LMFDB - Embedded newform 720.2.u.a.539.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(179,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 2]))

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

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

chi := DirichletCharacter("720.179");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.u (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			539.12
Character	$\chi$	$=$	720.539
Dual form			720.2.u.a.179.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.04776 + 0.949842i) q^{2} +(0.195601 - 1.99041i) q^{4} +(2.18619 + 0.469629i) q^{5} +2.94937i q^{7} +(1.68563 + 2.27126i) q^{8} +O(q^{10})$	\(q+(-1.04776 + 0.949842i) q^{2} +(0.195601 - 1.99041i) q^{4} +(2.18619 + 0.469629i) q^{5} +2.94937i q^{7} +(1.68563 + 2.27126i) q^{8} +(-2.73668 + 1.58448i) q^{10} +(3.81783 + 3.81783i) q^{11} +(-0.772847 - 0.772847i) q^{13} +(-2.80143 - 3.09023i) q^{14} +(-3.92348 - 0.778653i) q^{16} +2.27916 q^{17} +(-5.18129 - 5.18129i) q^{19} +(1.36238 - 4.25957i) q^{20} +(-7.62651 - 0.373835i) q^{22} -2.63370 q^{23} +(4.55890 + 2.05340i) q^{25} +(1.54384 + 0.0756756i) q^{26} +(5.87045 + 0.576899i) q^{28} +(3.25626 + 3.25626i) q^{29} +1.93666i q^{31} +(4.85046 - 2.91084i) q^{32} +(-2.38802 + 2.16484i) q^{34} +(-1.38511 + 6.44789i) q^{35} +(-2.66367 + 2.66367i) q^{37} +(10.3501 + 0.507341i) q^{38} +(2.61847 + 5.75705i) q^{40} -1.01630 q^{41} +(4.46535 + 4.46535i) q^{43} +(8.34584 - 6.85229i) q^{44} +(2.75948 - 2.50160i) q^{46} +6.93871i q^{47} -1.69876 q^{49} +(-6.72704 + 2.17876i) q^{50} +(-1.68945 + 1.38711i) q^{52} +(-9.01752 - 9.01752i) q^{53} +(6.55356 + 10.1395i) q^{55} +(-6.69879 + 4.97155i) q^{56} +(-6.50472 - 0.318847i) q^{58} +(2.82309 + 2.82309i) q^{59} +(10.8603 - 10.8603i) q^{61} +(-1.83952 - 2.02916i) q^{62} +(-2.31728 + 7.65704i) q^{64} +(-1.32664 - 2.05255i) q^{65} +(-7.21414 + 7.21414i) q^{67} +(0.445807 - 4.53647i) q^{68} +(-4.67321 - 8.07147i) q^{70} +8.03085i q^{71} -1.58003 q^{73} +(0.260821 - 5.32095i) q^{74} +(-11.3264 + 9.29943i) q^{76} +(-11.2602 + 11.2602i) q^{77} -0.288222i q^{79} +(-8.21181 - 3.54487i) q^{80} +(1.06484 - 0.965323i) q^{82} +(8.90062 + 8.90062i) q^{83} +(4.98270 + 1.07036i) q^{85} +(-8.91999 - 0.437238i) q^{86} +(-2.23584 + 15.1068i) q^{88} +6.44258 q^{89} +(2.27941 - 2.27941i) q^{91} +(-0.515154 + 5.24214i) q^{92} +(-6.59067 - 7.27010i) q^{94} +(-8.89402 - 13.7606i) q^{95} -18.1267i q^{97} +(1.77989 - 1.61355i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q+O(q^{10}) $ 96 * q	$ 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) $ 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$-1$	$-1$

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 $

$2$	−1.04776	+	0.949842i	−0.740878	+	0.671640i
$2$	−1.04776	+	0.949842i	−0.740878	+	0.671640i
$3$		0			0
$3$		0			0
$4$	0.195601	−	1.99041i	0.0978005	−	0.995206i
$5$	2.18619	+	0.469629i	0.977696	+	0.210025i
$5$	2.18619	+	0.469629i	0.977696	+	0.210025i
$6$		0			0
$7$			2.94937i			1.11476i	0.830259	+	0.557378i	$0.188193\pi$
$7$			2.94937i			1.11476i	−0.830259	+	0.557378i	$0.811807\pi$
$8$	1.68563	+	2.27126i	0.595962	+	0.803013i
$9$		0			0
$10$	−2.73668	+	1.58448i	−0.865414	+	0.501057i
$11$	3.81783	+	3.81783i	1.15112	+	1.15112i	0.986328	+	0.164792i	$0.0526952\pi$
$11$	3.81783	+	3.81783i	1.15112	+	1.15112i	0.164792	+	0.986328i	$0.447305\pi$
$12$		0			0
$13$	−0.772847	−	0.772847i	−0.214349	−	0.214349i	0.591763	−	0.806112i	$-0.298432\pi$
$13$	−0.772847	−	0.772847i	−0.214349	−	0.214349i	−0.806112	+	0.591763i	$0.798432\pi$
$14$	−2.80143	−	3.09023i	−0.748714	−	0.825898i
$15$		0			0
$16$	−3.92348	−	0.778653i	−0.980870	−	0.194663i
$17$	2.27916			0.552778			0.276389	−	0.961046i	$-0.410862\pi$
$17$	2.27916			0.552778			0.276389	+	0.961046i	$0.410862\pi$
$18$		0			0
$19$	−5.18129	−	5.18129i	−1.18867	−	1.18867i	−0.977436	−	0.211233i	$-0.932252\pi$
$19$	−5.18129	−	5.18129i	−1.18867	−	1.18867i	−0.211233	−	0.977436i	$-0.567748\pi$
$20$	1.36238	−	4.25957i	0.304637	−	0.952469i
$21$		0			0
$22$	−7.62651	−	0.373835i	−1.62598	−	0.0797018i
$23$	−2.63370			−0.549164			−0.274582	−	0.961564i	$-0.588539\pi$
$23$	−2.63370			−0.549164			−0.274582	+	0.961564i	$0.588539\pi$
$24$		0			0
$25$	4.55890	+	2.05340i	0.911779	+	0.410681i
$26$	1.54384	+	0.0756756i	0.302772	+	0.0148412i
$27$		0			0
$28$	5.87045	+	0.576899i	1.10941	+	0.109024i
$29$	3.25626	+	3.25626i	0.604673	+	0.604673i	0.941549	−	0.336876i	$-0.109370\pi$
$29$	3.25626	+	3.25626i	0.604673	+	0.604673i	−0.336876	+	0.941549i	$0.609370\pi$
$30$		0			0
$31$			1.93666i			0.347835i	0.984760	+	0.173917i	$0.0556426\pi$
$31$			1.93666i			0.347835i	−0.984760	+	0.173917i	$0.944357\pi$
$32$	4.85046	−	2.91084i	0.857449	−	0.514569i
$33$		0			0
$34$	−2.38802	+	2.16484i	−0.409541	+	0.371268i
$35$	−1.38511	+	6.44789i	−0.234126	+	1.08989i
$36$		0			0
$37$	−2.66367	+	2.66367i	−0.437904	+	0.437904i	−0.891306	−	0.453402i	$-0.850210\pi$
$37$	−2.66367	+	2.66367i	−0.437904	+	0.437904i	0.453402	+	0.891306i	$0.350210\pi$
$38$	10.3501	+	0.507341i	1.67902	+	0.0823016i
$39$		0			0
$40$	2.61847	+	5.75705i	0.414017	+	0.910269i
$41$	−1.01630			−0.158719			−0.0793596	−	0.996846i	$-0.525288\pi$
$41$	−1.01630			−0.158719			−0.0793596	+	0.996846i	$0.525288\pi$
$42$		0			0
$43$	4.46535	+	4.46535i	0.680959	+	0.680959i	0.960216	−	0.279257i	$-0.0900882\pi$
$43$	4.46535	+	4.46535i	0.680959	+	0.680959i	−0.279257	+	0.960216i	$0.590088\pi$
$44$	8.34584	−	6.85229i	1.25818	−	1.03302i
$45$		0			0
$46$	2.75948	−	2.50160i	0.406864	−	0.368840i
$47$			6.93871i			1.01211i	0.862500	+	0.506057i	$0.168898\pi$
$47$			6.93871i			1.01211i	−0.862500	+	0.506057i	$0.831102\pi$
$48$		0			0
$49$	−1.69876			−0.242680
$50$	−6.72704	+	2.17876i	−0.951347	+	0.308123i
$51$		0			0
$52$	−1.68945	+	1.38711i	−0.234285	+	0.192358i
$53$	−9.01752	−	9.01752i	−1.23865	−	1.23865i	−0.960552	−	0.278099i	$-0.910296\pi$
$53$	−9.01752	−	9.01752i	−1.23865	−	1.23865i	−0.278099	−	0.960552i	$-0.589704\pi$
$54$		0			0
$55$	6.55356	+	10.1395i	0.883682	+	1.36721i
$56$	−6.69879	+	4.97155i	−0.895163	+	0.664351i
$57$		0			0
$58$	−6.50472	−	0.318847i	−0.854111	−	0.0418666i
$59$	2.82309	+	2.82309i	0.367536	+	0.367536i	0.866578	−	0.499042i	$-0.166315\pi$
$59$	2.82309	+	2.82309i	0.367536	+	0.367536i	−0.499042	+	0.866578i	$0.666315\pi$
$60$		0			0
$61$	10.8603	−	10.8603i	1.39052	−	1.39052i	0.566365	−	0.824154i	$-0.308349\pi$
$61$	10.8603	−	10.8603i	1.39052	−	1.39052i	0.824154	−	0.566365i	$-0.191651\pi$
$62$	−1.83952	−	2.02916i	−0.233620	−	0.257703i
$63$		0			0
$64$	−2.31728	+	7.65704i	−0.289660	+	0.957130i
$65$	−1.32664	−	2.05255i	−0.164550	−	0.254587i
$66$		0			0
$67$	−7.21414	+	7.21414i	−0.881347	+	0.881347i	−0.993672	−	0.112324i	$-0.964170\pi$
$67$	−7.21414	+	7.21414i	−0.881347	+	0.881347i	0.112324	+	0.993672i	$0.464170\pi$
$68$	0.445807	−	4.53647i	0.0540620	−	0.550128i
$69$		0			0
$70$	−4.67321	−	8.07147i	−0.558556	−	0.964726i
$71$			8.03085i			0.953087i	0.879151	+	0.476543i	$0.158110\pi$
$71$			8.03085i			0.953087i	−0.879151	+	0.476543i	$0.841890\pi$
$72$		0			0
$73$	−1.58003			−0.184929			−0.0924645	−	0.995716i	$-0.529474\pi$
$73$	−1.58003			−0.184929			−0.0924645	+	0.995716i	$0.529474\pi$
$74$	0.260821	−	5.32095i	0.0303198	−	0.618548i
$75$		0			0
$76$	−11.3264	+	9.29943i	−1.29922	+	1.06672i
$77$	−11.2602	+	11.2602i	−1.28322	+	1.28322i
$78$		0			0
$79$		−	0.288222i		−	0.0324275i	−0.999869	−	0.0162137i	$-0.994839\pi$
$79$		−	0.288222i		−	0.0324275i	0.999869	−	0.0162137i	$-0.00516122\pi$
$80$	−8.21181	−	3.54487i	−0.918109	−	0.396329i
$81$		0			0
$82$	1.06484	−	0.965323i	0.117592	−	0.106602i
$83$	8.90062	+	8.90062i	0.976970	+	0.976970i	0.999741	−	0.0227710i	$-0.00724886\pi$
$83$	8.90062	+	8.90062i	0.976970	+	0.976970i	−0.0227710	+	0.999741i	$0.507249\pi$
$84$		0			0
$85$	4.98270	+	1.07036i	0.540449	+	0.116097i
$86$	−8.91999	−	0.437238i	−0.961867	−	0.0471486i
$87$		0			0
$88$	−2.23584	+	15.1068i	−0.238341	+	1.61039i
$89$	6.44258			0.682912			0.341456	−	0.939898i	$-0.389080\pi$
$89$	6.44258			0.682912			0.341456	+	0.939898i	$0.389080\pi$
$90$		0			0
$91$	2.27941	−	2.27941i	0.238947	−	0.238947i
$92$	−0.515154	+	5.24214i	−0.0537085	+	0.546531i
$93$		0			0
$94$	−6.59067	−	7.27010i	−0.679776	−	0.749853i
$95$	−8.89402	−	13.7606i	−0.912507	−	1.41181i
$96$		0			0
$97$		−	18.1267i		−	1.84049i	−0.391342	−	0.920245i	$-0.627989\pi$
$97$		−	18.1267i		−	1.84049i	0.391342	−	0.920245i	$-0.372011\pi$
$98$	1.77989	−	1.61355i	0.179796	−	0.162994i
$99$		0			0
$100$	4.97884	−	8.67243i	0.497884	−	0.867243i
$101$	−11.2655	+	11.2655i	−1.12096	+	1.12096i	−0.129357	+	0.991598i	$0.541291\pi$
$101$	−11.2655	+	11.2655i	−1.12096	+	1.12096i	−0.991598	+	0.129357i	$0.958709\pi$
$102$		0			0
$103$		−	4.58275i		−	0.451552i	−0.974179	−	0.225776i	$-0.927508\pi$
$103$		−	4.58275i		−	0.451552i	0.974179	−	0.225776i	$-0.0724918\pi$
$104$	0.452603	−	3.05808i	0.0443813	−	0.299869i
$105$		0			0
$106$	18.0134	+	0.882977i	1.74962	+	0.0857623i
$107$	2.70168	−	2.70168i	0.261181	−	0.261181i	−0.564353	−	0.825534i	$-0.690874\pi$
$107$	2.70168	−	2.70168i	0.261181	−	0.261181i	0.825534	+	0.564353i	$0.190874\pi$
$108$		0			0
$109$	5.05700	−	5.05700i	0.484372	−	0.484372i	−0.422152	−	0.906525i	$-0.638725\pi$
$109$	5.05700	−	5.05700i	0.484372	−	0.484372i	0.906525	+	0.422152i	$0.138725\pi$
$110$	−16.4975	−	4.39891i	−1.57297	−	0.419420i
$111$		0			0
$112$	2.29653	−	11.5718i	0.217002	−	1.09343i
$113$	−11.0909			−1.04334			−0.521672	−	0.853146i	$-0.674691\pi$
$113$	−11.0909			−1.04334			−0.521672	+	0.853146i	$0.674691\pi$
$114$		0			0
$115$	−5.75778	−	1.23686i	−0.536915	−	0.115338i
$116$	7.11824	−	5.84438i	0.660912	−	0.542637i
$117$		0			0
$118$	−5.63942	−	0.276432i	−0.519150	−	0.0254476i
$119$			6.72209i			0.616213i
$120$		0			0
$121$			18.1517i			1.65016i
$122$	−1.06342	+	21.6946i	−0.0962774	+	1.96413i
$123$		0			0
$124$	3.85475	+	0.378813i	0.346167	+	0.0340184i
$125$	9.00230	+	6.63013i	0.805190	+	0.593017i
$126$		0			0
$127$	−10.4288			−0.925403			−0.462701	−	0.886514i	$-0.653120\pi$
$127$	−10.4288			−0.925403			−0.462701	+	0.886514i	$0.653120\pi$
$128$	−4.84502	−	10.2238i	−0.428244	−	0.903663i
$129$		0			0
$130$	3.33960	+	0.890475i	0.292902	+	0.0780998i
$131$	13.5532	−	13.5532i	1.18415	−	1.18415i	0.205491	−	0.978659i	$-0.434121\pi$
$131$	13.5532	−	13.5532i	1.18415	−	1.18415i	0.978659	−	0.205491i	$-0.0658791\pi$
$132$		0			0
$133$	15.2815	−	15.2815i	1.32507	−	1.32507i
$134$	0.706394	−	14.4110i	0.0610231	−	1.24492i
$135$		0			0
$136$	3.84183	+	5.17658i	0.329435	+	0.443888i
$137$		−	7.61130i		−	0.650278i	−0.945666	−	0.325139i	$-0.894589\pi$
$137$		−	7.61130i		−	0.650278i	0.945666	−	0.325139i	$-0.105411\pi$
$138$		0			0
$139$	1.68008	−	1.68008i	0.142502	−	0.142502i	−0.632257	−	0.774759i	$-0.717871\pi$
$139$	1.68008	−	1.68008i	0.142502	−	0.142502i	0.774759	+	0.632257i	$0.217871\pi$
$140$	12.5630	+	4.01815i	1.06177	+	0.339596i
$141$		0			0
$142$	−7.62804	−	8.41440i	−0.640131	−	0.706121i
$143$		−	5.90120i		−	0.493484i
$144$		0			0
$145$	5.58959	+	8.64807i	0.464190	+	0.718183i
$146$	1.65550	−	1.50078i	0.137010	−	0.124206i
$147$		0			0
$148$	4.78078	+	5.82281i	0.392978	+	0.478632i
$149$	13.1900	−	13.1900i	1.08057	−	1.08057i	0.0841097	−	0.996456i	$-0.473195\pi$
$149$	13.1900	−	13.1900i	1.08057	−	1.08057i	0.996456	−	0.0841097i	$-0.0268046\pi$
$150$		0			0
$151$	−14.8005			−1.20444			−0.602222	−	0.798329i	$-0.705718\pi$
$151$	−14.8005			−1.20444			−0.602222	+	0.798329i	$0.705718\pi$
$152$	3.03432	−	20.5018i	0.246116	−	1.66292i
$153$		0			0
$154$	1.10257	−	22.4934i	0.0888480	−	1.81257i
$155$	−0.909513	+	4.23392i	−0.0730539	+	0.340077i
$156$		0			0
$157$	10.2112	+	10.2112i	0.814942	+	0.814942i	0.985370	−	0.170428i	$-0.0545151\pi$
$157$	10.2112	+	10.2112i	0.814942	+	0.814942i	−0.170428	+	0.985370i	$0.554515\pi$
$158$	0.273765	+	0.301987i	0.0217796	+	0.0240248i
$159$		0			0
$160$	11.9711	−	4.08575i	0.946397	−	0.323007i
$161$		−	7.76774i		−	0.612184i
$162$		0			0
$163$	11.3893	−	11.3893i	0.892077	−	0.892077i	−0.102641	−	0.994718i	$-0.532729\pi$
$163$	11.3893	−	11.3893i	0.892077	−	0.892077i	0.994718	+	0.102641i	$0.0327294\pi$
$164$	−0.198789	+	2.02285i	−0.0155228	+	0.157958i
$165$		0			0
$166$	−17.7799	−	0.871530i	−1.37999	−	0.0676439i
$167$	10.0783			0.779880			0.389940	−	0.920840i	$-0.372496\pi$
$167$	10.0783			0.779880			0.389940	+	0.920840i	$0.372496\pi$
$168$		0			0
$169$		−	11.8054i		−	0.908109i
$170$	−6.23734	+	3.61129i	−0.478382	+	0.276973i
$171$		0			0
$172$	9.76131	−	8.01446i	0.744293	−	0.611097i
$173$	−9.02442	+	9.02442i	−0.686114	+	0.686114i	−0.961371	−	0.275257i	$-0.911237\pi$
$173$	−9.02442	+	9.02442i	−0.686114	+	0.686114i	0.275257	+	0.961371i	$0.411237\pi$
$174$		0			0
$175$	−6.05624	+	13.4459i	−0.457809	+	1.01641i
$176$	−12.0064	−	17.9520i	−0.905019	−	1.35318i
$177$		0			0
$178$	−6.75028	+	6.11943i	−0.505955	+	0.458671i
$179$	10.3226	−	10.3226i	0.771547	−	0.771547i	−0.206830	−	0.978377i	$-0.566315\pi$
$179$	10.3226	−	10.3226i	0.771547	−	0.771547i	0.978377	+	0.206830i	$0.0663146\pi$
$180$		0			0
$181$	13.9184	+	13.9184i	1.03455	+	1.03455i	0.999381	+	0.0351674i	$0.0111964\pi$
$181$	13.9184	+	13.9184i	1.03455	+	1.03455i	0.0351674	+	0.999381i	$0.488804\pi$
$182$	−0.223195	+	4.55335i	−0.0165443	+	0.337517i
$183$		0			0
$184$	−4.43945	−	5.98182i	−0.327281	−	0.440986i
$185$	−7.07423	+	4.57236i	−0.520108	+	0.336167i
$186$		0			0
$187$	8.70147	+	8.70147i	0.636314	+	0.636314i
$188$	13.8109	+	1.35722i	1.00726	+	0.0989853i
$189$		0			0
$190$	22.3892	+	5.96988i	1.62428	+	0.433100i
$191$	−12.3885			−0.896403			−0.448202	−	0.893932i	$-0.647935\pi$
$191$	−12.3885			−0.896403			−0.448202	+	0.893932i	$0.647935\pi$
$192$		0			0
$193$		−	23.2784i		−	1.67562i	−0.545965	−	0.837808i	$-0.683837\pi$
$193$		−	23.2784i		−	1.67562i	0.545965	−	0.837808i	$-0.316163\pi$
$194$	17.2175	+	18.9925i	1.23615	+	1.36358i
$195$		0			0
$196$	−0.332279	+	3.38123i	−0.0237342	+	0.241517i
$197$	0.494769	+	0.494769i	0.0352508	+	0.0352508i	0.724513	−	0.689262i	$-0.242065\pi$
$197$	0.494769	+	0.494769i	0.0352508	+	0.0352508i	−0.689262	+	0.724513i	$0.742065\pi$
$198$		0			0
$199$	2.97860			0.211147			0.105574	−	0.994411i	$-0.466332\pi$
$199$	2.97860			0.211147			0.105574	+	0.994411i	$0.466332\pi$
$200$	3.02081	+	13.8157i	0.213603	+	0.976920i
$201$		0			0
$202$	1.10309	−	22.5039i	0.0776132	−	1.58337i
$203$	−9.60392	+	9.60392i	−0.674063	+	0.674063i
$204$		0			0
$205$	−2.22183	−	0.477284i	−0.155179	−	0.0333349i
$206$	4.35289	+	4.80163i	0.303280	+	0.334545i
$207$		0			0
$208$	2.43047	+	3.63403i	0.168523	+	0.251975i
$209$		−	39.5626i		−	2.73660i
$210$		0			0
$211$	−9.97252	−	9.97252i	−0.686537	−	0.686537i	0.274928	−	0.961465i	$-0.411346\pi$
$211$	−9.97252	−	9.97252i	−0.686537	−	0.686537i	−0.961465	+	0.274928i	$0.911346\pi$
$212$	−19.7124	+	16.1847i	−1.35385	+	1.11157i
$213$		0			0
$214$	−0.264543	+	5.39688i	−0.0180838	+	0.368923i
$215$	7.66506	+	11.8592i	0.522753	+	0.808790i
$216$		0			0
$217$	−5.71192			−0.387751
$218$	−0.495171	+	10.1019i	−0.0335372	+	0.684185i
$219$		0			0
$220$	21.4637	−	11.0610i	1.44708	−	0.745732i
$221$	−1.76144	−	1.76144i	−0.118488	−	0.118488i
$222$		0			0
$223$	−1.35577			−0.0907889			−0.0453945	−	0.998969i	$-0.514454\pi$
$223$	−1.35577			−0.0907889			−0.0453945	+	0.998969i	$0.514454\pi$
$224$	8.58514	+	14.3058i	0.573619	+	0.955846i
$225$		0			0
$226$	11.6206	−	10.5346i	0.772990	−	0.700751i
$227$	−0.282506	−	0.282506i	−0.0187506	−	0.0187506i	0.697669	−	0.716420i	$-0.254220\pi$
$227$	−0.282506	−	0.282506i	−0.0187506	−	0.0187506i	−0.716420	+	0.697669i	$0.754220\pi$
$228$		0			0
$229$	3.61973	+	3.61973i	0.239199	+	0.239199i	0.816518	−	0.577320i	$-0.195901\pi$
$229$	3.61973	+	3.61973i	0.239199	+	0.239199i	−0.577320	+	0.816518i	$0.695901\pi$
$230$	7.20759	−	4.17304i	0.475254	−	0.275162i
$231$		0			0
$232$	−1.90697	+	12.8847i	−0.125198	+	0.845922i
$233$		−	19.3142i		−	1.26531i	−0.774432	−	0.632657i	$-0.781964\pi$
$233$		−	19.3142i		−	1.26531i	0.774432	−	0.632657i	$-0.218036\pi$
$234$		0			0
$235$	−3.25862	+	15.1694i	−0.212569	+	0.989540i
$236$	6.17132	−	5.06692i	0.401719	−	0.329828i
$237$		0			0
$238$	−6.38492	−	7.04313i	−0.413873	−	0.456538i
$239$	−12.7616			−0.825481			−0.412740	−	0.910849i	$-0.635428\pi$
$239$	−12.7616			−0.825481			−0.412740	+	0.910849i	$0.635428\pi$
$240$		0			0
$241$	−9.03963			−0.582294			−0.291147	−	0.956678i	$-0.594037\pi$
$241$	−9.03963			−0.582294			−0.291147	+	0.956678i	$0.594037\pi$
$242$	−17.2413	−	19.0186i	−1.10831	−	1.22256i
$243$		0			0
$244$	−19.4922	−	23.7408i	−1.24786	−	1.51985i
$245$	−3.71382	−	0.797788i	−0.237267	−	0.0509688i
$246$		0			0
$247$			8.00868i			0.509580i
$248$	−4.39867	+	3.26450i	−0.279316	+	0.207296i
$249$		0			0
$250$	−15.7298	+	1.60397i	−0.994841	+	0.101444i
$251$	−7.63101	−	7.63101i	−0.481665	−	0.481665i	0.423998	−	0.905663i	$-0.360626\pi$
$251$	−7.63101	−	7.63101i	−0.481665	−	0.481665i	−0.905663	+	0.423998i	$0.860626\pi$
$252$		0			0
$253$	−10.0550	−	10.0550i	−0.632154	−	0.632154i
$254$	10.9268	−	9.90567i	0.685611	−	0.621537i
$255$		0			0
$256$	14.7874	+	6.11006i	0.924212	+	0.381879i
$257$	9.14111			0.570207			0.285103	−	0.958497i	$-0.407972\pi$
$257$	9.14111			0.570207			0.285103	+	0.958497i	$0.407972\pi$
$258$		0			0
$259$	−7.85613	−	7.85613i	−0.488156	−	0.488156i
$260$	−4.34491	+	2.23909i	−0.269460	+	0.138862i
$261$		0			0
$262$	−1.32710	+	27.0739i	−0.0819887	+	1.67263i
$263$	−5.35127			−0.329974			−0.164987	−	0.986296i	$-0.552758\pi$
$263$	−5.35127			−0.329974			−0.164987	+	0.986296i	$0.552758\pi$
$264$		0			0
$265$	−15.4792	−	23.9489i	−0.950877	−	1.47117i
$266$	−1.49633	+	30.5264i	−0.0917461	+	1.87169i
$267$		0			0
$268$	12.9480	+	15.7702i	0.790926	+	0.963318i
$269$	17.5132	+	17.5132i	1.06780	+	1.06780i	0.997528	+	0.0702731i	$0.0223871\pi$
$269$	17.5132	+	17.5132i	1.06780	+	1.06780i	0.0702731	+	0.997528i	$0.477613\pi$
$270$		0			0
$271$		−	14.8401i		−	0.901471i	−0.892657	−	0.450736i	$-0.851162\pi$
$271$		−	14.8401i		−	0.901471i	0.892657	−	0.450736i	$-0.148838\pi$
$272$	−8.94225	−	1.77468i	−0.542204	−	0.107606i
$273$		0			0
$274$	7.22953	+	7.97482i	0.436752	+	0.481776i
$275$	9.56556	+	25.2447i	0.576825	+	1.52231i
$276$		0			0
$277$	−9.59587	+	9.59587i	−0.576560	+	0.576560i	−0.933954	−	0.357394i	$-0.883665\pi$
$277$	−9.59587	+	9.59587i	−0.576560	+	0.576560i	0.357394	+	0.933954i	$0.383665\pi$
$278$	−0.164510	+	3.35613i	−0.00986665	+	0.201287i
$279$		0			0
$280$	−16.9796	+	7.72283i	−1.01473	+	0.461527i
$281$	−24.1743			−1.44212			−0.721059	−	0.692874i	$-0.756344\pi$
$281$	−24.1743			−1.44212			−0.721059	+	0.692874i	$0.756344\pi$
$282$		0			0
$283$	−22.5338	−	22.5338i	−1.33950	−	1.33950i	−0.896546	−	0.442950i	$-0.853932\pi$
$283$	−22.5338	−	22.5338i	−1.33950	−	1.33950i	−0.442950	−	0.896546i	$-0.646068\pi$
$284$	15.9847	+	1.57084i	0.948518	+	0.0932124i
$285$		0			0
$286$	5.60521	+	6.18304i	0.331443	+	0.365611i
$287$		−	2.99744i		−	0.176933i
$288$		0			0
$289$	−11.8054			−0.694436
$290$	−14.0708	−	3.75187i	−0.826268	−	0.220317i
$291$		0			0
$292$	−0.309057	+	3.14492i	−0.0180862	+	0.184043i
$293$	−2.21485	−	2.21485i	−0.129393	−	0.129393i	0.639445	−	0.768837i	$-0.279164\pi$
$293$	−2.21485	−	2.21485i	−0.129393	−	0.129393i	−0.768837	+	0.639445i	$0.779164\pi$
$294$		0			0
$295$	4.84603	+	7.49764i	0.282147	+	0.436530i
$296$	−10.5399	−	1.55992i	−0.612617	−	0.0906687i
$297$		0			0
$298$	−1.29154	+	26.3483i	−0.0748167	+	1.52632i
$299$	2.03545	+	2.03545i	0.117713	+	0.117713i
$300$		0			0
$301$	−13.1699	+	13.1699i	−0.759103	+	0.759103i
$302$	15.5073	−	14.0581i	0.892346	−	0.808952i
$303$		0			0
$304$	16.2942	+	24.3631i	0.934539	+	1.39732i
$305$	28.8431	−	18.6424i	1.65155	−	1.06746i
$306$		0			0
$307$	12.5025	−	12.5025i	0.713556	−	0.713556i	−0.253722	−	0.967277i	$-0.581655\pi$
$307$	12.5025	−	12.5025i	0.713556	−	0.713556i	0.967277	+	0.253722i	$0.0816547\pi$
$308$	20.2099	+	24.6149i	1.15157	+	1.40257i
$309$		0			0
$310$	−3.06860	−	5.30002i	−0.174285	−	0.301021i
$311$			3.75997i			0.213209i	0.994302	+	0.106604i	$0.0339978\pi$
$311$			3.75997i			0.213209i	−0.994302	+	0.106604i	$0.966002\pi$
$312$		0			0
$313$	6.19979			0.350433			0.175216	−	0.984530i	$-0.443938\pi$
$313$	6.19979			0.350433			0.175216	+	0.984530i	$0.443938\pi$
$314$	−20.3979	−	0.999859i	−1.15112	−	0.0564253i
$315$		0			0
$316$	−0.573680	−	0.0563765i	−0.0322720	−	0.00317143i
$317$	13.6244	−	13.6244i	0.765221	−	0.765221i	−0.212040	−	0.977261i	$-0.568011\pi$
$317$	13.6244	−	13.6244i	0.765221	−	0.765221i	0.977261	+	0.212040i	$0.0680108\pi$
$318$		0			0
$319$			24.8638i			1.39210i
$320$	−8.66199	+	15.6515i	−0.484220	+	0.874946i
$321$		0			0
$322$	7.37812	+	8.13873i	0.411167	+	0.453553i
$323$	−11.8090	−	11.8090i	−0.657070	−	0.657070i
$324$		0			0
$325$	−1.93636	−	5.11030i	−0.107410	−	0.283468i
$326$	−1.11521	+	22.7512i	−0.0617660	+	1.26007i
$327$		0			0
$328$	−1.71311	−	2.30828i	−0.0945905	−	0.127454i
$329$	−20.4648			−1.12826
$330$		0			0
$331$	11.4420	−	11.4420i	0.628910	−	0.628910i	−0.318884	−	0.947794i	$-0.603308\pi$
$331$	11.4420	−	11.4420i	0.628910	−	0.628910i	0.947794	+	0.318884i	$0.103308\pi$
$332$	19.4569	−	15.9749i	1.06783	−	0.876738i
$333$		0			0
$334$	−10.5596	+	9.57276i	−0.577796	+	0.523798i
$335$	−19.1595	+	12.3835i	−1.04679	+	0.676585i
$336$		0			0
$337$		−	9.70392i		−	0.528606i	−0.964440	−	0.264303i	$-0.914858\pi$
$337$		−	9.70392i		−	0.528606i	0.964440	−	0.264303i	$-0.0851419\pi$
$338$	11.2133	+	12.3692i	0.609922	+	0.672798i
$339$		0			0
$340$	3.10508	−	9.70825i	0.168397	−	0.526504i
$341$	−7.39385	+	7.39385i	−0.400400	+	0.400400i
$342$		0			0
$343$			15.6353i			0.844227i
$344$	−2.61504	+	17.6689i	−0.140994	+	0.952645i
$345$		0			0
$346$	0.883653	−	18.0272i	0.0475055	−	0.969149i
$347$	16.6678	−	16.6678i	0.894776	−	0.894776i	−0.100192	−	0.994968i	$-0.531946\pi$
$347$	16.6678	−	16.6678i	0.894776	−	0.894776i	0.994968	+	0.100192i	$0.0319458\pi$
$348$		0			0
$349$	0.985320	−	0.985320i	0.0527430	−	0.0527430i	−0.680243	−	0.732986i	$-0.738126\pi$
$349$	0.985320	−	0.985320i	0.0527430	−	0.0527430i	0.732986	+	0.680243i	$0.238126\pi$
$350$	−6.42595	−	19.8405i	−0.343482	−	1.06052i
$351$		0			0
$352$	29.6314	+	7.40514i	1.57936	+	0.394695i
$353$	18.6331			0.991742			0.495871	−	0.868396i	$-0.334849\pi$
$353$	18.6331			0.991742			0.495871	+	0.868396i	$0.334849\pi$
$354$		0			0
$355$	−3.77152	+	17.5570i	−0.200172	+	0.931829i
$356$	1.26018	−	12.8234i	0.0667892	−	0.679638i
$357$		0			0
$358$	−1.01077	+	20.6204i	−0.0534207	+	1.08982i
$359$		−	15.6789i		−	0.827503i	−0.910390	−	0.413751i	$-0.864218\pi$
$359$		−	15.6789i		−	0.827503i	0.910390	−	0.413751i	$-0.135782\pi$
$360$		0			0
$361$			34.6914i			1.82586i
$362$	−27.8035	−	1.36286i	−1.46132	−	0.0716306i
$363$		0			0
$364$	−4.09111	−	4.98282i	−0.214432	−	0.261171i
$365$	−3.45426	−	0.742031i	−0.180804	−	0.0388397i
$366$		0			0
$367$	−24.8012			−1.29461			−0.647305	−	0.762231i	$-0.724104\pi$
$367$	−24.8012			−1.29461			−0.647305	+	0.762231i	$0.724104\pi$
$368$	10.3333	+	2.05074i	0.538659	+	0.106902i
$369$		0			0
$370$	3.06908	−	11.5101i	0.159554	−	0.598384i
$371$	26.5960	−	26.5960i	1.38079	−	1.38079i
$372$		0			0
$373$	−7.99818	+	7.99818i	−0.414130	+	0.414130i	−0.883175	−	0.469045i	$-0.844598\pi$
$373$	−7.99818	+	7.99818i	−0.414130	+	0.414130i	0.469045	+	0.883175i	$0.344598\pi$
$374$	−17.3821	−	0.852030i	−0.898805	−	0.0440574i
$375$		0			0
$376$	−15.7596	+	11.6961i	−0.812741	+	0.603181i
$377$		−	5.03319i		−	0.259222i
$378$		0			0
$379$	−5.54375	+	5.54375i	−0.284763	+	0.284763i	−0.835005	−	0.550242i	$-0.814536\pi$
$379$	−5.54375	+	5.54375i	−0.284763	+	0.284763i	0.550242	+	0.835005i	$0.314536\pi$
$380$	−29.1289	+	15.0112i	−1.49428	+	0.770057i
$381$		0			0
$382$	12.9802	−	11.7672i	0.664126	−	0.602060i
$383$		−	35.2874i		−	1.80310i	−0.432675	−	0.901550i	$-0.642430\pi$
$383$		−	35.2874i		−	1.80310i	0.432675	−	0.901550i	$-0.357570\pi$
$384$		0			0
$385$	−29.9051	+	19.3289i	−1.52410	+	0.985090i
$386$	22.1108	+	24.3902i	1.12541	+	1.24143i
$387$		0			0
$388$	−36.0797	−	3.54561i	−1.83167	−	0.180001i
$389$	−10.5078	+	10.5078i	−0.532767	+	0.532767i	−0.921395	−	0.388628i	$-0.872949\pi$
$389$	−10.5078	+	10.5078i	−0.532767	+	0.532767i	0.388628	+	0.921395i	$0.372949\pi$
$390$		0			0
$391$	−6.00263			−0.303566
$392$	−2.86349	−	3.85833i	−0.144628	−	0.194875i
$393$		0			0
$394$	−0.988352	−	0.0484468i	−0.0497924	−	0.00244071i
$395$	0.135357	−	0.630109i	0.00681057	−	0.0317042i
$396$		0			0
$397$	10.4175	+	10.4175i	0.522838	+	0.522838i	0.918427	−	0.395589i	$-0.129460\pi$
$397$	10.4175	+	10.4175i	0.522838	+	0.522838i	−0.395589	+	0.918427i	$0.629460\pi$
$398$	−3.12086	+	2.82920i	−0.156434	+	0.141815i
$399$		0			0
$400$	−16.2879	−	11.6063i	−0.814393	−	0.580314i
$401$			15.4212i			0.770099i	0.922896	+	0.385049i	$0.125816\pi$
$401$			15.4212i			0.770099i	−0.922896	+	0.385049i	$0.874184\pi$
$402$		0			0
$403$	1.49674	−	1.49674i	0.0745581	−	0.0745581i
$404$	20.2194	+	24.6264i	1.00595	+	1.22521i
$405$		0			0
$406$	0.940396	−	19.1848i	0.0466711	−	0.952125i
$407$	−20.3389			−1.00816
$408$		0			0
$409$			5.10228i			0.252291i	0.992012	+	0.126146i	$0.0402607\pi$
$409$			5.10228i			0.252291i	−0.992012	+	0.126146i	$0.959739\pi$
$410$	2.78129	−	1.61031i	0.137358	−	0.0795273i
$411$		0			0
$412$	−9.12157	−	0.896392i	−0.449388	−	0.0441621i
$413$	−8.32634	+	8.32634i	−0.409712	+	0.409712i
$414$		0			0
$415$	15.2785	+	23.6385i	0.749992	+	1.16037i
$416$	−5.99830	−	1.49903i	−0.294091	−	0.0734959i
$417$		0			0
$418$	37.5782	+	41.4521i	1.83801	+	2.02749i
$419$	−0.0584508	+	0.0584508i	−0.00285551	+	0.00285551i	−0.708533	−	0.705678i	$-0.750643\pi$
$419$	−0.0584508	+	0.0584508i	−0.00285551	+	0.00285551i	0.705678	+	0.708533i	$0.250643\pi$
$420$		0			0
$421$	−6.66123	−	6.66123i	−0.324648	−	0.324648i	0.525899	−	0.850547i	$-0.323729\pi$
$421$	−6.66123	−	6.66123i	−0.324648	−	0.324648i	−0.850547	+	0.525899i	$0.823729\pi$
$422$	19.9211	+	0.976489i	0.969745	+	0.0475347i
$423$		0			0
$424$	5.28093	−	35.6814i	0.256465	−	1.73284i
$425$	10.3905	+	4.68004i	0.504012	+	0.227015i
$426$		0			0
$427$	32.0310	+	32.0310i	1.55009	+	1.55009i
$428$	−4.84900	−	5.90590i	−0.234385	−	0.285473i
$429$		0			0
$430$	−19.2955	−	5.14498i	−0.930511	−	0.248113i
$431$	12.3929			0.596946			0.298473	−	0.954418i	$-0.403523\pi$
$431$	12.3929			0.596946			0.298473	+	0.954418i	$0.403523\pi$
$432$		0			0
$433$		−	6.31623i		−	0.303539i	−0.988416	−	0.151769i	$-0.951503\pi$
$433$		−	6.31623i		−	0.303539i	0.988416	−	0.151769i	$-0.0484971\pi$
$434$	5.98472	−	5.42542i	0.287276	−	0.260429i
$435$		0			0
$436$	−9.07635	−	11.0547i	−0.434678	−	0.529422i
$437$	13.6459	+	13.6459i	0.652774	+	0.652774i
$438$		0			0
$439$	−5.22876			−0.249555			−0.124778	−	0.992185i	$-0.539822\pi$
$439$	−5.22876			−0.249555			−0.124778	+	0.992185i	$0.539822\pi$
$440$	−11.9826	+	31.9763i	−0.571246	+	1.52441i
$441$		0			0
$442$	3.51867	+	0.172477i	0.167366	+	0.00820390i
$443$	−4.30848	+	4.30848i	−0.204702	+	0.204702i	−0.802011	−	0.597309i	$-0.796237\pi$
$443$	−4.30848	+	4.30848i	−0.204702	+	0.204702i	0.597309	+	0.802011i	$0.296237\pi$
$444$		0			0
$445$	14.0847	+	3.02562i	0.667680	+	0.143428i
$446$	1.42052	−	1.28776i	0.0672635	−	0.0609774i
$447$		0			0
$448$	−22.5834	−	6.83450i	−1.06697	−	0.322900i
$449$			22.8023i			1.07611i	0.842911	+	0.538053i	$0.180840\pi$
$449$			22.8023i			1.07611i	−0.842911	+	0.538053i	$0.819160\pi$
$450$		0			0
$451$	−3.88006	−	3.88006i	−0.182705	−	0.182705i
$452$	−2.16939	+	22.0755i	−0.102040	+	1.03834i
$453$		0			0
$454$	0.564334	+	0.0276624i	0.0264855	+	0.00129826i
$455$	6.05371	−	3.91276i	0.283802	−	0.183433i
$456$		0			0
$457$	23.8294			1.11469			0.557345	−	0.830281i	$-0.311820\pi$
$457$	23.8294			1.11469			0.557345	+	0.830281i	$0.311820\pi$
$458$	−7.23078	−	0.354437i	−0.337872	−	0.0165617i
$459$		0			0
$460$	−3.58809	+	11.2184i	−0.167296	+	0.523061i
$461$	7.75855	+	7.75855i	0.361352	+	0.361352i	0.864310	−	0.502959i	$-0.167755\pi$
$461$	7.75855	+	7.75855i	0.361352	+	0.361352i	−0.502959	+	0.864310i	$0.667755\pi$
$462$		0			0
$463$	9.96705			0.463208			0.231604	−	0.972810i	$-0.425603\pi$
$463$	9.96705			0.463208			0.231604	+	0.972810i	$0.425603\pi$
$464$	−10.2404	−	15.3114i	−0.475398	−	0.710813i
$465$		0			0
$466$	18.3454	+	20.2366i	0.849835	+	0.937443i
$467$	25.6782	+	25.6782i	1.18824	+	1.18824i	0.977553	+	0.210692i	$0.0675716\pi$
$467$	25.6782	+	25.6782i	1.18824	+	1.18824i	0.210692	+	0.977553i	$0.432428\pi$
$468$		0			0
$469$	−21.2771	−	21.2771i	−0.982487	−	0.982487i
$470$	−10.9942	−	18.9890i	−0.507127	−	0.875898i
$471$		0			0
$472$	−1.65329	+	11.1707i	−0.0760988	+	0.514173i
$473$			34.0959i			1.56773i
$474$		0			0
$475$	−12.9817	−	34.2602i	−0.595640	−	1.57197i
$476$	13.3797	+	1.31485i	0.613259	+	0.0602659i
$477$		0			0
$478$	13.3711	−	12.1215i	0.611581	−	0.554426i
$479$	−19.8901			−0.908803			−0.454402	−	0.890797i	$-0.650147\pi$
$479$	−19.8901			−0.908803			−0.454402	+	0.890797i	$0.650147\pi$
$480$		0			0
$481$	4.11722			0.187729
$482$	9.47137	−	8.58622i	0.431409	−	0.391092i
$483$		0			0
$484$	36.1294	+	3.55049i	1.64224	+	0.161386i
$485$	8.51284	−	39.6286i	0.386548	−	1.79944i
$486$		0			0
$487$		−	24.3871i		−	1.10508i	−0.833485	−	0.552541i	$-0.813658\pi$
$487$		−	24.3871i		−	1.10508i	0.833485	−	0.552541i	$-0.186342\pi$
$488$	42.9731	+	6.36012i	1.94530	+	0.287909i
$489$		0			0
$490$	4.64897	−	2.69165i	0.210019	−	0.121597i
$491$	16.7013	+	16.7013i	0.753719	+	0.753719i	0.975171	−	0.221452i	$-0.0710797\pi$
$491$	16.7013	+	16.7013i	0.753719	+	0.753719i	−0.221452	+	0.975171i	$0.571080\pi$
$492$		0			0
$493$	7.42156	+	7.42156i	0.334250	+	0.334250i
$494$	−7.60698	−	8.39118i	−0.342254	−	0.377537i
$495$		0			0
$496$	1.50799	−	7.59845i	0.0677107	−	0.341181i
$497$	−23.6859			−1.06246
$498$		0			0
$499$	6.16191	+	6.16191i	0.275845	+	0.275845i	0.831448	−	0.555603i	$-0.187512\pi$
$499$	6.16191	+	6.16191i	0.275845	+	0.275845i	−0.555603	+	0.831448i	$0.687512\pi$
$500$	14.9576	−	16.6214i	0.668922	−	0.743333i
$501$		0			0
$502$	15.2437	+	0.747213i	0.680360	+	0.0333497i
$503$	−15.6520			−0.697889			−0.348945	−	0.937143i	$-0.613460\pi$
$503$	−15.6520			−0.697889			−0.348945	+	0.937143i	$0.613460\pi$
$504$		0			0
$505$	−29.9191	+	19.3379i	−1.33138	+	0.860525i
$506$	20.0859	+	0.984567i	0.892928	+	0.0437693i
$507$		0			0
$508$	−2.03988	+	20.7575i	−0.0905049	+	0.920966i
$509$	−13.0382	−	13.0382i	−0.577908	−	0.577908i	0.356418	−	0.934326i	$-0.383998\pi$
$509$	−13.0382	−	13.0382i	−0.577908	−	0.577908i	−0.934326	+	0.356418i	$0.883998\pi$
$510$		0			0
$511$		−	4.66010i		−	0.206151i
$512$	−21.2972	+	7.64381i	−0.941214	+	0.337812i
$513$		0			0
$514$	−9.57769	+	8.68261i	−0.422454	+	0.382973i
$515$	2.15220	−	10.0188i	0.0948371	−	0.441481i
$516$		0			0
$517$	−26.4908	+	26.4908i	−1.16507	+	1.16507i
$518$	15.6934	+	0.769256i	0.689529	+	0.0337992i
$519$		0			0
$520$	2.42564	−	6.47300i	0.106371	−	0.283860i
$521$	−11.6740			−0.511445			−0.255723	−	0.966750i	$-0.582313\pi$
$521$	−11.6740			−0.511445			−0.255723	+	0.966750i	$0.582313\pi$
$522$		0			0
$523$	−12.7738	−	12.7738i	−0.558559	−	0.558559i	0.370338	−	0.928897i	$-0.379242\pi$
$523$	−12.7738	−	12.7738i	−0.558559	−	0.558559i	−0.928897	+	0.370338i	$0.879242\pi$
$524$	−24.3255	−	29.6275i	−1.06266	−	1.29428i
$525$		0			0
$526$	5.60685	−	5.08286i	0.244470	−	0.221623i
$527$			4.41397i			0.192275i
$528$		0			0
$529$	−16.0636			−0.698419
$530$	38.9662	+	10.3900i	1.69258	+	0.451312i
$531$		0			0
$532$	−27.4274	−	33.4056i	−1.18913	−	1.44832i
$533$	0.785444	+	0.785444i	0.0340213	+	0.0340213i
$534$		0			0
$535$	7.17518	−	4.63761i	0.310210	−	0.200501i
$536$	−28.5456	−	4.22482i	−1.23298	−	0.182484i
$537$		0			0
$538$	−34.9845	−	1.71486i	−1.50829	−	0.0739329i
$539$	−6.48559	−	6.48559i	−0.279354	−	0.279354i
$540$		0			0
$541$	23.1601	−	23.1601i	0.995729	−	0.995729i	−0.00426226	−	0.999991i	$-0.501357\pi$
$541$	23.1601	−	23.1601i	0.995729	−	0.995729i	0.999991	+	0.00426226i	$0.00135673\pi$
$542$	14.0957	+	15.5488i	0.605464	+	0.667880i
$543$		0			0
$544$	11.0550	−	6.63429i	0.473979	−	0.284443i
$545$	13.4305	−	8.68066i	0.575299	−	0.371839i
$546$		0			0
$547$	32.6697	−	32.6697i	1.39686	−	1.39686i	0.587983	−	0.808873i	$-0.299922\pi$
$547$	32.6697	−	32.6697i	1.39686	−	1.39686i	0.808873	−	0.587983i	$-0.200078\pi$
$548$	−15.1496	−	1.48878i	−0.647160	−	0.0635975i
$549$		0			0
$550$	−34.0008	−	17.3646i	−1.44980	−	0.740428i
$551$		−	33.7433i		−	1.43751i
$552$		0			0
$553$	0.850072			0.0361487
$554$	0.939608	−	19.1687i	0.0399201	−	0.814401i
$555$		0			0
$556$	−3.01542	−	3.67267i	−0.127882	−	0.155756i
$557$	27.6869	−	27.6869i	1.17313	−	1.17313i	0.191673	−	0.981459i	$-0.438609\pi$
$557$	27.6869	−	27.6869i	1.17313	−	1.17313i	0.981459	−	0.191673i	$-0.0613912\pi$
$558$		0			0
$559$		−	6.90206i		−	0.291926i
$560$	10.4551	−	24.2196i	0.441809	−	1.02347i
$561$		0			0
$562$	25.3289	−	22.9618i	1.06843	−	0.968583i
$563$	−12.9042	−	12.9042i	−0.543845	−	0.543845i	0.380809	−	0.924654i	$-0.375646\pi$
$563$	−12.9042	−	12.9042i	−0.543845	−	0.543845i	−0.924654	+	0.380809i	$0.875646\pi$
$564$		0			0
$565$	−24.2469	−	5.20861i	−1.02007	−	0.219128i
$566$	45.0136	+	2.20647i	1.89206	+	0.0927446i
$567$		0			0
$568$	−18.2402	+	13.5371i	−0.765341	+	0.568003i
$569$	39.4363			1.65326			0.826628	−	0.562749i	$-0.190256\pi$
$569$	39.4363			1.65326			0.826628	+	0.562749i	$0.190256\pi$
$570$		0			0
$571$	−1.54757	+	1.54757i	−0.0647637	+	0.0647637i	−0.738747	−	0.673983i	$-0.764582\pi$
$571$	−1.54757	+	1.54757i	−0.0647637	+	0.0647637i	0.673983	+	0.738747i	$0.264582\pi$
$572$	−11.7458	−	1.15428i	−0.491118	−	0.0482630i
$573$		0			0
$574$	2.84709	+	3.14059i	0.118835	+	0.131086i
$575$	−12.0068	−	5.40804i	−0.500716	−	0.225531i
$576$		0			0
$577$			26.5133i			1.10376i	0.833923	+	0.551881i	$0.186090\pi$
$577$			26.5133i			1.10376i	−0.833923	+	0.551881i	$0.813910\pi$
$578$	12.3692	−	11.2133i	0.514492	−	0.466411i
$579$		0			0
$580$	18.3065	−	9.43402i	0.760138	−	0.391726i
$581$	−26.2512	+	26.2512i	−1.08908	+	1.08908i
$582$		0			0
$583$		−	68.8548i		−	2.85167i
$584$	−2.66336	−	3.58868i	−0.110211	−	0.148500i
$585$		0			0
$586$	4.42438	+	0.216873i	0.182769	+	0.00895895i
$587$	4.43417	−	4.43417i	0.183018	−	0.183018i	−0.609652	−	0.792669i	$-0.708691\pi$
$587$	4.43417	−	4.43417i	0.183018	−	0.183018i	0.792669	+	0.609652i	$0.208691\pi$
$588$		0			0
$589$	10.0344	−	10.0344i	0.413460	−	0.413460i
$590$	−12.1990	−	3.25277i	−0.502227	−	0.133914i
$591$		0			0
$592$	12.5249	−	8.37677i	0.514771	−	0.344283i
$593$	20.0418			0.823019			0.411510	−	0.911405i	$-0.365002\pi$
$593$	20.0418			0.823019			0.411510	+	0.911405i	$0.365002\pi$
$594$		0			0
$595$	−3.15689	+	14.6958i	−0.129420	+	0.602469i
$596$	−23.6735	−	28.8335i	−0.969706	−	1.18107i
$597$		0			0
$598$	−4.06601	−	0.199307i	−0.166272	−	0.00815026i
$599$			30.5731i			1.24918i	0.780951	+	0.624592i	$0.214735\pi$
$599$			30.5731i			1.24918i	−0.780951	+	0.624592i	$0.785265\pi$
$600$		0			0
$601$		−	36.4715i		−	1.48770i	−0.668344	−	0.743852i	$-0.732997\pi$
$601$		−	36.4715i		−	1.48770i	0.668344	−	0.743852i	$-0.267003\pi$
$602$	1.28957	−	26.3083i	0.0525591	−	1.07225i
$603$		0			0
$604$	−2.89498	+	29.4590i	−0.117795	+	1.19867i
$605$	−8.52458	+	39.6832i	−0.346573	+	1.61335i
$606$		0			0
$607$	−18.5659			−0.753566			−0.376783	−	0.926302i	$-0.622970\pi$
$607$	−18.5659			−0.753566			−0.376783	+	0.926302i	$0.622970\pi$
$608$	−40.2135	−	10.0497i	−1.63087	−	0.407570i
$609$		0			0
$610$	−12.5132	+	46.9291i	−0.506647	+	1.90011i
$611$	5.36256	−	5.36256i	0.216946	−	0.216946i
$612$		0			0
$613$	17.3170	−	17.3170i	0.699425	−	0.699425i	−0.264861	−	0.964286i	$-0.585326\pi$
$613$	17.3170	−	17.3170i	0.699425	−	0.699425i	0.964286	+	0.264861i	$0.0853262\pi$
$614$	−1.22422	+	24.9750i	−0.0494055	+	1.00791i
$615$		0			0
$616$	−44.5554	−	6.59431i	−1.79519	−	0.265692i
$617$			1.18526i			0.0477167i	0.999715	+	0.0238584i	$0.00759508\pi$
$617$			1.18526i			0.0477167i	−0.999715	+	0.0238584i	$0.992405\pi$
$618$		0			0
$619$	−0.522478	+	0.522478i	−0.0210002	+	0.0210002i	−0.717529	−	0.696529i	$-0.754727\pi$
$619$	−0.522478	+	0.522478i	−0.0210002	+	0.0210002i	0.696529	+	0.717529i	$0.254727\pi$
$620$	8.24934	+	2.63847i	0.331302	+	0.105963i
$621$		0			0
$622$	−3.57138	−	3.93955i	−0.143199	−	0.157962i
$623$			19.0015i			0.761280i
$624$		0			0
$625$	16.5671	+	18.7225i	0.662683	+	0.748900i
$626$	−6.49589	+	5.88882i	−0.259628	+	0.235364i
$627$		0			0
$628$	22.3218	−	18.3272i	0.890737	−	0.731333i
$629$	−6.07093	+	6.07093i	−0.242064	+	0.242064i
$630$		0			0
$631$	33.4437			1.33137			0.665687	−	0.746231i	$-0.268139\pi$
$631$	33.4437			1.33137			0.665687	+	0.746231i	$0.268139\pi$
$632$	0.654628	−	0.485836i	0.0260397	−	0.0193255i
$633$		0			0
$634$	−1.33407	+	27.2161i	−0.0529827	+	1.08089i
$635$	−22.7993	−	4.89765i	−0.904763	−	0.194357i
$636$		0			0
$637$	1.31288	+	1.31288i	0.0520183	+	0.0520183i
$638$	−23.6166	−	26.0512i	−0.934991	−	1.03138i
$639$		0			0
$640$	−5.79078	−	24.6265i	−0.228901	−	0.973450i
$641$		−	0.0475126i		−	0.00187664i	−1.00000		0.000938318i	$-0.999701\pi$
$641$		−	0.0475126i		−	0.00187664i	1.00000		0.000938318i	$-0.000298676\pi$
$642$		0			0
$643$	6.27347	−	6.27347i	0.247402	−	0.247402i	−0.572502	−	0.819903i	$-0.694027\pi$
$643$	6.27347	−	6.27347i	0.247402	−	0.247402i	0.819903	+	0.572502i	$0.194027\pi$
$644$	−15.4610	−	1.51938i	−0.609249	−	0.0598719i
$645$		0			0
$646$	23.5897	+	1.15631i	0.928123	+	0.0454945i
$647$	−30.1491			−1.18529			−0.592643	−	0.805465i	$-0.701915\pi$
$647$	−30.1491			−1.18529			−0.592643	+	0.805465i	$0.701915\pi$
$648$		0			0
$649$			21.5562i			0.846155i
$650$	6.88282	+	3.51512i	0.269966	+	0.137875i
$651$		0			0
$652$	−20.4416	−	24.8971i	−0.800555	−	0.975046i
$653$	−19.4196	+	19.4196i	−0.759947	+	0.759947i	−0.976312	−	0.216365i	$-0.930580\pi$
$653$	−19.4196	+	19.4196i	−0.759947	+	0.759947i	0.216365	+	0.976312i	$0.430580\pi$
$654$		0			0
$655$	35.9950	−	23.2650i	1.40644	−	0.909038i
$656$	3.98743	+	0.791345i	0.155683	+	0.0308968i
$657$		0			0
$658$	21.4422	−	19.4383i	0.835903	−	0.757784i
$659$	−29.1034	+	29.1034i	−1.13371	+	1.13371i	−0.144153	+	0.989555i	$0.546046\pi$
$659$	−29.1034	+	29.1034i	−1.13371	+	1.13371i	−0.989555	+	0.144153i	$0.953954\pi$
$660$		0			0
$661$	27.9971	+	27.9971i	1.08896	+	1.08896i	0.995636	+	0.0933236i	$0.0297491\pi$
$661$	27.9971	+	27.9971i	1.08896	+	1.08896i	0.0933236	+	0.995636i	$0.470251\pi$
$662$	−1.12038	+	22.8566i	−0.0435447	+	0.888346i
$663$		0			0
$664$	−5.21247	+	35.2188i	−0.202283	+	1.36676i
$665$	40.5850	−	26.2317i	1.57382	−	1.01722i
$666$		0			0
$667$	−8.57602	−	8.57602i	−0.332065	−	0.332065i
$668$	1.97132	−	20.0599i	0.0762727	−	0.776141i
$669$		0			0
$670$	8.31213	−	31.1735i	0.321126	−	1.20434i
$671$	82.9257			3.20131
$672$		0			0
$673$			24.1910i			0.932495i	0.884654	+	0.466248i	$0.154394\pi$
$673$			24.1910i			0.932495i	−0.884654	+	0.466248i	$0.845606\pi$
$674$	9.21719	+	10.1674i	0.355033	+	0.391633i
$675$		0			0
$676$	−23.4976	−	2.30915i	−0.903755	−	0.0888135i
$677$	22.7749	+	22.7749i	0.875311	+	0.875311i	0.993045	−	0.117734i	$-0.0375631\pi$
$677$	22.7749	+	22.7749i	0.875311	+	0.875311i	−0.117734	+	0.993045i	$0.537563\pi$
$678$		0			0
$679$	53.4624			2.05170
$680$	5.96792	+	13.1213i	0.228859	+	0.503177i
$681$		0			0
$682$	0.723991	−	14.7700i	0.0277230	−	0.565571i
$683$	−11.1813	+	11.1813i	−0.427842	+	0.427842i	−0.887893	−	0.460051i	$-0.847831\pi$
$683$	−11.1813	+	11.1813i	−0.427842	+	0.427842i	0.460051	+	0.887893i	$0.347831\pi$
$684$		0			0
$685$	3.57449	−	16.6398i	0.136574	−	0.635774i
$686$	−14.8511	−	16.3820i	−0.567016	−	0.625469i
$687$		0			0
$688$	−14.0427	−	20.9967i	−0.535375	−	0.800490i
$689$			13.9383i			0.531008i
$690$		0			0
$691$	−30.4888	−	30.4888i	−1.15985	−	1.15985i	−0.984507	−	0.175343i	$-0.943897\pi$
$691$	−30.4888	−	30.4888i	−1.15985	−	1.15985i	−0.175343	−	0.984507i	$-0.556103\pi$
$692$	16.1971	+	19.7275i	0.615723	+	0.749927i
$693$		0			0
$694$	−1.63208	+	33.2957i	−0.0619529	+	1.26389i
$695$	4.46199	−	2.88397i	0.169253	−	0.109395i
$696$		0			0
$697$	−2.31631			−0.0877365
$698$	−0.0964805	+	1.96828i	−0.00365184	+	0.0745004i
$699$		0			0
$700$	25.5782	+	14.6844i	0.966765	+	0.555019i
$701$	−10.1167	−	10.1167i	−0.382102	−	0.382102i	0.489757	−	0.871859i	$-0.337086\pi$
$701$	−10.1167	−	10.1167i	−0.382102	−	0.382102i	−0.871859	+	0.489757i	$0.837086\pi$
$702$		0			0
$703$	27.6024			1.04105
$704$	−38.0803	+	20.3863i	−1.43520	+	0.768338i
$705$		0			0
$706$	−19.5231	+	17.6985i	−0.734760	+	0.666093i
$707$	−33.2260	−	33.2260i	−1.24959	−	1.24959i
$708$		0			0
$709$	10.9333	+	10.9333i	0.410608	+	0.410608i	0.881950	−	0.471342i	$-0.156230\pi$
$709$	10.9333	+	10.9333i	0.410608	+	0.410608i	−0.471342	+	0.881950i	$0.656230\pi$
$710$	−12.7247	−	21.9779i	−0.477550	−	0.824815i
$711$		0			0
$712$	10.8598	+	14.6328i	0.406989	+	0.548387i
$713$		−	5.10058i		−	0.191018i
$714$		0			0
$715$	2.77138	−	12.9012i	0.103644	−	0.482477i
$716$	−18.5271	−	22.5653i	−0.692391	−	0.843306i
$717$		0			0
$718$	14.8925	+	16.4278i	0.555784	+	0.613079i
$719$	−17.0081			−0.634295			−0.317148	−	0.948376i	$-0.602725\pi$
$719$	−17.0081			−0.634295			−0.317148	+	0.948376i	$0.602725\pi$
$720$		0			0
$721$	13.5162			0.503370
$722$	−32.9514	−	36.3483i	−1.22632	−	1.35274i
$723$		0			0
$724$	30.4259	−	24.9810i	1.13077	−	0.928410i
$725$	8.15855	+	21.5314i	0.303001	+	0.799656i
$726$		0			0
$727$			9.36040i			0.347158i	0.984820	+	0.173579i	$0.0555332\pi$
$727$			9.36040i			0.347158i	−0.984820	+	0.173579i	$0.944467\pi$
$728$	9.01939	+	1.33489i	0.334281	+	0.0494743i
$729$		0			0
$730$	4.32405	−	2.50353i	0.160040	−	0.0926600i
$731$	10.1773	+	10.1773i	0.376420	+	0.376420i
$732$		0			0
$733$	0.534164	+	0.534164i	0.0197298	+	0.0197298i	0.716903	−	0.697173i	$-0.245559\pi$
$733$	0.534164	+	0.534164i	0.0197298	+	0.0197298i	−0.697173	+	0.716903i	$0.745559\pi$
$734$	25.9857	−	23.5572i	0.959148	−	0.869511i
$735$		0			0
$736$	−12.7747	+	7.66628i	−0.470880	+	0.282583i
$737$	−55.0848			−2.02907
$738$		0			0
$739$	29.8329	+	29.8329i	1.09742	+	1.09742i	0.994712	+	0.102708i	$0.0327506\pi$
$739$	29.8329	+	29.8329i	1.09742	+	1.09742i	0.102708	+	0.994712i	$0.467249\pi$
$740$	7.71715	+	14.9750i	0.283688	+	0.550492i
$741$		0			0
$742$	−2.60422	+	53.1281i	−0.0956040	+	1.95040i
$743$	−18.5297			−0.679788			−0.339894	−	0.940464i	$-0.610391\pi$
$743$	−18.5297			−0.679788			−0.339894	+	0.940464i	$0.610391\pi$
$744$		0			0
$745$	35.0303	−	22.6415i	1.28341	−	0.829520i
$746$	0.783165	−	15.9772i	0.0286737	−	0.584966i
$747$		0			0
$748$	19.0215	−	15.6175i	0.695496	−	0.571032i
$749$	7.96824	+	7.96824i	0.291153	+	0.291153i
$750$		0			0
$751$			14.3204i			0.522560i	0.965263	+	0.261280i	$0.0841446\pi$
$751$			14.3204i			0.522560i	−0.965263	+	0.261280i	$0.915855\pi$
$752$	5.40285	−	27.2239i	0.197022	−	0.992753i
$753$		0			0
$754$	4.78073	+	5.27357i	0.174104	+	0.192052i
$755$	−32.3567	−	6.95073i	−1.17758	−	0.252963i
$756$		0			0
$757$	−19.9592	+	19.9592i	−0.725431	+	0.725431i	−0.969706	−	0.244275i	$-0.921450\pi$
$757$	−19.9592	+	19.9592i	−0.725431	+	0.725431i	0.244275	+	0.969706i	$0.421450\pi$
$758$	0.542833	−	11.0742i	0.0197166	−	0.402233i
$759$		0			0
$760$	16.2619	−	43.3960i	0.589880	−	1.57414i
$761$	−44.8390			−1.62541			−0.812706	−	0.582674i	$-0.802006\pi$
$761$	−44.8390			−1.62541			−0.812706	+	0.582674i	$0.802006\pi$
$762$		0			0
$763$	14.9149	+	14.9149i	0.539957	+	0.539957i
$764$	−2.42321	+	24.6583i	−0.0876687	+	0.892106i
$765$		0			0
$766$	33.5174	+	36.9727i	1.21103	+	1.33588i
$767$		−	4.36364i		−	0.157562i
$768$		0			0
$769$	7.94970			0.286673			0.143337	−	0.989674i	$-0.454217\pi$
$769$	7.94970			0.286673			0.143337	+	0.989674i	$0.454217\pi$
$770$	12.9740	−	48.6571i	0.467550	−	1.75348i
$771$		0			0
$772$	−46.3336	−	4.55328i	−1.66758	−	0.163876i
$773$	−6.73346	−	6.73346i	−0.242186	−	0.242186i	0.575568	−	0.817754i	$-0.304781\pi$
$773$	−6.73346	−	6.73346i	−0.242186	−	0.242186i	−0.817754	+	0.575568i	$0.804781\pi$
$774$		0			0
$775$	−3.97675	+	8.82904i	−0.142849	+	0.317148i
$776$	41.1706	−	30.5550i	1.47794	−	1.09686i
$777$		0			0
$778$	1.02890	−	20.9904i	0.0368880	−	0.752543i
$779$	5.26573	+	5.26573i	0.188664	+	0.188664i
$780$		0			0
$781$	−30.6605	+	30.6605i	−1.09712	+	1.09712i
$782$	6.28931	−	5.70155i	0.224905	−	0.203887i
$783$		0			0
$784$	6.66506	+	1.32275i	0.238038	+	0.0472409i
$785$	17.5282	+	27.1191i	0.625608	+	0.967923i
$786$		0			0
$787$	−2.03543	+	2.03543i	−0.0725554	+	0.0725554i	−0.742453	−	0.669898i	$-0.766338\pi$
$787$	−2.03543	+	2.03543i	−0.0725554	+	0.0725554i	0.669898	+	0.742453i	$0.266338\pi$
$788$	1.08157	−	0.888017i	0.0385294	−	0.0316343i
$789$		0			0
$790$	0.456682	+	0.788771i	0.0162480	+	0.0280632i
$791$		−	32.7111i		−	1.16307i
$792$		0			0
$793$	−16.7867			−0.596114
$794$	−20.8100	−	1.02006i	−0.738518	−	0.0362005i
$795$		0			0
$796$	0.582617	−	5.92864i	0.0206503	−	0.210135i
$797$	−14.7768	+	14.7768i	−0.523422	+	0.523422i	−0.918603	−	0.395181i	$-0.870682\pi$
$797$	−14.7768	+	14.7768i	−0.523422	+	0.523422i	0.395181	+	0.918603i	$0.370682\pi$
$798$		0			0
$799$			15.8144i			0.559475i
$800$	28.0899	−	3.31028i	0.993128	−	0.117036i
$801$		0			0
$802$	−14.6477	−	16.1577i	−0.517229	−	0.570549i
$803$	−6.03231	−	6.03231i	−0.212876	−	0.212876i
$804$		0			0
$805$	3.64796	−	16.9818i	0.128574	−	0.598530i
$806$	−0.146558	+	2.98990i	−0.00516229	+	0.105315i
$807$		0			0
$808$	−44.5763	−	6.59739i	−1.56819	−	0.232095i
$809$	−6.77033			−0.238032			−0.119016	−	0.992892i	$-0.537974\pi$
$809$	−6.77033			−0.238032			−0.119016	+	0.992892i	$0.537974\pi$
$810$		0			0
$811$	−18.8412	+	18.8412i	−0.661604	+	0.661604i	−0.955758	−	0.294154i	$-0.904962\pi$
$811$	−18.8412	+	18.8412i	−0.661604	+	0.661604i	0.294154	+	0.955758i	$0.404962\pi$
$812$	17.2372	+	20.9943i	0.604908	+	0.736755i
$813$		0			0
$814$	21.3103	−	19.3187i	0.746924	−	0.677121i
$815$	30.2479	−	19.5504i	1.05954	−	0.684822i
$816$		0			0
$817$		−	46.2725i		−	1.61887i
$818$	−4.84636	−	5.34596i	−0.169449	−	0.186917i
$819$		0			0
$820$	−1.38458	+	4.32899i	−0.0483517	+	0.151175i
$821$	−4.33164	+	4.33164i	−0.151175	+	0.151175i	−0.778643	−	0.627467i	$-0.784092\pi$
$821$	−4.33164	+	4.33164i	−0.151175	+	0.151175i	0.627467	+	0.778643i	$0.284092\pi$
$822$		0			0
$823$			22.3521i			0.779144i	0.920996	+	0.389572i	$0.127377\pi$
$823$			22.3521i			0.779144i	−0.920996	+	0.389572i	$0.872623\pi$
$824$	10.4086	−	7.72485i	0.362602	−	0.269108i
$825$		0			0
$826$	0.815298	−	16.6327i	0.0283679	−	0.578726i
$827$	−33.1708	+	33.1708i	−1.15346	+	1.15346i	−0.167609	+	0.985854i	$0.553605\pi$
$827$	−33.1708	+	33.1708i	−1.15346	+	1.15346i	−0.985854	+	0.167609i	$0.946395\pi$
$828$		0			0
$829$	−22.9388	+	22.9388i	−0.796696	+	0.796696i	−0.982573	−	0.185877i	$-0.940488\pi$
$829$	−22.9388	+	22.9388i	−0.796696	+	0.796696i	0.185877	+	0.982573i	$0.440488\pi$
$830$	−38.4610	−	10.2553i	−1.33500	−	0.355966i
$831$		0			0
$832$	7.70862	−	4.12682i	0.267248	−	0.143072i
$833$	−3.87175			−0.134148
$834$		0			0
$835$	22.0331	+	4.73305i	0.762485	+	0.163794i
$836$	−78.7458	−	7.73848i	−2.72348	−	0.267641i
$837$		0			0
$838$	0.00572338	−	0.116761i	0.000197711	−	0.00403345i
$839$			19.8135i			0.684040i	0.939693	+	0.342020i	$0.111111\pi$
$839$			19.8135i			0.684040i	−0.939693	+	0.342020i	$0.888889\pi$
$840$		0			0
$841$		−	7.79349i		−	0.268741i
$842$	13.3065	+	0.652254i	0.458571	+	0.0224781i
$843$		0			0
$844$	−21.8001	+	17.8988i	−0.750389	+	0.616102i
$845$	5.54417	−	25.8089i	0.190725	−	0.887854i
$846$		0			0
$847$	−53.5360			−1.83952
$848$	28.3585	+	42.4016i	0.973836	+	1.45608i
$849$		0			0
$850$	−15.3320	+	4.96574i	−0.525884	+	0.170324i
$851$	7.01530	−	7.01530i	0.240481	−	0.240481i
$852$		0			0
$853$	21.6771	−	21.6771i	0.742211	−	0.742211i	−0.230792	−	0.973003i	$-0.574132\pi$
$853$	21.6771	−	21.6771i	0.742211	−	0.742211i	0.973003	+	0.230792i	$0.0741318\pi$
$854$	−63.9852	−	3.13641i	−2.18953	−	0.107326i
$855$		0			0
$856$	10.6903	+	1.58218i	0.365386	+	0.0540779i
$857$		−	9.66909i		−	0.330290i	−0.986269	−	0.165145i	$-0.947191\pi$
$857$		−	9.66909i		−	0.330290i	0.986269	−	0.165145i	$-0.0528092\pi$
$858$		0			0
$859$	24.3747	−	24.3747i	0.831652	−	0.831652i	−0.156090	−	0.987743i	$-0.549889\pi$
$859$	24.3747	−	24.3747i	0.831652	−	0.831652i	0.987743	+	0.156090i	$0.0498891\pi$
$860$	25.1040	−	12.9370i	0.856038	−	0.441147i
$861$		0			0
$862$	−12.9848	+	11.7713i	−0.442264	+	0.400932i
$863$			11.2656i			0.383485i	0.981445	+	0.191742i	$0.0614138\pi$
$863$			11.2656i			0.383485i	−0.981445	+	0.191742i	$0.938586\pi$
$864$		0			0
$865$	−23.9673	+	15.4910i	−0.814912	+	0.526710i
$866$	5.99942	+	6.61789i	0.203869	+	0.224885i
$867$		0			0
$868$	−1.11726	+	11.3691i	−0.0379222	+	0.385892i
$869$	1.10038	−	1.10038i	0.0373279	−	0.0373279i
$870$		0			0
$871$	11.1509			0.377832
$872$	20.0100	+	2.96153i	0.677625	+	0.100290i
$873$		0			0
$874$	−27.2592	−	1.33618i	−0.922055	−	0.0451971i
$875$	−19.5547	+	26.5511i	−0.661069	+	0.897590i
$876$		0			0
$877$	−14.2210	−	14.2210i	−0.480210	−	0.480210i	0.424989	−	0.905199i	$-0.360278\pi$
$877$	−14.2210	−	14.2210i	−0.480210	−	0.480210i	−0.905199	+	0.424989i	$0.860278\pi$
$878$	5.47848	−	4.96649i	0.184890	−	0.167611i
$879$		0			0
$880$	−17.8176	−	44.8851i	−0.600632	−	1.51308i
$881$			43.8480i			1.47728i	0.674103	+	0.738638i	$0.264531\pi$
$881$			43.8480i			1.47728i	−0.674103	+	0.738638i	$0.735469\pi$
$882$		0			0
$883$	−23.8519	+	23.8519i	−0.802681	+	0.802681i	−0.983514	−	0.180833i	$-0.942121\pi$
$883$	−23.8519	+	23.8519i	−0.802681	+	0.802681i	0.180833	+	0.983514i	$0.442121\pi$
$884$	−3.85054	+	3.16146i	−0.129508	+	0.106331i
$885$		0			0
$886$	0.421878	−	8.60663i	0.0141733	−	0.289145i
$887$	12.2892			0.412632			0.206316	−	0.978485i	$-0.433852\pi$
$887$	12.2892			0.412632			0.206316	+	0.978485i	$0.433852\pi$
$888$		0			0
$889$		−	30.7582i		−	1.03160i
$890$	−17.6313	+	10.2081i	−0.591002	+	0.342178i
$891$		0			0
$892$	−0.265190	+	2.69854i	−0.00887920	+	0.0903537i
$893$	35.9514	−	35.9514i	1.20307	−	1.20307i
$894$		0			0
$895$	27.4150	−	17.7194i	0.916383	−	0.592295i
$896$	30.1537	−	14.2897i	1.00736	−	0.477387i
$897$		0			0
$898$	−21.6586	−	23.8913i	−0.722755	−	0.797263i
$899$	−6.30628	+	6.30628i	−0.210326	+	0.210326i
$900$		0			0
$901$	−20.5524	−	20.5524i	−0.684700	−	0.684700i
$902$	7.75081	+	0.379928i	0.258074	+	0.0126502i
$903$		0			0
$904$	−18.6952	−	25.1903i	−0.621793	−	0.837818i
$905$	23.8919	+	36.9649i	0.794194	+	1.22876i
$906$		0			0
$907$	31.4979	+	31.4979i	1.04587	+	1.04587i	0.998896	+	0.0469745i	$0.0149580\pi$
$907$	31.4979	+	31.4979i	1.04587	+	1.04587i	0.0469745	+	0.998896i	$0.485042\pi$
$908$	−0.617562	+	0.507045i	−0.0204945	+	0.0168269i
$909$		0			0
$910$	−2.62634	+	9.84970i	−0.0870622	+	0.326514i
$911$	−9.04962			−0.299827			−0.149914	−	0.988699i	$-0.547900\pi$
$911$	−9.04962			−0.299827			−0.149914	+	0.988699i	$0.547900\pi$
$912$		0			0
$913$			67.9622i			2.24922i
$914$	−24.9674	+	22.6341i	−0.825850	+	0.748670i
$915$		0			0
$916$	7.91278	−	6.49674i	0.261446	−	0.214658i
$917$	39.9734	+	39.9734i	1.32004	+	1.32004i
$918$		0			0
$919$	4.82428			0.159138			0.0795692	−	0.996829i	$-0.474646\pi$
$919$	4.82428			0.159138			0.0795692	+	0.996829i	$0.474646\pi$
$920$	−6.89626	−	15.1623i	−0.227363	−	0.499887i
$921$		0			0
$922$	−15.4985	−	0.759701i	−0.510416	−	0.0250194i
$923$	6.20662	−	6.20662i	0.204293	−	0.204293i
$924$		0			0
$925$	−17.6130	+	6.67380i	−0.579111	+	0.219433i
$926$	−10.4431	+	9.46712i	−0.343181	+	0.311109i
$927$		0			0
$928$	25.2729	+	6.31591i	0.829622	+	0.207330i
$929$			15.4281i			0.506180i	0.967443	+	0.253090i	$0.0814468\pi$
$929$			15.4281i			0.506180i	−0.967443	+	0.253090i	$0.918553\pi$
$930$		0			0
$931$	8.80177	+	8.80177i	0.288466	+	0.288466i
$932$	−38.4432	−	3.77787i	−1.25925	−	0.123748i
$933$		0			0
$934$	−51.2948	−	2.51435i	−1.67842	−	0.0822722i
$935$	14.9366	+	23.1096i	0.488480	+	0.755764i
$936$		0			0
$937$	12.7904			0.417845			0.208923	−	0.977932i	$-0.433004\pi$
$937$	12.7904			0.417845			0.208923	+	0.977932i	$0.433004\pi$
$938$	42.5032	+	2.08341i	1.38778	+	0.0680259i
$939$		0			0
$940$	29.5559	+	9.45314i	0.964007	+	0.308327i
$941$	3.02632	+	3.02632i	0.0986553	+	0.0986553i	0.754712	−	0.656056i	$-0.227777\pi$
$941$	3.02632	+	3.02632i	0.0986553	+	0.0986553i	−0.656056	+	0.754712i	$0.727777\pi$
$942$		0			0
$943$	2.67662			0.0871629
$944$	−8.87814	−	13.2746i	−0.288959	−	0.432050i
$945$		0			0
$946$	−32.3857	−	35.7243i	−1.05295	−	1.16150i
$947$	−13.2910	−	13.2910i	−0.431898	−	0.431898i	0.457375	−	0.889274i	$-0.348790\pi$
$947$	−13.2910	−	13.2910i	−0.431898	−	0.431898i	−0.889274	+	0.457375i	$0.848790\pi$
$948$		0			0
$949$	1.22113	+	1.22113i	0.0396394	+	0.0396394i
$950$	46.1435	+	23.5659i	1.49709	+	0.764580i
$951$		0			0
$952$	−15.2676	+	11.3310i	−0.494827	+	0.367239i
$953$		−	24.7645i		−	0.802200i	−0.916034	−	0.401100i	$-0.868628\pi$
$953$		−	24.7645i		−	0.802200i	0.916034	−	0.401100i	$-0.131372\pi$
$954$		0			0
$955$	−27.0838	−	5.81802i	−0.876410	−	0.188267i
$956$	−2.49619	+	25.4009i	−0.0807325	+	0.821523i
$957$		0			0
$958$	20.8401	−	18.8925i	0.673313	−	0.610388i
$959$	22.4485			0.724901
$960$		0			0
$961$	27.2493			0.879011
$962$	−4.31385	+	3.91070i	−0.139084	+	0.126086i
$963$		0			0
$964$	−1.76816	+	17.9926i	−0.0569487	+	0.579503i
$965$	10.9322	−	50.8911i	0.351921	−	1.63824i
$966$		0			0
$967$		−	50.8732i		−	1.63597i	−0.575238	−	0.817986i	$-0.695091\pi$
$967$		−	50.8732i		−	1.63597i	0.575238	−	0.817986i	$-0.304909\pi$
$968$	−41.2273	+	30.5971i	−1.32510	+	0.983429i
$969$		0			0
$970$	28.7214	+	49.6071i	0.922190	+	1.59279i
$971$	9.95162	+	9.95162i	0.319363	+	0.319363i	0.848522	−	0.529160i	$-0.177493\pi$
$971$	9.95162	+	9.95162i	0.319363	+	0.319363i	−0.529160	+	0.848522i	$0.677493\pi$
$972$		0			0
$973$	4.95517	+	4.95517i	0.158855	+	0.158855i
$974$	23.1638	+	25.5518i	0.742217	+	0.818732i
$975$		0			0
$976$	−51.0666	+	34.1538i	−1.63460	+	1.09324i
$977$	5.29541			0.169415			0.0847076	−	0.996406i	$-0.473004\pi$
$977$	5.29541			0.169415			0.0847076	+	0.996406i	$0.473004\pi$
$978$		0			0
$979$	24.5967	+	24.5967i	0.786114	+	0.786114i
$980$	−2.31436	+	7.23599i	−0.0739294	+	0.231145i
$981$		0			0
$982$	−33.3625	−	1.63536i	−1.06464	−	0.0521863i
$983$	42.1592			1.34467			0.672335	−	0.740247i	$-0.265291\pi$
$983$	42.1592			1.34467			0.672335	+	0.740247i	$0.265291\pi$
$984$		0			0
$985$	0.849304	+	1.31402i	0.0270611	+	0.0418682i
$986$	−14.8253	−	0.726704i	−0.472134	−	0.0231430i
$987$		0			0
$988$	15.9406	+	1.56651i	0.507137	+	0.0498372i
$989$	−11.7604	−	11.7604i	−0.373958	−	0.373958i
$990$		0			0
$991$		−	40.3299i		−	1.28112i	−0.767907	−	0.640561i	$-0.778702\pi$
$991$		−	40.3299i		−	1.28112i	0.767907	−	0.640561i	$-0.221298\pi$
$992$	5.63732	+	9.39370i	0.178985	+	0.298250i
$993$		0			0
$994$	24.8172	−	22.4979i	0.787152	−	0.713589i
$995$	6.51180	+	1.39884i	0.206438	+	0.0443461i
$996$		0			0
$997$	−35.3041	+	35.3041i	−1.11809	+	1.11809i	−0.126069	+	0.992021i	$0.540236\pi$
$997$	−35.3041	+	35.3041i	−1.11809	+	1.11809i	−0.992021	+	0.126069i	$0.959764\pi$
$998$	−12.3090	−	0.603362i	−0.389636	−	0.0190991i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.u.a.539.12	yes	96
3.2	odd	2	inner	720.2.u.a.539.37	yes	96
4.3	odd	2		2880.2.u.a.719.44		96
5.4	even	2	inner	720.2.u.a.539.38	yes	96
12.11	even	2		2880.2.u.a.719.5		96
15.14	odd	2	inner	720.2.u.a.539.11	yes	96
16.3	odd	4	inner	720.2.u.a.179.11	✓	96
16.13	even	4		2880.2.u.a.2159.29		96
20.19	odd	2		2880.2.u.a.719.20		96
48.29	odd	4		2880.2.u.a.2159.20		96
48.35	even	4	inner	720.2.u.a.179.38	yes	96
60.59	even	2		2880.2.u.a.719.29		96
80.19	odd	4	inner	720.2.u.a.179.37	yes	96
80.29	even	4		2880.2.u.a.2159.5		96
240.29	odd	4		2880.2.u.a.2159.44		96
240.179	even	4	inner	720.2.u.a.179.12	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.u.a.179.11	✓	96	16.3	odd	4	inner
720.2.u.a.179.12	yes	96	240.179	even	4	inner
720.2.u.a.179.37	yes	96	80.19	odd	4	inner
720.2.u.a.179.38	yes	96	48.35	even	4	inner
720.2.u.a.539.11	yes	96	15.14	odd	2	inner
720.2.u.a.539.12	yes	96	1.1	even	1	trivial
720.2.u.a.539.37	yes	96	3.2	odd	2	inner
720.2.u.a.539.38	yes	96	5.4	even	2	inner
2880.2.u.a.719.5		96	12.11	even	2
2880.2.u.a.719.20		96	20.19	odd	2
2880.2.u.a.719.29		96	60.59	even	2
2880.2.u.a.719.44		96	4.3	odd	2
2880.2.u.a.2159.5		96	80.29	even	4
2880.2.u.a.2159.20		96	48.29	odd	4
2880.2.u.a.2159.29		96	16.13	even	4
2880.2.u.a.2159.44		96	240.29	odd	4

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.04776 + 0.949842i) q^{2} +(0.195601 - 1.99041i) q^{4} +(2.18619 + 0.469629i) q^{5} +2.94937i q^{7} +(1.68563 + 2.27126i) q^{8} +O(q^{10})\)	\(q+(-1.04776 + 0.949842i) q^{2} +(0.195601 - 1.99041i) q^{4} +(2.18619 + 0.469629i) q^{5} +2.94937i q^{7} +(1.68563 + 2.27126i) q^{8} +(-2.73668 + 1.58448i) q^{10} +(3.81783 + 3.81783i) q^{11} +(-0.772847 - 0.772847i) q^{13} +(-2.80143 - 3.09023i) q^{14} +(-3.92348 - 0.778653i) q^{16} +2.27916 q^{17} +(-5.18129 - 5.18129i) q^{19} +(1.36238 - 4.25957i) q^{20} +(-7.62651 - 0.373835i) q^{22} -2.63370 q^{23} +(4.55890 + 2.05340i) q^{25} +(1.54384 + 0.0756756i) q^{26} +(5.87045 + 0.576899i) q^{28} +(3.25626 + 3.25626i) q^{29} +1.93666i q^{31} +(4.85046 - 2.91084i) q^{32} +(-2.38802 + 2.16484i) q^{34} +(-1.38511 + 6.44789i) q^{35} +(-2.66367 + 2.66367i) q^{37} +(10.3501 + 0.507341i) q^{38} +(2.61847 + 5.75705i) q^{40} -1.01630 q^{41} +(4.46535 + 4.46535i) q^{43} +(8.34584 - 6.85229i) q^{44} +(2.75948 - 2.50160i) q^{46} +6.93871i q^{47} -1.69876 q^{49} +(-6.72704 + 2.17876i) q^{50} +(-1.68945 + 1.38711i) q^{52} +(-9.01752 - 9.01752i) q^{53} +(6.55356 + 10.1395i) q^{55} +(-6.69879 + 4.97155i) q^{56} +(-6.50472 - 0.318847i) q^{58} +(2.82309 + 2.82309i) q^{59} +(10.8603 - 10.8603i) q^{61} +(-1.83952 - 2.02916i) q^{62} +(-2.31728 + 7.65704i) q^{64} +(-1.32664 - 2.05255i) q^{65} +(-7.21414 + 7.21414i) q^{67} +(0.445807 - 4.53647i) q^{68} +(-4.67321 - 8.07147i) q^{70} +8.03085i q^{71} -1.58003 q^{73} +(0.260821 - 5.32095i) q^{74} +(-11.3264 + 9.29943i) q^{76} +(-11.2602 + 11.2602i) q^{77} -0.288222i q^{79} +(-8.21181 - 3.54487i) q^{80} +(1.06484 - 0.965323i) q^{82} +(8.90062 + 8.90062i) q^{83} +(4.98270 + 1.07036i) q^{85} +(-8.91999 - 0.437238i) q^{86} +(-2.23584 + 15.1068i) q^{88} +6.44258 q^{89} +(2.27941 - 2.27941i) q^{91} +(-0.515154 + 5.24214i) q^{92} +(-6.59067 - 7.27010i) q^{94} +(-8.89402 - 13.7606i) q^{95} -18.1267i q^{97} +(1.77989 - 1.61355i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q+O(q^{10}) \) 96 * q	\( 96 q - 8 q^{16} - 16 q^{19} + 72 q^{34} + 8 q^{40} + 8 q^{46} - 96 q^{49} + 64 q^{55} - 32 q^{61} + 48 q^{64} + 24 q^{70} + 40 q^{76} - 88 q^{94}+O(q^{100}) \) 96 * q - 8 * q^16 - 16 * q^19 + 72 * q^34 + 8 * q^40 + 8 * q^46 - 96 * q^49 + 64 * q^55 - 32 * q^61 + 48 * q^64 + 24 * q^70 + 40 * q^76 - 88 * q^94

Introduction

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