$
$212$	−20.6932	+	17.3637i	−1.42121	+	1.19254i
$213$		0			0
$214$	10.2846	−	3.74329i	0.703040	−	0.255886i
$215$	−15.0012			−1.02307
$216$		0			0
$217$	−8.43326			−0.572487
$218$	−14.5407	+	5.29238i	−0.984821	+	0.358445i
$219$		0			0
$220$	1.61541	−	1.35549i	0.108911	−	0.0913872i
$221$	−0.308835	−	1.75149i	−0.0207745	−	0.117818i
$222$		0			0
$223$	13.5542	+	11.3734i	0.907659	+	0.761616i	0.971672	−	0.236333i	$-0.0759456\pi$
$223$	13.5542	+	11.3734i	0.907659	+	0.761616i	−0.0640133	+	0.997949i	$0.520390\pi$
$224$	−3.87894	+	6.71853i	−0.259173	+	0.448901i
$225$		0			0
$226$	10.9807	+	19.0191i	0.730423	+	1.26513i
$227$	−2.73878	+	15.5324i	−0.181779	+	1.03092i	0.748245	+	0.663422i	$0.230897\pi$
$227$	−2.73878	+	15.5324i	−0.181779	+	1.03092i	−0.930024	+	0.367498i	$0.880215\pi$
$228$		0			0
$229$	1.66031	+	0.604303i	0.109716	+	0.0399335i	0.396295	−	0.918123i	$-0.370296\pi$
$229$	1.66031	+	0.604303i	0.109716	+	0.0399335i	−0.286579	+	0.958057i	$0.592518\pi$
$230$	−11.5417	−	4.20084i	−0.761038	−	0.276995i
$231$		0			0
$232$	0.777275	−	4.40815i	0.0510306	−	0.289409i
$233$	6.94920	+	12.0364i	0.455257	+	0.788529i	0.998703	−	0.0509157i	$-0.0162140\pi$
$233$	6.94920	+	12.0364i	0.455257	+	0.788529i	−0.543446	+	0.839444i	$0.682881\pi$
$234$		0			0
$235$	−3.32177	+	5.75347i	−0.216688	+	0.375315i
$236$	−3.27576	−	2.74869i	−0.213234	−	0.178924i
$237$		0			0
$238$	−0.419807	−	2.38084i	−0.0272120	−	0.154327i
$239$	−15.1927	+	12.7482i	−0.982735	+	0.824613i	−0.984500	−	0.175386i	$-0.943883\pi$
$239$	−15.1927	+	12.7482i	−0.982735	+	0.824613i	0.00176451	+	0.999998i	$0.499438\pi$
$240$		0			0
$241$	−18.2063	+	6.62654i	−1.17277	+	0.426853i	−0.853642	−	0.520859i	$-0.825612\pi$
$241$	−18.2063	+	6.62654i	−1.17277	+	0.426853i	−0.319126	+	0.947712i	$0.603389\pi$
$242$	23.0703			1.48301
$243$		0			0
$244$	2.51674			0.161118
$245$	−15.2653	+	5.55612i	−0.975265	+	0.354967i
$246$		0			0
$247$	−7.21498	+	6.05409i	−0.459078	+	0.385212i
$248$	1.53045	+	8.67960i	0.0971835	+	0.551155i
$249$		0			0
$250$	−12.1855	−	10.2249i	−0.770681	−	0.646678i
$251$	2.73786	−	4.74212i	0.172812	−	0.299320i	−0.766590	−	0.642137i	$-0.778048\pi$
$251$	2.73786	−	4.74212i	0.172812	−	0.299320i	0.939402	+	0.342818i	$0.111381\pi$
$252$		0			0
$253$	0.342689	+	0.593554i	0.0215447	+	0.0373164i
$254$	−1.92133	+	10.8964i	−0.120555	+	0.683701i
$255$		0			0
$256$	−5.47570	−	1.99299i	−0.342231	−	0.124562i
$257$	10.8677	+	3.95552i	0.677909	+	0.246739i	0.657949	−	0.753062i	$-0.271424\pi$
$257$	10.8677	+	3.95552i	0.677909	+	0.246739i	0.0199594	+	0.999801i	$0.493646\pi$
$258$		0			0
$259$	−0.754166	+	4.27709i	−0.0468616	+	0.265765i
$260$	−5.03743	−	8.72508i	−0.312408	−	0.541107i
$261$		0			0
$262$	−7.65614	+	13.2608i	−0.472998	+	0.819257i
$263$	4.96239	+	4.16394i	0.305994	+	0.256759i	0.782834	−	0.622231i	$-0.213773\pi$
$263$	4.96239	+	4.16394i	0.305994	+	0.256759i	−0.476840	+	0.878990i	$0.658218\pi$
$264$		0			0
$265$	5.07473	+	28.7802i	0.311738	+	1.76795i
$266$	−9.80751	+	8.22948i	−0.601337	+	0.504582i
$267$		0			0
$268$	−1.99621	+	0.726562i	−0.121938	+	0.0443818i
$269$	−13.8387			−0.843758			−0.421879	−	0.906652i	$-0.638629\pi$
$269$	−13.8387			−0.843758			−0.421879	+	0.906652i	$0.638629\pi$
$270$		0			0
$271$	1.94536			0.118172			0.0590860	−	0.998253i	$-0.481181\pi$
$271$	1.94536			0.118172			0.0590860	+	0.998253i	$0.481181\pi$
$272$	3.10106	−	1.12869i	0.188029	−	0.0684370i
$273$		0			0
$274$	−18.2399	+	15.3051i	−1.10192	+	0.924617i
$275$	−0.121011	−	0.686285i	−0.00729721	−	0.0413846i
$276$		0			0
$277$	9.55463	+	8.01729i	0.574082	+	0.481712i	0.882998	−	0.469377i	$-0.155522\pi$
$277$	9.55463	+	8.01729i	0.574082	+	0.481712i	−0.308915	+	0.951090i	$0.599966\pi$
$278$	9.92713	−	17.1943i	0.595390	−	1.03125i
$279$		0			0
$280$	−1.32553	−	2.29588i	−0.0792154	−	0.137205i
$281$	1.69409	−	9.60766i	0.101061	−	0.573145i	−0.891660	−	0.452706i	$-0.850459\pi$
$281$	1.69409	−	9.60766i	0.101061	−	0.573145i	0.992721	−	0.120439i	$-0.0384301\pi$
$282$		0			0
$283$	−24.9688	−	9.08790i	−1.48424	−	0.540220i	−0.532315	−	0.846547i	$-0.678678\pi$
$283$	−24.9688	−	9.08790i	−1.48424	−	0.540220i	−0.951926	+	0.306327i	$0.900900\pi$
$284$	22.3632	+	8.13953i	1.32701	+	0.482992i
$285$		0			0
$286$	−0.176349	+	1.00013i	−0.0104277	+	0.0591387i
$287$	−2.84173	−	4.92202i	−0.167742	−	0.290538i
$288$		0			0
$289$	7.81006	−	13.5274i	0.459415	−	0.795730i
$290$	−19.1633	−	16.0799i	−1.12531	−	0.944247i
$291$		0			0
$292$	−6.56410	−	37.2268i	−0.384135	−	2.17854i
$293$	9.38976	−	7.87895i	0.548556	−	0.460293i	−0.325896	−	0.945406i	$-0.605666\pi$
$293$	9.38976	−	7.87895i	0.548556	−	0.460293i	0.874452	+	0.485113i	$0.161221\pi$
$294$		0			0
$295$	−4.34723	+	1.58226i	−0.253106	+	0.0921229i
$296$	4.53888			0.263817
$297$		0			0
$298$	−40.3243			−2.33592
$299$	3.07698	−	1.11993i	0.177947	−	0.0647672i
$300$		0			0
$301$	4.16445	−	3.49439i	0.240035	−	0.201413i
$302$	−1.47534	−	8.36705i	−0.0848961	−	0.481470i
$303$		0			0
$304$	−13.3876	−	11.2335i	−0.767832	−	0.644288i
$305$	1.36137	−	2.35797i	0.0779521	−	0.135017i
$306$		0			0
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	0.945138	+	0.326671i	$0.105927\pi$
$307$	13.2370	+	22.9271i	0.755475	+	1.30852i	−0.189663	+	0.981849i	$0.560740\pi$
$308$	−0.132702	+	0.752591i	−0.00756141	+	0.0428829i
$309$		0			0
$310$	46.2857	+	16.8466i	2.62885	+	0.956823i
$311$	16.5945	+	6.03990i	0.940987	+	0.342491i	0.766556	−	0.642178i	$-0.221969\pi$
$311$	16.5945	+	6.03990i	0.940987	+	0.342491i	0.174432	+	0.984669i	$0.444191\pi$
$312$		0			0
$313$	1.67522	−	9.50064i	0.0946890	−	0.537008i	−0.900153	−	0.435574i	$-0.856546\pi$
$313$	1.67522	−	9.50064i	0.0946890	−	0.537008i	0.994842	−	0.101435i	$-0.0323433\pi$
$314$	7.70019	+	13.3371i	0.434547	+	0.752657i
$315$		0			0
$316$	13.9056	−	24.0852i	0.782250	−	1.35490i
$317$	−2.84240	−	2.38506i	−0.159645	−	0.133958i	0.559466	−	0.828853i	$-0.311006\pi$
$317$	−2.84240	−	2.38506i	−0.159645	−	0.133958i	−0.719111	+	0.694895i	$0.755451\pi$
$318$		0			0
$319$	0.242400	+	1.37472i	0.0135718	+	0.0769694i
$320$	23.1622	−	19.4354i	1.29481	−	1.08647i
$321$		0			0
$322$	4.18262	−	1.52235i	0.233089	−	0.0848373i
$323$	7.30748			0.406599
$324$		0			0
$325$	−3.32937			−0.184680
$326$	24.7611	−	9.01229i	1.37139	−	0.499145i
$327$		0			0
$328$	−4.55009	+	3.81798i	−0.251236	+	0.210812i
$329$	−0.418069	−	2.37099i	−0.0230489	−	0.130717i
$330$		0			0
$331$	−1.08226	−	0.908128i	−0.0594866	−	0.0499152i	0.612560	−	0.790424i	$-0.290140\pi$
$331$	−1.08226	−	0.908128i	−0.0594866	−	0.0499152i	−0.672046	+	0.740509i	$0.734584\pi$
$332$	−5.80953	+	10.0624i	−0.318839	+	0.552246i
$333$		0			0
$334$	−2.46786	−	4.27446i	−0.135035	−	0.233888i
$335$	−0.399080	+	2.26330i	−0.0218041	+	0.123657i
$336$		0			0
$337$	12.2067	+	4.44287i	0.664940	+	0.242018i	0.652368	−	0.757903i	$-0.273776\pi$
$337$	12.2067	+	4.44287i	0.664940	+	0.242018i	0.0125722	+	0.999921i	$0.495998\pi$
$338$	−21.2974	−	7.75161i	−1.15842	−	0.421632i
$339$		0			0
$340$	−1.35736	+	7.69798i	−0.0736133	+	0.417482i
$341$	−1.37428	−	2.38033i	−0.0744215	−	0.128902i
$342$		0			0
$343$	6.34669	−	10.9928i	0.342689	−	0.593555i
$344$	−4.35221	−	3.65194i	−0.234656	−	0.196899i
$345$		0			0
$346$	1.31665	+	7.46712i	0.0707838	+	0.401435i
$347$	−3.67737	+	3.08568i	−0.197411	+	0.165648i	−0.736135	−	0.676835i	$-0.763351\pi$
$347$	−3.67737	+	3.08568i	−0.197411	+	0.165648i	0.538724	+	0.842483i	$0.318907\pi$
$348$		0			0
$349$	21.2160	−	7.72198i	1.13567	−	0.413348i	0.295319	−	0.955399i	$-0.404574\pi$
$349$	21.2160	−	7.72198i	1.13567	−	0.413348i	0.840346	+	0.542050i	$0.182352\pi$
$350$	−4.52571			−0.241909
$351$		0			0
$352$	−2.52845			−0.134767
$353$	27.9150	−	10.1602i	1.48577	−	0.540775i	0.533436	−	0.845840i	$-0.320900\pi$
$353$	27.9150	−	10.1602i	1.48577	−	0.540775i	0.952331	+	0.305065i	$0.0986783\pi$
$354$		0			0
$355$	19.7229	−	16.5495i	1.04678	−	0.878354i
$356$	−6.67507	−	37.8562i	−0.353778	−	2.00638i
$357$		0			0
$358$	32.4216	+	27.2049i	1.71353	+	1.43783i
$359$	−6.70991	+	11.6219i	−0.354136	+	0.613381i	−0.986970	−	0.160906i	$-0.948558\pi$
$359$	−6.70991	+	11.6219i	−0.354136	+	0.613381i	0.632834	+	0.774288i	$0.281892\pi$
$360$		0			0
$361$	−9.84920	−	17.0593i	−0.518379	−	0.897858i
$362$	−3.57709	+	20.2867i	−0.188008	+	1.06625i
$363$		0			0
$364$	3.43086	+	1.24873i	0.179826	+	0.0654513i
$365$	−38.4290	−	13.9870i	−2.01147	−	0.732114i
$366$		0			0
$367$	−1.38050	+	7.82920i	−0.0720615	+	0.408681i	0.927344	+	0.374209i	$0.122086\pi$
$367$	−1.38050	+	7.82920i	−0.0720615	+	0.408681i	−0.999406	+	0.0344715i	$0.989025\pi$
$368$	3.03793	+	5.26184i	0.158363	+	0.274293i
$369$		0			0
$370$	12.6833	−	21.9681i	0.659372	−	1.14207i
$371$	−8.11288	−	6.80751i	−0.421200	−	0.353428i
$372$		0			0
$373$	−1.98315	−	11.2470i	−0.102684	−	0.582348i	−0.992120	−	0.125289i	$-0.960014\pi$
$373$	−1.98315	−	11.2470i	−0.102684	−	0.582348i	0.889437	−	0.457059i	$-0.151097\pi$
$374$	0.603592	−	0.506474i	0.0312110	−	0.0261891i
$375$		0			0
$376$	−2.36437	+	0.860561i	−0.121933	+	0.0443801i
$377$	6.66917			0.343480
$378$		0			0
$379$	−24.1705			−1.24155			−0.620777	−	0.783987i	$-0.713183\pi$
$379$	−24.1705			−1.24155			−0.620777	+	0.783987i	$0.713183\pi$
$380$	38.8988	−	14.1580i	1.99547	−	0.726291i
$381$		0			0
$382$	28.7909	−	24.1584i	1.47307	−	1.23605i
$383$	1.63981	+	9.29982i	0.0837903	+	0.475199i	0.997611	+	0.0690808i	$0.0220066\pi$
$383$	1.63981	+	9.29982i	0.0837903	+	0.475199i	−0.913821	+	0.406118i	$0.866882\pi$
$384$		0			0
$385$	0.633331	+	0.531428i	0.0322775	+	0.0270841i
$386$	11.2015	−	19.4016i	0.570143	−	0.987516i
$387$		0			0
$388$	6.88162	+	11.9193i	0.349361	+	0.605111i
$389$	−0.442405	+	2.50900i	−0.0224308	+	0.127211i	−0.993967	−	0.109680i	$-0.965017\pi$
$389$	−0.442405	+	2.50900i	−0.0224308	+	0.127211i	0.971536	+	0.236891i	$0.0761285\pi$
$390$		0			0
$391$	−2.38733	−	0.868915i	−0.120732	−	0.0439429i
$392$	−5.78145	−	2.10427i	−0.292007	−	0.106282i
$393$		0			0
$394$	−5.20407	+	29.5137i	−0.262177	+	1.48688i
$395$	−15.0438	−	26.0567i	−0.756937	−	1.31105i
$396$		0			0
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	−0.908447	−	0.417999i	$-0.862731\pi$
$397$	−1.83759	+	3.18279i	−0.0922258	+	0.159740i	0.816222	+	0.577739i	$0.196065\pi$
$398$	−12.2259	−	10.2587i	−0.612828	−	0.514223i
$399$		0			0
$400$	−1.07276	−	6.08390i	−0.0536378	−	0.304195i
$401$	12.3706	−	10.3802i	0.617760	−	0.518362i	−0.279338	−	0.960193i	$-0.590115\pi$
$401$	12.3706	−	10.3802i	0.617760	−	0.518362i	0.897099	+	0.441830i	$0.145671\pi$
$402$		0			0
$403$	−12.3396	+	4.49125i	−0.614679	+	0.223725i
$404$	−25.1458			−1.25105
$405$		0			0
$406$	9.06558			0.449917
$407$	−1.33013	+	0.484126i	−0.0659319	+	0.0239972i
$408$		0			0
$409$	7.03380	−	5.90206i	0.347799	−	0.291838i	−0.452107	−	0.891964i	$-0.649327\pi$
$409$	7.03380	−	5.90206i	0.347799	−	0.291838i	0.799906	+	0.600126i	$0.204883\pi$
$410$	5.76432	+	32.6911i	0.284680	+	1.61450i
$411$		0			0
$412$	−18.7199	−	15.7078i	−0.922262	−	0.773870i
$413$	0.838253	−	1.45190i	0.0412477	−	0.0714432i
$414$		0			0
$415$	6.28506	+	10.8860i	0.308522	+	0.534375i
$416$	−2.09765	+	11.8964i	−0.102846	+	0.583268i
$417$		0			0
$418$	−3.92104	−	1.42714i	−0.191784	−	0.0698037i
$419$	6.55800	+	2.38692i	0.320379	+	0.116608i	0.497204	−	0.867634i	$-0.334360\pi$
$419$	6.55800	+	2.38692i	0.320379	+	0.116608i	−0.176824	+	0.984242i	$0.556582\pi$
$420$		0			0
$421$	5.35021	−	30.3425i	0.260753	−	1.47880i	−0.520108	−	0.854100i	$-0.674108\pi$
$421$	5.35021	−	30.3425i	0.260753	−	1.47880i	0.780861	−	0.624704i	$-0.214781\pi$
$422$	5.51765	+	9.55686i	0.268595	+	0.465221i
$423$		0			0
$424$	−5.53405	+	9.58526i	−0.268757	+	0.465502i
$425$	1.97881	+	1.66042i	0.0959862	+	0.0805420i
$426$		0			0
$427$	0.171339	+	0.971712i	0.00829167	+	0.0470244i
$428$	9.82380	−	8.24315i	0.474851	−	0.398448i
$429$		0			0
$430$	−29.8370	+	10.8598i	−1.43887	+	0.523704i
$431$	27.8971			1.34376			0.671879	−	0.740661i	$-0.265487\pi$
$431$	27.8971			1.34376			0.671879	+	0.740661i	$0.265487\pi$
$432$		0			0
$433$	19.1706			0.921278			0.460639	−	0.887588i	$-0.347620\pi$
$433$	19.1706			0.921278			0.460639	+	0.887588i	$0.347620\pi$
$434$	−16.7735	+	6.10507i	−0.805156	+	0.293053i
$435$		0			0
$436$	−13.8892	+	11.6544i	−0.665173	+	0.558146i
$437$	2.33626	+	13.2496i	0.111759	+	0.633814i
$438$		0			0
$439$	−18.1928	−	15.2656i	−0.868294	−	0.728585i	0.0954443	−	0.995435i	$-0.469573\pi$
$439$	−18.1928	−	15.2656i	−0.868294	−	0.728585i	−0.963738	+	0.266850i	$0.914017\pi$
$440$	0.432015	−	0.748272i	0.0205955	−	0.0356725i
$441$		0			0
$442$	−1.88221	−	3.26009i	−0.0895278	−	0.155067i
$443$	4.05612	−	23.0034i	0.192712	−	1.09292i	−0.722927	−	0.690924i	$-0.757204\pi$
$443$	4.05612	−	23.0034i	0.192712	−	1.09292i	0.915639	−	0.402000i	$-0.131685\pi$
$444$		0			0
$445$	−39.0787	−	14.2235i	−1.85251	−	0.674258i
$446$	35.1925	+	12.8090i	1.66641	+	0.606525i
$447$		0			0
$448$	−1.90272	+	10.7908i	−0.0898950	+	0.509820i
$449$	−2.40953	−	4.17343i	−0.113713	−	0.196956i	0.803552	−	0.595235i	$-0.202941\pi$
$449$	−2.40953	−	4.17343i	−0.113713	−	0.196956i	−0.917264	+	0.398279i	$0.869608\pi$
$450$		0			0
$451$	0.926176	−	1.60418i	0.0436119	−	0.0755380i
$452$	19.7123	+	16.5406i	0.927187	+	0.778002i
$453$		0			0
$454$	5.79696	+	32.8762i	0.272065	+	1.54296i
$455$	3.02580	−	2.53895i	0.141852	−	0.119028i
$456$		0			0
$457$	4.59848	−	1.67371i	0.215108	−	0.0782929i	−0.232219	−	0.972664i	$-0.574598\pi$
$457$	4.59848	−	1.67371i	0.215108	−	0.0782929i	0.447326	+	0.894371i	$0.352376\pi$
$458$	3.73978			0.174749
$459$		0			0
$460$	−14.3916			−0.671012
$461$	−26.3024	+	9.57330i	−1.22503	+	0.445873i	−0.871891	−	0.489699i	$-0.837107\pi$
$461$	−26.3024	+	9.57330i	−1.22503	+	0.445873i	−0.353135	+	0.935572i	$0.614884\pi$
$462$		0			0
$463$	−21.0473	+	17.6608i	−0.978152	+	0.820767i	−0.983810	−	0.179217i	$-0.942644\pi$
$463$	−21.0473	+	17.6608i	−0.978152	+	0.820767i	0.00565725	+	0.999984i	$0.498199\pi$
$464$	2.14887	+	12.1868i	0.0997587	+	0.565760i
$465$		0			0
$466$	22.5352	+	18.9093i	1.04392	+	0.875957i
$467$	10.6232	−	18.4000i	0.491585	−	0.851450i	−0.508368	−	0.861140i	$-0.669751\pi$
$467$	10.6232	−	18.4000i	0.491585	−	0.851450i	0.999953	+	0.00968963i	$0.00308435\pi$
$468$		0			0
$469$	−0.416426	−	0.721272i	−0.0192288	−	0.0333052i
$470$	−2.44182	+	13.8482i	−0.112633	+	0.638771i
$471$		0			0
$472$	−1.64643	−	0.599252i	−0.0757831	−	0.0275828i
$473$	1.66494	+	0.605990i	0.0765542	+	0.0278635i
$474$		0			0
$475$	2.37544	−	13.4718i	0.108993	−	0.618129i
$476$	−1.41636	−	2.45321i	−0.0649188	−	0.112443i
$477$		0			0
$478$	−20.9892	+	36.3543i	−0.960022	+	1.66281i
$479$	−31.9278	−	26.7906i	−1.45882	−	1.22410i	−0.925811	−	0.377986i	$-0.876617\pi$
$479$	−31.9278	−	26.7906i	−1.45882	−	1.22410i	−0.533009	−	0.846109i	$-0.678939\pi$
$480$		0			0
$481$	1.17432	+	6.65990i	0.0535444	+	0.303665i
$482$	−31.4147	+	26.3600i	−1.43090	+	1.20067i
$483$		0			0
$484$	25.4017	−	9.24547i	1.15462	−	0.420249i
$485$	14.8898			0.676112
$486$		0			0
$487$	4.02801			0.182527			0.0912634	−	0.995827i	$-0.470909\pi$
$487$	4.02801			0.182527			0.0912634	+	0.995827i	$0.470909\pi$
$488$	0.969001	−	0.352688i	0.0438646	−	0.0159654i
$489$		0			0
$490$	−26.3401	+	22.1020i	−1.18992	+	0.998465i
$491$	−6.70653	−	38.0346i	−0.302661	−	1.71648i	−0.634313	−	0.773076i	$-0.718717\pi$
$491$	−6.70653	−	38.0346i	−0.302661	−	1.71648i	0.331652	−	0.943402i	$-0.392394\pi$
$492$		0			0
$493$	−3.96380	−	3.32603i	−0.178521	−	0.149797i
$494$	−9.96769	+	17.2645i	−0.448468	+	0.776769i
$495$		0			0
$496$	−12.1830	−	21.1015i	−0.547032	−	0.947487i
$497$	−1.62019	+	9.18853i	−0.0726753	+	0.412162i
$498$		0			0
$499$	3.82629	+	1.39266i	0.171288	+	0.0623439i	0.426241	−	0.904610i	$-0.359838\pi$
$499$	3.82629	+	1.39266i	0.171288	+	0.0623439i	−0.254952	+	0.966954i	$0.582060\pi$
$500$	−17.5146	−	6.37480i	−0.783278	−	0.285090i
$501$		0			0
$502$	2.01259	−	11.4140i	0.0898263	−	0.509430i
$503$	1.71297	+	2.96695i	0.0763775	+	0.132290i	0.901684	−	0.432395i	$-0.142331\pi$
$503$	1.71297	+	2.96695i	0.0763775	+	0.132290i	−0.825307	+	0.564684i	$0.808998\pi$
$504$		0			0
$505$	−13.6020	+	23.5594i	−0.605282	+	1.04838i
$506$	1.11129	+	0.932483i	0.0494028	+	0.0414539i
$507$		0			0
$508$	2.25126	+	12.7675i	0.0998837	+	0.566468i
$509$	−9.39432	+	7.88277i	−0.416396	+	0.349398i	−0.826790	−	0.562511i	$-0.809836\pi$
$509$	−9.39432	+	7.88277i	−0.416396	+	0.349398i	0.410394	+	0.911908i	$0.365391\pi$
$510$		0			0
$511$	13.9264	−	5.06878i	0.616066	−	0.224230i
$512$	−28.1241			−1.24292
$513$		0			0
$514$	24.4791			1.07973
$515$	−24.8430	+	9.04210i	−1.09471	+	0.398443i
$516$		0			0
$517$	0.601093	−	0.504377i	0.0264360	−	0.0221825i
$518$	1.59628	+	9.05298i	0.0701367	+	0.397765i
$519$		0			0
$520$	−3.16222	−	2.65342i	−0.138673	−	0.116360i
$521$	−7.04117	+	12.1957i	−0.308479	+	0.534302i	−0.978030	−	0.208465i	$-0.933153\pi$
$521$	−7.04117	+	12.1957i	−0.308479	+	0.534302i	0.669551	+	0.742766i	$0.266487\pi$
$522$		0			0
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	0.739097	−	0.673599i	$-0.235253\pi$
$523$	−4.88956	−	8.46897i	−0.213806	−	0.370322i	−0.952902	+	0.303277i	$0.901919\pi$
$524$	−3.11555	+	17.6692i	−0.136103	+	0.771881i
$525$		0			0
$526$	12.8845	+	4.68956i	0.561789	+	0.204474i
$527$	9.57387	+	3.48460i	0.417044	+	0.151792i
$528$		0			0
$529$	−3.18168	+	18.0442i	−0.138334	+	0.784530i
$530$	30.9283	+	53.5694i	1.34344	+	2.32691i
$531$		0			0
$532$	−7.50065	+	12.9915i	−0.325195	+	0.563254i
$533$	−6.77933	−	5.68853i	−0.293645	−	0.246398i
$534$		0			0
$535$	−2.40915	−	13.6630i	−0.104157	−	0.590703i
$536$	−0.666768	+	0.559485i	−0.0288000	+	0.0241661i
$537$		0			0
$538$	−27.5247	+	10.0182i	−1.18668	+	0.431915i
$539$	1.91871			0.0826445
$540$		0			0
$541$	40.9454			1.76038			0.880189	−	0.474623i	$-0.157416\pi$
$541$	40.9454			1.76038			0.880189	+	0.474623i	$0.157416\pi$
$542$	3.86927	−	1.40830i	0.166199	−	0.0604916i
$543$		0			0
$544$	7.17966	−	6.02445i	0.307825	−	0.258296i
$545$	3.40614	+	19.3172i	0.145903	+	0.827458i
$546$		0			0
$547$	0.850521	+	0.713672i	0.0363657	+	0.0305144i	0.660789	−	0.750571i	$-0.270222\pi$
$547$	0.850521	+	0.713672i	0.0363657	+	0.0305144i	−0.624424	+	0.781086i	$0.714666\pi$
$548$	−13.9497	+	24.1615i	−0.595900	+	1.03213i
$549$		0			0
$550$	−0.737508	−	1.27740i	−0.0314474	−	0.0544686i
$551$	−4.75832	+	26.9858i	−0.202711	+	1.14963i
$552$		0			0
$553$	10.2459	+	3.72922i	0.435702	+	0.158583i
$554$	24.8079	+	9.02932i	1.05399	+	0.383619i
$555$		0			0
$556$	4.03969	−	22.9102i	0.171321	−	0.971610i
$557$	−17.5201	−	30.3458i	−0.742352	−	1.28579i	−0.951422	−	0.307890i	$-0.900377\pi$
$557$	−17.5201	−	30.3458i	−0.742352	−	1.28579i	0.209070	−	0.977901i	$-0.432956\pi$
$558$		0			0
$559$	4.23247	−	7.33084i	0.179014	−	0.310062i
$560$	5.61446	+	4.71109i	0.237254	+	0.199080i
$561$		0			0
$562$	−3.58575	−	20.3358i	−0.151256	−	0.857813i
$563$	−29.7005	+	24.9216i	−1.25172	+	1.05032i	−0.255212	+	0.966885i	$0.582145\pi$
$563$	−29.7005	+	24.9216i	−1.25172	+	1.05032i	−0.996513	+	0.0834367i	$0.973410\pi$
$564$		0			0
$565$	26.1600	−	9.52145i	1.10056	−	0.400570i
$566$	−56.2413			−2.36400
$567$		0			0
$568$	9.75095			0.409141
$569$	31.9198	−	11.6179i	1.33815	−	0.487046i	0.428919	−	0.903343i	$-0.358895\pi$
$569$	31.9198	−	11.6179i	1.33815	−	0.487046i	0.909229	+	0.416297i	$0.136672\pi$
$570$		0			0
$571$	7.72852	−	6.48500i	0.323428	−	0.271389i	−0.466587	−	0.884475i	$-0.654517\pi$
$571$	7.72852	−	6.48500i	0.323428	−	0.271389i	0.790016	+	0.613086i	$0.210072\pi$
$572$	0.206632	+	1.17187i	0.00863972	+	0.0489983i
$573$		0			0
$574$	−9.21532	−	7.73257i	−0.384640	−	0.322751i
$575$	−2.37795	+	4.11873i	−0.0991674	+	0.171763i
$576$		0			0
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	0.964224	−	0.265090i	$-0.0854017\pi$
$577$	6.06615	+	10.5069i	0.252537	+	0.437407i	−0.711687	+	0.702497i	$0.752068\pi$
$578$	5.74114	−	32.5596i	0.238800	−	1.35430i
$579$		0			0
$580$	−27.5440	−	10.0252i	−1.14370	−	0.416274i
$581$	−4.28059	−	1.55801i	−0.177589	−	0.0646371i
$582$		0			0
$583$	0.599379	−	3.39925i	0.0248237	−	0.140782i
$584$	−7.74416	−	13.4133i	−0.320456	−	0.555046i
$585$		0			0
$586$	12.9722	−	22.4685i	0.535877	−	0.928167i
$587$	24.3213	+	20.4080i	1.00385	+	0.842328i	0.987513	−	0.157539i	$-0.0503559\pi$
$587$	24.3213	+	20.4080i	1.00385	+	0.842328i	0.0163344	+	0.999867i	$0.494800\pi$
$588$		0			0
$589$	−9.36909	−	53.1348i	−0.386047	−	2.18938i
$590$	−7.50109	+	6.29416i	−0.308815	+	0.259126i
$591$		0			0
$592$	−11.7915	+	4.29176i	−0.484629	+	0.176390i
$593$	13.4906			0.553993			0.276996	−	0.960871i	$-0.410661\pi$
$593$	13.4906			0.553993			0.276996	+	0.960871i	$0.410661\pi$
$594$		0			0
$595$	−3.06459			−0.125636
$596$	−44.3994	+	16.1601i	−1.81867	+	0.661942i
$597$		0			0
$598$	5.30929	−	4.45503i	0.217113	−	0.182180i
$599$	−7.36796	−	41.7858i	−0.301047	−	1.70732i	−0.641554	−	0.767078i	$-0.721710\pi$
$599$	−7.36796	−	41.7858i	−0.301047	−	1.70732i	0.340507	−	0.940242i	$-0.389401\pi$
$600$		0			0
$601$	−15.1713	−	12.7302i	−0.618851	−	0.519277i	0.278591	−	0.960410i	$-0.410132\pi$
$601$	−15.1713	−	12.7302i	−0.618851	−	0.519277i	−0.897442	+	0.441132i	$0.854577\pi$
$602$	5.75330	−	9.96501i	0.234487	−	0.406144i
$603$		0			0
$604$	−4.97755	−	8.62136i	−0.202533	−	0.350798i
$605$	5.07828	−	28.8003i	0.206461	−	1.17090i
$606$		0			0
$607$	33.8280	+	12.3124i	1.37304	+	0.499745i	0.920060	−	0.391778i	$-0.128140\pi$
$607$	33.8280	+	12.3124i	1.37304	+	0.499745i	0.452977	+	0.891522i	$0.350362\pi$
$608$	−46.6403	−	16.9757i	−1.89151	−	0.688454i
$609$		0			0
$610$	1.00074	−	5.67548i	0.0405188	−	0.229793i
$611$	−1.87442	−	3.24659i	−0.0758310	−	0.131343i
$612$		0			0
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	0.464780	+	0.885426i	$0.346133\pi$
$613$	−13.2314	+	22.9175i	−0.534411	+	0.925627i	−0.999192	+	0.0402013i	$0.987200\pi$
$614$	42.9256	+	36.0189i	1.73234	+	1.45360i
$615$		0			0
$616$	0.0543723	+	0.308361i	0.00219072	+	0.0124242i
$617$	37.6256	−	31.5716i	1.51475	−	1.27103i	0.660943	−	0.750436i	$-0.270157\pi$
$617$	37.6256	−	31.5716i	1.51475	−	1.27103i	0.853807	−	0.520590i	$-0.174288\pi$
$618$		0			0
$619$	22.7464	−	8.27901i	0.914255	−	0.332762i	0.158304	−	0.987390i	$-0.449397\pi$
$619$	22.7464	−	8.27901i	0.914255	−	0.332762i	0.755950	+	0.654629i	$0.227175\pi$
$620$	57.7145			2.31787
$621$		0			0
$622$	37.3785			1.49874
$623$	14.1618	−	5.15448i	0.567381	−	0.206510i
$624$		0			0
$625$	−23.8695	+	20.0289i	−0.954780	+	0.801155i
$626$	−3.54581	−	20.1093i	−0.141719	−	0.803728i
$627$		0			0
$628$	13.8232	+	11.5991i	0.551607	+	0.462853i
$629$	2.62345	−	4.54395i	0.104604	−	0.181179i
$630$		0			0
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	0.634393	−	0.773010i	$-0.281250\pi$
$631$	−8.84842	−	15.3259i	−0.352250	−	0.610115i	−0.986643	+	0.162895i	$0.947917\pi$
$632$	1.97874	−	11.2220i	0.0787101	−	0.446387i
$633$		0			0
$634$	−7.38007	−	2.68613i	−0.293100	−	0.106680i
$635$	13.1799	+	4.79708i	0.523027	+	0.190366i
$636$		0			0
$637$	1.59180	−	9.02754i	0.0630693	−	0.357684i
$638$	1.47732	+	2.55880i	0.0584878	+	0.101304i
$639$		0			0
$640$	10.5917	−	18.3454i	0.418676	−	0.725167i
$641$	29.1483	+	24.4583i	1.15129	+	0.966046i	0.999749	−	0.0224050i	$-0.00713234\pi$
$641$	29.1483	+	24.4583i	1.15129	+	0.966046i	0.151540	+	0.988451i	$0.451577\pi$
$642$		0			0
$643$	8.15148	+	46.2293i	0.321463	+	1.82311i	0.533447	+	0.845834i	$0.320896\pi$
$643$	8.15148	+	46.2293i	0.321463	+	1.82311i	−0.211984	+	0.977273i	$0.567992\pi$
$644$	3.99523	−	3.35239i	0.157434	−	0.132103i
$645$		0			0
$646$	14.5344	−	5.29009i	0.571848	−	0.208136i
$647$	−28.2333			−1.10997			−0.554983	−	0.831862i	$-0.687275\pi$
$647$	−28.2333			−1.10997			−0.554983	+	0.831862i	$0.687275\pi$
$648$		0			0
$649$	0.546406			0.0214483
$650$	−6.62204	+	2.41023i	−0.259738	+	0.0945368i
$651$		0			0
$652$	23.6517	−	19.8461i	0.926271	−	0.777234i
$653$	6.13103	+	34.7708i	0.239926	+	1.36069i	0.831988	+	0.554794i	$0.187203\pi$
$653$	6.13103	+	34.7708i	0.239926	+	1.36069i	−0.592062	+	0.805893i	$0.701686\pi$
$654$		0			0
$655$	14.8692	+	12.4767i	0.580987	+	0.487506i
$656$	8.21052	−	14.2210i	0.320567	−	0.555239i
$657$		0			0
$658$	−2.54795	−	4.41318i	−0.0993295	−	0.172044i
$659$	7.24004	−	41.0603i	0.282032	−	1.59948i	−0.433667	−	0.901073i	$-0.642781\pi$
$659$	7.24004	−	41.0603i	0.282032	−	1.59948i	0.715699	−	0.698409i	$-0.246108\pi$
$660$		0			0
$661$	−1.19709	−	0.435704i	−0.0465613	−	0.0169469i	0.318635	−	0.947878i	$-0.396776\pi$
$661$	−1.19709	−	0.435704i	−0.0465613	−	0.0169469i	−0.365196	+	0.930931i	$0.618998\pi$
$662$	−2.81002	−	1.02276i	−0.109214	−	0.0397508i
$663$		0			0
$664$	−0.826686	+	4.68837i	−0.0320817	+	0.181944i
$665$	8.11461	+	14.0549i	0.314671	+	0.545027i
$666$		0			0
$667$	4.76334	−	8.25035i	0.184437	−	0.319455i
$668$	−4.43026	−	3.71743i	−0.171412	−	0.143832i
$669$		0			0
$670$	0.844702	+	4.79054i	0.0326337	+	0.185075i
$671$	−0.246349	+	0.206711i	−0.00951018	+	0.00797999i
$672$		0			0
$673$	−33.4838	+	12.1871i	−1.29071	+	0.469779i	−0.893959	−	0.448149i	$-0.852084\pi$
$673$	−33.4838	+	12.1871i	−1.29071	+	0.469779i	−0.396748	+	0.917928i	$0.629861\pi$
$674$	27.4951			1.05907
$675$		0			0
$676$	−26.5561			−1.02139
$677$	−16.9162	+	6.15701i	−0.650144	+	0.236633i	−0.645975	−	0.763358i	$-0.723549\pi$
$677$	−16.9162	+	6.15701i	−0.650144	+	0.236633i	−0.00416861	+	0.999991i	$0.501327\pi$
$678$		0			0
$679$	−4.13353	+	3.46845i	−0.158630	+	0.133107i
$680$	0.556154	+	3.15411i	0.0213275	+	0.120955i
$681$		0			0
$682$	−4.45660	−	3.73953i	−0.170652	−	0.143194i
$683$	−19.8807	+	34.4344i	−0.760715	+	1.31760i	0.181768	+	0.983341i	$0.441818\pi$
$683$	−19.8807	+	34.4344i	−0.760715	+	1.31760i	−0.942483	+	0.334255i	$0.891515\pi$
$684$		0			0
$685$	15.0915	+	26.1393i	0.576617	+	0.998730i
$686$	4.66542	−	26.4589i	0.178127	−	1.01021i
$687$		0			0
$688$	14.7597	+	5.37209i	0.562708	+	0.204809i
$689$	−15.4962	−	5.64017i	−0.590360	−	0.214873i
$690$		0			0
$691$	−2.92436	+	16.5849i	−0.111248	+	0.630918i	0.877292	+	0.479957i	$0.159348\pi$
$691$	−2.92436	+	16.5849i	−0.111248	+	0.630918i	−0.988540	+	0.150961i	$0.951763\pi$
$692$	4.44218	+	7.69408i	0.168866	+	0.292485i
$693$		0			0
$694$	−5.08038	+	8.79948i	−0.192849	+	0.334024i
$695$	−19.2797	−	16.1776i	−0.731322	−	0.613652i
$696$		0			0
$697$	1.19231	+	6.76193i	0.0451620	+	0.256126i
$698$	36.6079	−	30.7177i	1.38563	−	1.16268i
$699$		0			0
$700$	−4.98306	+	1.81369i	−0.188342	+	0.0685509i
$701$	−8.96921			−0.338762			−0.169381	−	0.985551i	$-0.554177\pi$
$701$	−8.96921			−0.338762			−0.169381	+	0.985551i	$0.554177\pi$
$702$		0			0
$703$	−27.7861			−1.04797
$704$	−3.35583	+	1.22142i	−0.126478	+	0.0460341i
$705$		0			0
$706$	48.1670	−	40.4169i	1.81279	−	1.52111i
$707$	−1.71191	−	9.70875i	−0.0643832	−	0.365135i
$708$		0			0
$709$	13.8973	+	11.6612i	0.521924	+	0.437946i	0.865302	−	0.501251i	$-0.167127\pi$
$709$	13.8973	+	11.6612i	0.521924	+	0.437946i	−0.343378	+	0.939197i	$0.611571\pi$
$710$	27.2477	−	47.1944i	1.02259	−	1.77117i
$711$		0			0
$712$	−7.87509	−	13.6401i	−0.295131	−	0.511183i
$713$	−3.25728	+	18.4730i	−0.121986	+	0.691818i
$714$		0			0
$715$	1.20971	+	0.440299i	0.0452407	+	0.0164663i
$716$	46.6005	+	16.9612i	1.74154	+	0.633869i
$717$		0			0
$718$	−4.93243	+	27.9732i	−0.184077	+	1.04395i
$719$	−15.7860	−	27.3421i	−0.588718	−	1.01969i	−0.994401	−	0.105675i	$-0.966300\pi$
$719$	−15.7860	−	27.3421i	−0.588718	−	1.01969i	0.405683	−	0.914014i	$-0.367034\pi$
$720$		0			0
$721$	4.79034	−	8.29711i	0.178402	−	0.309001i
$722$	−31.9395	−	26.8004i	−1.18867	−	0.997409i
$723$		0			0
$724$	4.19135	+	23.7704i	0.155770	+	0.883418i
$725$	−7.42026	+	6.22634i	−0.275582	+	0.231240i
$726$		0			0
$727$	−36.0929	+	13.1367i	−1.33861	+	0.487215i	−0.909375	−	0.415977i	$-0.863440\pi$
$727$	−36.0929	+	13.1367i	−1.33861	+	0.487215i	−0.429237	+	0.903192i	$0.641217\pi$
$728$	1.49595			0.0554436
$729$		0			0
$730$	−86.5599			−3.20373
$731$	−6.17157	+	2.24627i	−0.228264	+	0.0830812i
$732$		0			0
$733$	−23.2344	+	19.4959i	−0.858181	+	0.720099i	−0.961575	−	0.274541i	$-0.911474\pi$
$733$	−23.2344	+	19.4959i	−0.858181	+	0.720099i	0.103395	+	0.994640i	$0.467030\pi$
$734$	2.92200	+	16.5715i	0.107853	+	0.611664i
$735$		0			0
$736$	13.2187	+	11.0918i	0.487246	+	0.408848i
$737$	0.135721	−	0.235076i	0.00499936	−	0.00865915i
$738$		0			0
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	0.759256	−	0.650792i	$-0.225563\pi$
$739$	−5.00127	−	8.66245i	−0.183975	−	0.318653i	−0.943230	+	0.332139i	$0.892230\pi$
$740$	5.16126	−	29.2710i	0.189732	−	1.07602i
$741$		0			0
$742$	−21.0645	−	7.66683i	−0.773300	−	0.281458i
$743$	−34.0862	−	12.4064i	−1.25050	−	0.455145i	−0.369931	−	0.929059i	$-0.620619\pi$
$743$	−34.0862	−	12.4064i	−1.25050	−	0.455145i	−0.880571	+	0.473914i	$0.842841\pi$
$744$		0			0
$745$	−8.87626	+	50.3398i	−0.325201	+	1.84431i
$746$	−12.0865	−	20.9344i	−0.442517	−	0.766461i
$747$		0			0
$748$	0.461619	−	0.799548i	0.0168785	−	0.0292344i
$749$	3.85147	+	3.23177i	0.140730	+	0.118086i
$750$		0			0
$751$	−2.52734	−	14.3332i	−0.0922239	−	0.523028i	−0.995563	−	0.0941000i	$-0.970003\pi$
$751$	−2.52734	−	14.3332i	−0.0922239	−	0.523028i	0.903339	−	0.428928i	$-0.141108\pi$
$752$	5.32868	−	4.47129i	0.194317	−	0.163051i
$753$		0			0
$754$	13.2648	−	4.82799i	0.483076	−	0.175825i
$755$	−10.7700			−0.391959
$756$		0			0
$757$	−45.5754			−1.65646			−0.828232	−	0.560385i	$-0.810653\pi$
$757$	−45.5754			−1.65646			−0.828232	+	0.560385i	$0.810653\pi$
$758$	−48.0745	+	17.4977i	−1.74614	+	0.635544i
$759$		0			0
$760$	12.9928	−	10.9023i	0.471300	−	0.395468i
$761$	3.86290	+	21.9076i	0.140030	+	0.794150i	0.971224	+	0.238167i	$0.0765467\pi$
$761$	3.86290	+	21.9076i	0.140030	+	0.794150i	−0.831194	+	0.555982i	$0.812342\pi$
$762$		0			0
$763$	−5.44534	−	4.56918i	−0.197135	−	0.165416i
$764$	22.0189	−	38.1379i	0.796616	−	1.37978i
$765$		0			0
$766$	9.99393	+	17.3100i	0.361096	+	0.625436i
$767$	0.453310	−	2.57085i	0.0163681	−	0.0928279i
$768$		0			0
$769$	−12.8408	−	4.67368i	−0.463053	−	0.168537i	0.0999501	−	0.994992i	$-0.468132\pi$
$769$	−12.8408	−	4.67368i	−0.463053	−	0.168537i	−0.563003	+	0.826455i	$0.690354\pi$
$770$	1.64439	+	0.598510i	0.0592598	+	0.0215688i
$771$		0			0
$772$	4.55829	−	25.8513i	0.164056	−	0.930410i
$773$	10.3270	+	17.8869i	0.371436	+	0.643345i	0.989787	−	0.142557i	$-0.0455323\pi$
$773$	10.3270	+	17.8869i	0.371436	+	0.643345i	−0.618351	+	0.785902i	$0.712199\pi$
$774$		0			0
$775$	9.53628	−	16.5173i	0.342553	−	0.593319i
$776$	4.31990	+	3.62483i	0.155076	+	0.130124i
$777$		0			0
$778$	0.936404	+	5.31061i	0.0335717	+	0.190395i
$779$	27.8547	−	23.3729i	0.997999	−	0.837420i
$780$		0			0
$781$	−2.85753	+	1.04006i	−0.102250

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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	243.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +O(q^{10})\)	\(q+(1.98897 - 0.723928i) q^{2} +(1.89986 - 1.59417i) q^{4} +(-0.465915 - 2.64234i) q^{5} +(0.744850 + 0.625003i) q^{7} +(0.508086 - 0.880031i) q^{8} +(-2.83955 - 4.91825i) q^{10} +(-0.0550295 + 0.312088i) q^{11} +(1.42272 + 0.517829i) q^{13} +(1.93395 + 0.703898i) q^{14} +(-0.487835 + 2.76665i) q^{16} +(-0.587342 - 1.01731i) q^{17} +(-3.11040 + 5.38737i) q^{19} +(-5.09751 - 4.27732i) q^{20} +(0.116477 + 0.660572i) q^{22} +(1.65676 - 1.39018i) q^{23} +(-2.06640 + 0.752107i) q^{25} +3.20463 q^{26} +2.41147 q^{28} +(4.13926 - 1.50657i) q^{29} +(-6.64408 + 5.57504i) q^{31} +(1.38548 + 7.85742i) q^{32} +(-1.90466 - 1.59820i) q^{34} +(1.30443 - 2.25934i) q^{35} +(2.23332 + 3.86823i) q^{37} +(-2.28644 + 12.9671i) q^{38} +(-2.56206 - 0.932515i) q^{40} +(-5.49268 - 1.99917i) q^{41} +(0.970865 - 5.50605i) q^{43} +(0.392973 + 0.680649i) q^{44} +(2.28885 - 3.96441i) q^{46} +(-1.89678 - 1.59159i) q^{47} +(-1.05136 - 5.96259i) q^{49} +(-3.56554 + 2.99184i) q^{50} +(3.52848 - 1.28426i) q^{52} -10.8920 q^{53} +0.850279 q^{55} +(0.928471 - 0.337936i) q^{56} +(7.14224 - 5.99305i) q^{58} +(-0.299406 - 1.69802i) q^{59} +(0.777365 + 0.652287i) q^{61} +(-9.17898 + 15.8985i) q^{62} +(5.63455 + 9.75933i) q^{64} +(0.705410 - 4.00058i) q^{65} +(-0.804895 - 0.292958i) q^{67} +(-2.73763 - 0.996416i) q^{68} +(0.958882 - 5.43809i) q^{70} +(4.79788 + 8.31018i) q^{71} +(7.62091 - 13.1998i) q^{73} +(7.24234 + 6.07705i) q^{74} +(2.67907 + 15.1938i) q^{76} +(-0.236045 + 0.198065i) q^{77} +(10.5375 - 3.83533i) q^{79} +7.53771 q^{80} -12.3721 q^{82} +(-4.40239 + 1.60234i) q^{83} +(-2.41441 + 2.02593i) q^{85} +(-2.05496 - 11.6542i) q^{86} +(0.246687 + 0.206995i) q^{88} +(7.74976 - 13.4230i) q^{89} +(0.736071 + 1.27491i) q^{91} +(0.931414 - 5.28231i) q^{92} +(-4.92484 - 1.79249i) q^{94} +(15.6844 + 5.70867i) q^{95} +(-0.963658 + 5.46518i) q^{97} +(-6.40762 - 11.0983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8	\( 12 q + 3 q^{2} + 3 q^{4} - 3 q^{5} + 3 q^{7} + 6 q^{8} - 3 q^{10} + 3 q^{11} + 3 q^{13} + 6 q^{14} - 9 q^{16} + 9 q^{17} - 3 q^{19} - 21 q^{20} - 15 q^{22} + 24 q^{23} - 15 q^{25} - 30 q^{26} - 12 q^{28} + 30 q^{29} - 15 q^{31} - 27 q^{32} - 9 q^{34} + 12 q^{35} - 3 q^{37} - 12 q^{38} - 6 q^{40} - 21 q^{41} + 12 q^{43} + 3 q^{44} - 3 q^{46} + 3 q^{47} + 21 q^{49} + 12 q^{50} + 36 q^{52} - 18 q^{53} - 12 q^{55} + 3 q^{56} + 30 q^{58} + 15 q^{59} + 21 q^{61} - 12 q^{62} + 12 q^{64} - 24 q^{65} + 21 q^{67} - 18 q^{68} + 30 q^{70} + 27 q^{71} + 6 q^{73} - 12 q^{74} + 42 q^{76} - 3 q^{77} + 21 q^{79} + 42 q^{80} - 12 q^{82} - 33 q^{83} - 9 q^{85} - 30 q^{86} - 12 q^{88} + 9 q^{89} + 6 q^{91} + 42 q^{92} - 33 q^{94} + 30 q^{95} - 42 q^{97} - 45 q^{98}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 + 3 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 3 * q^13 + 6 * q^14 - 9 * q^16 + 9 * q^17 - 3 * q^19 - 21 * q^20 - 15 * q^22 + 24 * q^23 - 15 * q^25 - 30 * q^26 - 12 * q^28 + 30 * q^29 - 15 * q^31 - 27 * q^32 - 9 * q^34 + 12 * q^35 - 3 * q^37 - 12 * q^38 - 6 * q^40 - 21 * q^41 + 12 * q^43 + 3 * q^44 - 3 * q^46 + 3 * q^47 + 21 * q^49 + 12 * q^50 + 36 * q^52 - 18 * q^53 - 12 * q^55 + 3 * q^56 + 30 * q^58 + 15 * q^59 + 21 * q^61 - 12 * q^62 + 12 * q^64 - 24 * q^65 + 21 * q^67 - 18 * q^68 + 30 * q^70 + 27 * q^71 + 6 * q^73 - 12 * q^74 + 42 * q^76 - 3 * q^77 + 21 * q^79 + 42 * q^80 - 12 * q^82 - 33 * q^83 - 9 * q^85 - 30 * q^86 - 12 * q^88 + 9 * q^89 + 6 * q^91 + 42 * q^92 - 33 * q^94 + 30 * q^95 - 42 * q^97 - 45 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more