LMFDB - Embedded newform 720.2.u.a.179.12

Newspace parameters

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

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			179.12
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.12

$q$-expansion

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$-1$	$-1$

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	$-0.811807\pi$
$7$		−	2.94937i		−	1.11476i	0.830259	−	0.557378i	$-0.188193\pi$
$8$	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	0.164792	−	0.986328i	$-0.447305\pi$
$11$	3.81783	−	3.81783i	1.15112	−	1.15112i	0.986328	−	0.164792i	$-0.0526952\pi$
$12$		0			0
$13$	−0.772847	+	0.772847i	−0.214349	+	0.214349i	−0.806112	−	0.591763i	$-0.798432\pi$
$13$	−0.772847	+	0.772847i	−0.214349	+	0.214349i	0.591763	+	0.806112i	$0.298432\pi$
$14$	−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	−0.211233	+	0.977436i	$0.567748\pi$
$19$	−5.18129	+	5.18129i	−1.18867	+	1.18867i	−0.977436	+	0.211233i	$0.932252\pi$
$20$	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	−0.336876	−	0.941549i	$-0.609370\pi$
$29$	3.25626	−	3.25626i	0.604673	−	0.604673i	0.941549	+	0.336876i	$0.109370\pi$
$30$		0			0
$31$		−	1.93666i		−	0.347835i	−0.984760	−	0.173917i	$-0.944357\pi$
$31$		−	1.93666i		−	0.347835i	0.984760	−	0.173917i	$-0.0556426\pi$
$32$	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	0.453402	−	0.891306i	$-0.350210\pi$
$37$	−2.66367	−	2.66367i	−0.437904	−	0.437904i	−0.891306	+	0.453402i	$0.850210\pi$
$38$	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	−0.279257	−	0.960216i	$-0.590088\pi$
$43$	4.46535	−	4.46535i	0.680959	−	0.680959i	0.960216	+	0.279257i	$0.0900882\pi$
$44$	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	$-0.831102\pi$
$47$		−	6.93871i		−	1.01211i	0.862500	−	0.506057i	$-0.168898\pi$
$48$		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	−0.278099	+	0.960552i	$0.589704\pi$
$53$	−9.01752	+	9.01752i	−1.23865	+	1.23865i	−0.960552	+	0.278099i	$0.910296\pi$
$54$		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	−0.499042	−	0.866578i	$-0.666315\pi$
$59$	2.82309	−	2.82309i	0.367536	−	0.367536i	0.866578	+	0.499042i	$0.166315\pi$
$60$		0			0
$61$	10.8603	+	10.8603i	1.39052	+	1.39052i	0.824154	+	0.566365i	$0.191651\pi$
$61$	10.8603	+	10.8603i	1.39052	+	1.39052i	0.566365	+	0.824154i	$0.308349\pi$
$62$	−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	0.112324	−	0.993672i	$-0.464170\pi$
$67$	−7.21414	−	7.21414i	−0.881347	−	0.881347i	−0.993672	+	0.112324i	$0.964170\pi$
$68$	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	$-0.841890\pi$
$71$		−	8.03085i		−	0.953087i	0.879151	−	0.476543i	$-0.158110\pi$
$72$		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	$0.00516122\pi$
$79$			0.288222i			0.0324275i	−0.999869	+	0.0162137i	$0.994839\pi$
$80$	−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	−0.0227710	−	0.999741i	$-0.507249\pi$
$83$	8.90062	−	8.90062i	0.976970	−	0.976970i	0.999741	+	0.0227710i	$0.00724886\pi$
$84$		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	$0.372011\pi$
$97$			18.1267i			1.84049i	−0.391342	+	0.920245i	$0.627989\pi$
$98$	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	−0.991598	−	0.129357i	$-0.958709\pi$
$101$	−11.2655	−	11.2655i	−1.12096	−	1.12096i	−0.129357	−	0.991598i	$-0.541291\pi$
$102$		0			0
$103$			4.58275i			0.451552i	0.974179	+	0.225776i	$0.0724918\pi$
$103$			4.58275i			0.451552i	−0.974179	+	0.225776i	$0.927508\pi$
$104$	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	0.825534	−	0.564353i	$-0.190874\pi$
$107$	2.70168	+	2.70168i	0.261181	+	0.261181i	−0.564353	+	0.825534i	$0.690874\pi$
$108$		0			0
$109$	5.05700	+	5.05700i	0.484372	+	0.484372i	0.906525	−	0.422152i	$-0.138725\pi$
$109$	5.05700	+	5.05700i	0.484372	+	0.484372i	−0.422152	+	0.906525i	$0.638725\pi$
$110$	−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	0.978659	+	0.205491i	$0.0658791\pi$
$131$	13.5532	+	13.5532i	1.18415	+	1.18415i	0.205491	+	0.978659i	$0.434121\pi$
$132$		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	$0.105411\pi$
$137$			7.61130i			0.650278i	−0.945666	+	0.325139i	$0.894589\pi$
$138$		0			0
$139$	1.68008	+	1.68008i	0.142502	+	0.142502i	0.774759	−	0.632257i	$-0.217871\pi$
$139$	1.68008	+	1.68008i	0.142502	+	0.142502i	−0.632257	+	0.774759i	$0.717871\pi$
$140$	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	0.996456	+	0.0841097i	$0.0268046\pi$
$149$	13.1900	+	13.1900i	1.08057	+	1.08057i	0.0841097	+	0.996456i	$0.473195\pi$
$150$		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	−0.170428	−	0.985370i	$-0.554515\pi$
$157$	10.2112	−	10.2112i	0.814942	−	0.814942i	0.985370	+	0.170428i	$0.0545151\pi$
$158$	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	0.994718	−	0.102641i	$-0.0327294\pi$
$163$	11.3893	+	11.3893i	0.892077	+	0.892077i	−0.102641	+	0.994718i	$0.532729\pi$
$164$	−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	0.275257	−	0.961371i	$-0.411237\pi$
$173$	−9.02442	−	9.02442i	−0.686114	−	0.686114i	−0.961371	+	0.275257i	$0.911237\pi$
$174$		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	0.978377	−	0.206830i	$-0.0663146\pi$
$179$	10.3226	+	10.3226i	0.771547	+	0.771547i	−0.206830	+	0.978377i	$0.566315\pi$
$180$		0			0
$181$	13.9184	−	13.9184i	1.03455	−	1.03455i	0.0351674	−	0.999381i	$-0.488804\pi$
$181$	13.9184	−	13.9184i	1.03455	−	1.03455i	0.999381	−	0.0351674i	$-0.0111964\pi$
$182$	−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	$0.316163\pi$
$193$			23.2784i			1.67562i	−0.545965	+	0.837808i	$0.683837\pi$
$194$	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	−0.689262	−	0.724513i	$-0.742065\pi$
$197$	0.494769	−	0.494769i	0.0352508	−	0.0352508i	0.724513	+	0.689262i	$0.242065\pi$
$198$		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	−0.961465	−	0.274928i	$-0.911346\pi$
$211$	−9.97252	+	9.97252i	−0.686537	+	0.686537i	0.274928	+	0.961465i	$0.411346\pi$
$212$	−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	−0.716420	−	0.697669i	$-0.754220\pi$
$227$	−0.282506	+	0.282506i	−0.0187506	+	0.0187506i	0.697669	+	0.716420i	$0.254220\pi$
$228$		0			0
$229$	3.61973	−	3.61973i	0.239199	−	0.239199i	−0.577320	−	0.816518i	$-0.695901\pi$
$229$	3.61973	−	3.61973i	0.239199	−	0.239199i	0.816518	+	0.577320i	$0.195901\pi$
$230$	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	$0.218036\pi$
$233$			19.3142i			1.26531i	−0.774432	+	0.632657i	$0.781964\pi$
$234$		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	−0.905663	−	0.423998i	$-0.860626\pi$
$251$	−7.63101	+	7.63101i	−0.481665	+	0.481665i	0.423998	+	0.905663i	$0.360626\pi$
$252$		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	0.0702731	−	0.997528i	$-0.477613\pi$
$269$	17.5132	−	17.5132i	1.06780	−	1.06780i	0.997528	−	0.0702731i	$-0.0223871\pi$
$270$		0			0
$271$			14.8401i			0.901471i	0.892657	+	0.450736i	$0.148838\pi$
$271$			14.8401i			0.901471i	−0.892657	+	0.450736i	$0.851162\pi$
$272$	−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	0.357394	−	0.933954i	$-0.383665\pi$
$277$	−9.59587	−	9.59587i	−0.576560	−	0.576560i	−0.933954	+	0.357394i	$0.883665\pi$
$278$	−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	−0.442950	+	0.896546i	$0.646068\pi$
$283$	−22.5338	+	22.5338i	−1.33950	+	1.33950i	−0.896546	+	0.442950i	$0.853932\pi$
$284$	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	−0.768837	−	0.639445i	$-0.779164\pi$
$293$	−2.21485	+	2.21485i	−0.129393	+	0.129393i	0.639445	+	0.768837i	$0.279164\pi$
$294$		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	0.967277	−	0.253722i	$-0.0816547\pi$
$307$	12.5025	+	12.5025i	0.713556	+	0.713556i	−0.253722	+	0.967277i	$0.581655\pi$
$308$	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	$-0.966002\pi$
$311$		−	3.75997i		−	0.213209i	0.994302	−	0.106604i	$-0.0339978\pi$
$312$		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	0.977261	−	0.212040i	$-0.0680108\pi$
$317$	13.6244	+	13.6244i	0.765221	+	0.765221i	−0.212040	+	0.977261i	$0.568011\pi$
$318$		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	0.947794	−	0.318884i	$-0.103308\pi$
$331$	11.4420	+	11.4420i	0.628910	+	0.628910i	−0.318884	+	0.947794i	$0.603308\pi$
$332$	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	$0.0851419\pi$
$337$			9.70392i			0.528606i	−0.964440	+	0.264303i	$0.914858\pi$
$338$	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	0.994968	−	0.100192i	$-0.0319458\pi$
$347$	16.6678	+	16.6678i	0.894776	+	0.894776i	−0.100192	+	0.994968i	$0.531946\pi$
$348$		0			0
$349$	0.985320	+	0.985320i	0.0527430	+	0.0527430i	0.732986	−	0.680243i	$-0.238126\pi$
$349$	0.985320	+	0.985320i	0.0527430	+	0.0527430i	−0.680243	+	0.732986i	$0.738126\pi$
$350$	−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	$0.135782\pi$
$359$			15.6789i			0.827503i	−0.910390	+	0.413751i	$0.864218\pi$
$360$		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	0.469045	−	0.883175i	$-0.344598\pi$
$373$	−7.99818	−	7.99818i	−0.414130	−	0.414130i	−0.883175	+	0.469045i	$0.844598\pi$
$374$	−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	0.550242	−	0.835005i	$-0.314536\pi$
$379$	−5.54375	−	5.54375i	−0.284763	−	0.284763i	−0.835005	+	0.550242i	$0.814536\pi$
$380$	−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	$0.357570\pi$
$383$			35.2874i			1.80310i	−0.432675	+	0.901550i	$0.642430\pi$
$384$		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	0.388628	−	0.921395i	$-0.372949\pi$
$389$	−10.5078	−	10.5078i	−0.532767	−	0.532767i	−0.921395	+	0.388628i	$0.872949\pi$
$390$		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	−0.395589	−	0.918427i	$-0.629460\pi$
$397$	10.4175	−	10.4175i	0.522838	−	0.522838i	0.918427	+	0.395589i	$0.129460\pi$
$398$	−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	$-0.874184\pi$
$401$		−	15.4212i		−	0.770099i	0.922896	−	0.385049i	$-0.125816\pi$
$402$		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	$-0.959739\pi$
$409$		−	5.10228i		−	0.252291i	0.992012	−	0.126146i	$-0.0402607\pi$
$410$	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	0.705678	−	0.708533i	$-0.250643\pi$
$419$	−0.0584508	−	0.0584508i	−0.00285551	−	0.00285551i	−0.708533	+	0.705678i	$0.750643\pi$
$420$		0			0
$421$	−6.66123	+	6.66123i	−0.324648	+	0.324648i	−0.850547	−	0.525899i	$-0.823729\pi$
$421$	−6.66123	+	6.66123i	−0.324648	+	0.324648i	0.525899	+	0.850547i	$0.323729\pi$
$422$	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	$0.0484971\pi$
$433$			6.31623i			0.303539i	−0.988416	+	0.151769i	$0.951503\pi$
$434$	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	0.597309	−	0.802011i	$-0.296237\pi$
$443$	−4.30848	−	4.30848i	−0.204702	−	0.204702i	−0.802011	+	0.597309i	$0.796237\pi$
$444$		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	$-0.819160\pi$
$449$		−	22.8023i		−	1.07611i	0.842911	−	0.538053i	$-0.180840\pi$
$450$		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	−0.502959	−	0.864310i	$-0.667755\pi$
$461$	7.75855	−	7.75855i	0.361352	−	0.361352i	0.864310	+	0.502959i	$0.167755\pi$
$462$		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	0.210692	−	0.977553i	$-0.432428\pi$
$467$	25.6782	−	25.6782i	1.18824	−	1.18824i	0.977553	−	0.210692i	$-0.0675716\pi$
$468$		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	$0.186342\pi$
$487$			24.3871i			1.10508i	−0.833485	+	0.552541i	$0.813658\pi$
$488$	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	−0.221452	−	0.975171i	$-0.571080\pi$
$491$	16.7013	−	16.7013i	0.753719	−	0.753719i	0.975171	+	0.221452i	$0.0710797\pi$
$492$		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	−0.555603	−	0.831448i	$-0.687512\pi$
$499$	6.16191	−	6.16191i	0.275845	−	0.275845i	0.831448	+	0.555603i	$0.187512\pi$
$500$	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	−0.934326	−	0.356418i	$-0.883998\pi$
$509$	−13.0382	+	13.0382i	−0.577908	+	0.577908i	0.356418	+	0.934326i	$0.383998\pi$
$510$		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	−0.928897	−	0.370338i	$-0.879242\pi$
$523$	−12.7738	+	12.7738i	−0.558559	+	0.558559i	0.370338	+	0.928897i	$0.379242\pi$
$524$	−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	0.999991	−	0.00426226i	$-0.00135673\pi$
$541$	23.1601	+	23.1601i	0.995729	+	0.995729i	−0.00426226	+	0.999991i	$0.501357\pi$
$542$	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	0.808873	+	0.587983i	$0.200078\pi$
$547$	32.6697	+	32.6697i	1.39686	+	1.39686i	0.587983	+	0.808873i	$0.299922\pi$
$548$	−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	0.981459	+	0.191673i	$0.0613912\pi$
$557$	27.6869	+	27.6869i	1.17313	+	1.17313i	0.191673	+	0.981459i	$0.438609\pi$
$558$		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	−0.924654	−	0.380809i	$-0.875646\pi$
$563$	−12.9042	+	12.9042i	−0.543845	+	0.543845i	0.380809	+	0.924654i	$0.375646\pi$
$564$		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	0.673983	−	0.738747i	$-0.264582\pi$
$571$	−1.54757	−	1.54757i	−0.0647637	−	0.0647637i	−0.738747	+	0.673983i	$0.764582\pi$
$572$	−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	$-0.813910\pi$
$577$		−	26.5133i		−	1.10376i	0.833923	−	0.551881i	$-0.186090\pi$
$578$	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	0.792669	−	0.609652i	$-0.208691\pi$
$587$	4.43417	+	4.43417i	0.183018	+	0.183018i	−0.609652	+	0.792669i	$0.708691\pi$
$588$		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	$-0.785265\pi$
$599$		−	30.5731i		−	1.24918i	0.780951	−	0.624592i	$-0.214735\pi$
$600$		0			0
$601$			36.4715i			1.48770i	0.668344	+	0.743852i	$0.267003\pi$
$601$			36.4715i			1.48770i	−0.668344	+	0.743852i	$0.732997\pi$
$602$	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	0.964286	−	0.264861i	$-0.0853262\pi$
$613$	17.3170	+	17.3170i	0.699425	+	0.699425i	−0.264861	+	0.964286i	$0.585326\pi$
$614$	−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	$-0.992405\pi$
$617$		−	1.18526i		−	0.0477167i	0.999715	−	0.0238584i	$-0.00759508\pi$
$618$		0			0
$619$	−0.522478	−	0.522478i	−0.0210002	−	0.0210002i	0.696529	−	0.717529i	$-0.254727\pi$
$619$	−0.522478	−	0.522478i	−0.0210002	−	0.0210002i	−0.717529	+	0.696529i	$0.754727\pi$
$620$	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	$0.000298676\pi$
$641$			0.0475126i			0.00187664i	−1.00000		0.000938318i	$0.999701\pi$
$642$		0			0
$643$	6.27347	+	6.27347i	0.247402	+	0.247402i	0.819903	−	0.572502i	$-0.194027\pi$
$643$	6.27347	+	6.27347i	0.247402	+	0.247402i	−0.572502	+	0.819903i	$0.694027\pi$
$644$	−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	0.216365	−	0.976312i	$-0.430580\pi$
$653$	−19.4196	−	19.4196i	−0.759947	−	0.759947i	−0.976312	+	0.216365i	$0.930580\pi$
$654$		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	−0.989555	−	0.144153i	$-0.953954\pi$
$659$	−29.1034	−	29.1034i	−1.13371	−	1.13371i	−0.144153	−	0.989555i	$-0.546046\pi$
$660$		0			0
$661$	27.9971	−	27.9971i	1.08896	−	1.08896i	0.0933236	−	0.995636i	$-0.470251\pi$
$661$	27.9971	−	27.9971i	1.08896	−	1.08896i	0.995636	−	0.0933236i	$-0.0297491\pi$
$662$	−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	$-0.845606\pi$
$673$		−	24.1910i		−	0.932495i	0.884654	−	0.466248i	$-0.154394\pi$
$674$	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	−0.117734	−	0.993045i	$-0.537563\pi$
$677$	22.7749	−	22.7749i	0.875311	−	0.875311i	0.993045	+	0.117734i	$0.0375631\pi$
$678$		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	0.460051	−	0.887893i	$-0.347831\pi$
$683$	−11.1813	−	11.1813i	−0.427842	−	0.427842i	−0.887893	+	0.460051i	$0.847831\pi$
$684$		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	−0.175343	+	0.984507i	$0.556103\pi$
$691$	−30.4888	+	30.4888i	−1.15985	+	1.15985i	−0.984507	+	0.175343i	$0.943897\pi$
$692$	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	−0.871859	−	0.489757i	$-0.837086\pi$
$701$	−10.1167	+	10.1167i	−0.382102	+	0.382102i	0.489757	+	0.871859i	$0.337086\pi$
$702$		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	−0.471342	−	0.881950i	$-0.656230\pi$
$709$	10.9333	−	10.9333i	0.410608	−	0.410608i	0.881950	+	0.471342i	$0.156230\pi$
$710$	−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	$-0.944467\pi$
$727$		−	9.36040i		−	0.347158i	0.984820	−	0.173579i	$-0.0555332\pi$
$728$	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	−0.697173	−	0.716903i	$-0.745559\pi$
$733$	0.534164	−	0.534164i	0.0197298	−	0.0197298i	0.716903	+	0.697173i	$0.245559\pi$
$734$	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	0.102708	−	0.994712i	$-0.467249\pi$
$739$	29.8329	−	29.8329i	1.09742	−	1.09742i	0.994712	−	0.102708i	$-0.0327506\pi$
$740$	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	$-0.915855\pi$
$751$		−	14.3204i		−	0.522560i	0.965263	−	0.261280i	$-0.0841446\pi$
$752$	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	0.244275	−	0.969706i	$-0.421450\pi$
$757$	−19.9592	−	19.9592i	−0.725431	−	0.725431i	−0.969706	+	0.244275i	$0.921450\pi$
$758$	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	−0.817754	−	0.575568i	$-0.804781\pi$
$773$	−6.73346	+	6.73346i	−0.242186	+	0.242186i	0.575568	+	0.817754i	$0.304781\pi$
$774$		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	0.669898	−	0.742453i	$-0.266338\pi$
$787$	−2.03543	−	2.03543i	−0.0725554	−	0.0725554i	−0.742453	+	0.669898i	$0.766338\pi$
$788$	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

Overview	Random
Universe	Knowledge

Degree 1	Degree 2
Degree 3	Degree 4
$\zeta$ zeros

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)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

Related objects

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