LMFDB - Embedded newform 720.2.u.a.179.2

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			179.2
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.2

$q$-expansion

$f(q)$	$=$	$q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +O(q^{10})$	\(q+(-1.41373 + 0.0371259i) q^{2} +(1.99724 - 0.104972i) q^{4} +(1.31281 + 1.81012i) q^{5} -1.40695i q^{7} +(-2.81966 + 0.222551i) q^{8} +(-1.92316 - 2.51027i) q^{10} +(-0.176123 + 0.176123i) q^{11} +(1.72742 - 1.72742i) q^{13} +(0.0522343 + 1.98904i) q^{14} +(3.97796 - 0.419308i) q^{16} +3.15721 q^{17} +(3.47385 - 3.47385i) q^{19} +(2.81201 + 3.47744i) q^{20} +(0.242451 - 0.255528i) q^{22} +1.97613 q^{23} +(-1.55305 + 4.75269i) q^{25} +(-2.37796 + 2.50623i) q^{26} +(-0.147690 - 2.81002i) q^{28} +(-2.62046 + 2.62046i) q^{29} -5.95492i q^{31} +(-5.60818 + 0.740472i) q^{32} +(-4.46342 + 0.117214i) q^{34} +(2.54675 - 1.84706i) q^{35} +(5.72522 + 5.72522i) q^{37} +(-4.78211 + 5.04005i) q^{38} +(-4.10452 - 4.81175i) q^{40} -0.159470 q^{41} +(-6.63058 + 6.63058i) q^{43} +(-0.333273 + 0.370248i) q^{44} +(-2.79371 + 0.0733658i) q^{46} +1.15223i q^{47} +5.02049 q^{49} +(2.01915 - 6.77665i) q^{50} +(3.26874 - 3.63141i) q^{52} +(5.35087 - 5.35087i) q^{53} +(-0.550020 - 0.0875872i) q^{55} +(0.313118 + 3.96712i) q^{56} +(3.60733 - 3.80190i) q^{58} +(4.48547 - 4.48547i) q^{59} +(6.80718 + 6.80718i) q^{61} +(0.221082 + 8.41862i) q^{62} +(7.90094 - 1.25503i) q^{64} +(5.39461 + 0.859057i) q^{65} +(9.97278 + 9.97278i) q^{67} +(6.30571 - 0.331417i) q^{68} +(-3.53183 + 2.70579i) q^{70} -0.0951463i q^{71} -7.99125 q^{73} +(-8.30645 - 7.88134i) q^{74} +(6.57347 - 7.30278i) q^{76} +(0.247796 + 0.247796i) q^{77} -5.66620i q^{79} +(5.98131 + 6.65011i) q^{80} +(0.225446 - 0.00592045i) q^{82} +(12.2672 - 12.2672i) q^{83} +(4.14481 + 5.71492i) q^{85} +(9.12765 - 9.61998i) q^{86} +(0.457410 - 0.535803i) q^{88} -10.9299 q^{89} +(-2.43039 - 2.43039i) q^{91} +(3.94682 - 0.207438i) q^{92} +(-0.0427774 - 1.62893i) q^{94} +(10.8486 + 1.72757i) q^{95} +10.4415i q^{97} +(-7.09760 + 0.186390i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41373	+	0.0371259i	−0.999655	+	0.0262520i
$2$	−1.41373	+	0.0371259i	−0.999655	+	0.0262520i
$3$		0			0
$3$		0			0
$4$	1.99724	−	0.104972i	0.998622	−	0.0524859i
$5$	1.31281	+	1.81012i	0.587107	+	0.809509i
$5$	1.31281	+	1.81012i	0.587107	+	0.809509i
$6$		0			0
$7$		−	1.40695i		−	0.531777i	−0.964004	−	0.265889i	$-0.914335\pi$
$7$		−	1.40695i		−	0.531777i	0.964004	−	0.265889i	$-0.0856653\pi$
$8$	−2.81966	+	0.222551i	−0.996900	+	0.0786836i
$9$		0			0
$10$	−1.92316	−	2.51027i	−0.608156	−	0.793818i
$11$	−0.176123	+	0.176123i	−0.0531031	+	0.0531031i	−0.733160	−	0.680057i	$-0.761955\pi$
$11$	−0.176123	+	0.176123i	−0.0531031	+	0.0531031i	0.680057	+	0.733160i	$0.261955\pi$
$12$		0			0
$13$	1.72742	−	1.72742i	0.479100	−	0.479100i	−0.425744	−	0.904844i	$-0.639988\pi$
$13$	1.72742	−	1.72742i	0.479100	−	0.479100i	0.904844	+	0.425744i	$0.139988\pi$
$14$	0.0522343	+	1.98904i	0.0139602	+	0.531594i
$15$		0			0
$16$	3.97796	−	0.419308i	0.994490	−	0.104827i
$17$	3.15721			0.765735			0.382867	−	0.923803i	$-0.374937\pi$
$17$	3.15721			0.765735			0.382867	+	0.923803i	$0.374937\pi$
$18$		0			0
$19$	3.47385	−	3.47385i	0.796956	−	0.796956i	−0.185658	−	0.982614i	$-0.559442\pi$
$19$	3.47385	−	3.47385i	0.796956	−	0.796956i	0.982614	+	0.185658i	$0.0594417\pi$
$20$	2.81201	+	3.47744i	0.628786	+	0.777579i
$21$		0			0
$22$	0.242451	−	0.255528i	0.0516907	−	0.0544788i
$23$	1.97613			0.412052			0.206026	−	0.978546i	$-0.433947\pi$
$23$	1.97613			0.412052			0.206026	+	0.978546i	$0.433947\pi$
$24$		0			0
$25$	−1.55305	+	4.75269i	−0.310611	+	0.950537i
$26$	−2.37796	+	2.50623i	−0.466357	+	0.491512i
$27$		0			0
$28$	−0.147690	−	2.81002i	−0.0279108	−	0.531044i
$29$	−2.62046	+	2.62046i	−0.486607	+	0.486607i	−0.907234	−	0.420627i	$-0.861810\pi$
$29$	−2.62046	+	2.62046i	−0.486607	+	0.486607i	0.420627	+	0.907234i	$0.361810\pi$
$30$		0			0
$31$		−	5.95492i		−	1.06953i	−0.844999	−	0.534767i	$-0.820399\pi$
$31$		−	5.95492i		−	1.06953i	0.844999	−	0.534767i	$-0.179601\pi$
$32$	−5.60818	+	0.740472i	−0.991396	+	0.130898i
$33$		0			0
$34$	−4.46342	+	0.117214i	−0.765471	+	0.0201021i
$35$	2.54675	−	1.84706i	0.430479	−	0.312210i
$36$		0			0
$37$	5.72522	+	5.72522i	0.941221	+	0.941221i	0.998366	−	0.0571453i	$-0.0181998\pi$
$37$	5.72522	+	5.72522i	0.941221	+	0.941221i	−0.0571453	+	0.998366i	$0.518200\pi$
$38$	−4.78211	+	5.04005i	−0.775760	+	0.817603i
$39$		0			0
$40$	−4.10452	−	4.81175i	−0.648982	−	0.760804i
$41$	−0.159470			−0.0249050			−0.0124525	−	0.999922i	$-0.503964\pi$
$41$	−0.159470			−0.0249050			−0.0124525	+	0.999922i	$0.503964\pi$
$42$		0			0
$43$	−6.63058	+	6.63058i	−1.01115	+	1.01115i	−0.0112162	+	0.999937i	$0.503570\pi$
$43$	−6.63058	+	6.63058i	−1.01115	+	1.01115i	−0.999937	+	0.0112162i	$0.996430\pi$
$44$	−0.333273	+	0.370248i	−0.0502427	+	0.0558170i
$45$		0			0
$46$	−2.79371	+	0.0733658i	−0.411910	+	0.0108172i
$47$			1.15223i			0.168069i	0.996463	+	0.0840347i	$0.0267807\pi$
$47$			1.15223i			0.168069i	−0.996463	+	0.0840347i	$0.973219\pi$
$48$		0			0
$49$	5.02049			0.717213
$50$	2.01915	−	6.77665i	0.285550	−	0.958364i
$51$		0			0
$52$	3.26874	−	3.63141i	0.453293	−	0.503585i
$53$	5.35087	−	5.35087i	0.734999	−	0.734999i	−0.236606	−	0.971606i	$-0.576035\pi$
$53$	5.35087	−	5.35087i	0.734999	−	0.734999i	0.971606	+	0.236606i	$0.0760352\pi$
$54$		0			0
$55$	−0.550020	−	0.0875872i	−0.0741646	−	0.0118103i
$56$	0.313118	+	3.96712i	0.0418421	+	0.530128i
$57$		0			0
$58$	3.60733	−	3.80190i	0.473665	−	0.499214i
$59$	4.48547	−	4.48547i	0.583959	−	0.583959i	−0.352030	−	0.935989i	$-0.614508\pi$
$59$	4.48547	−	4.48547i	0.583959	−	0.583959i	0.935989	+	0.352030i	$0.114508\pi$
$60$		0			0
$61$	6.80718	+	6.80718i	0.871570	+	0.871570i	0.992643	−	0.121074i	$-0.0386338\pi$
$61$	6.80718	+	6.80718i	0.871570	+	0.871570i	−0.121074	+	0.992643i	$0.538634\pi$
$62$	0.221082	+	8.41862i	0.0280774	+	1.06917i
$63$		0			0
$64$	7.90094	−	1.25503i	0.987618	−	0.156879i
$65$	5.39461	+	0.859057i	0.669118	+	0.106553i
$66$		0			0
$67$	9.97278	+	9.97278i	1.21837	+	1.21837i	0.968203	+	0.250166i	$0.0804851\pi$
$67$	9.97278	+	9.97278i	1.21837	+	1.21837i	0.250166	+	0.968203i	$0.419515\pi$
$68$	6.30571	−	0.331417i	0.764679	−	0.0401903i
$69$		0			0
$70$	−3.53183	+	2.70579i	−0.422134	+	0.323403i
$71$		−	0.0951463i		−	0.0112918i	−0.999984	−	0.00564589i	$-0.998203\pi$
$71$		−	0.0951463i		−	0.0112918i	0.999984	−	0.00564589i	$-0.00179715\pi$
$72$		0			0
$73$	−7.99125			−0.935305			−0.467653	−	0.883912i	$-0.654900\pi$
$73$	−7.99125			−0.935305			−0.467653	+	0.883912i	$0.654900\pi$
$74$	−8.30645	−	7.88134i	−0.965605	−	0.916187i
$75$		0			0
$76$	6.57347	−	7.30278i	0.754029	−	0.837687i
$77$	0.247796	+	0.247796i	0.0282390	+	0.0282390i
$78$		0			0
$79$		−	5.66620i		−	0.637497i	−0.947839	−	0.318748i	$-0.896737\pi$
$79$		−	5.66620i		−	0.637497i	0.947839	−	0.318748i	$-0.103263\pi$
$80$	5.98131	+	6.65011i	0.668731	+	0.743505i
$81$		0			0
$82$	0.225446	−	0.00592045i	0.0248964	−	0.000653804i
$83$	12.2672	−	12.2672i	1.34650	−	1.34650i	0.457068	−	0.889432i	$-0.348900\pi$
$83$	12.2672	−	12.2672i	1.34650	−	1.34650i	0.889432	−	0.457068i	$-0.151100\pi$
$84$		0			0
$85$	4.14481	+	5.71492i	0.449568	+	0.619870i
$86$	9.12765	−	9.61998i	0.984260	−	1.03735i
$87$		0			0
$88$	0.457410	−	0.535803i	0.0487601	−	0.0571168i
$89$	−10.9299			−1.15857			−0.579284	−	0.815126i	$-0.696668\pi$
$89$	−10.9299			−1.15857			−0.579284	+	0.815126i	$0.696668\pi$
$90$		0			0
$91$	−2.43039	−	2.43039i	−0.254774	−	0.254774i
$92$	3.94682	−	0.207438i	0.411484	−	0.0216269i
$93$		0			0
$94$	−0.0427774	−	1.62893i	−0.00441216	−	0.168011i
$95$	10.8486	+	1.72757i	1.11304	+	0.177245i
$96$		0			0
$97$			10.4415i			1.06017i	0.847944	+	0.530086i	$0.177840\pi$
$97$			10.4415i			1.06017i	−0.847944	+	0.530086i	$0.822160\pi$
$98$	−7.09760	+	0.186390i	−0.716966	+	0.0188283i
$99$		0			0
$100$	−2.60293	+	9.65530i	−0.260293	+	0.965530i
$101$	−4.54532	−	4.54532i	−0.452276	−	0.452276i	0.443833	−	0.896109i	$-0.353618\pi$
$101$	−4.54532	−	4.54532i	−0.452276	−	0.452276i	−0.896109	+	0.443833i	$0.853618\pi$
$102$		0			0
$103$		−	7.65680i		−	0.754447i	−0.926122	−	0.377224i	$-0.876879\pi$
$103$		−	7.65680i		−	0.754447i	0.926122	−	0.377224i	$-0.123121\pi$
$104$	−4.48629	+	5.25517i	−0.439917	+	0.515312i
$105$		0			0
$106$	−7.36601	+	7.76333i	−0.715451	+	0.754041i
$107$	4.25185	+	4.25185i	0.411042	+	0.411042i	0.882102	−	0.471059i	$-0.156128\pi$
$107$	4.25185	+	4.25185i	0.411042	+	0.411042i	−0.471059	+	0.882102i	$0.656128\pi$
$108$		0			0
$109$	0.180834	+	0.180834i	0.0173208	+	0.0173208i	0.715714	−	0.698393i	$-0.246101\pi$
$109$	0.180834	+	0.180834i	0.0173208	+	0.0173208i	−0.698393	+	0.715714i	$0.746101\pi$
$110$	0.780829	+	0.103404i	0.0744491	+	0.00985921i
$111$		0			0
$112$	−0.589946	−	5.59679i	−0.0557446	−	0.528847i
$113$	6.88868			0.648032			0.324016	−	0.946052i	$-0.394967\pi$
$113$	6.88868			0.648032			0.324016	+	0.946052i	$0.394967\pi$
$114$		0			0
$115$	2.59429	+	3.57703i	0.241919	+	0.333560i
$116$	−4.95862	+	5.50877i	−0.460396	+	0.511476i
$117$		0			0
$118$	−6.17471	+	6.50776i	−0.568428	+	0.599088i
$119$		−	4.44203i		−	0.407200i
$120$		0			0
$121$			10.9380i			0.994360i
$122$	−9.87621	−	9.37076i	−0.894150	−	0.848389i
$123$		0			0
$124$	−0.625098	−	11.8934i	−0.0561355	−	1.06806i
$125$	−10.6418	+	3.42817i	−0.951831	+	0.306625i
$126$		0			0
$127$	−3.18115			−0.282281			−0.141141	−	0.989990i	$-0.545077\pi$
$127$	−3.18115			−0.282281			−0.141141	+	0.989990i	$0.545077\pi$
$128$	−11.1232	+	2.06760i	−0.983159	+	0.182752i
$129$		0			0
$130$	−7.65839	−	1.01419i	−0.671685	−	0.0889505i
$131$	8.49459	+	8.49459i	0.742175	+	0.742175i	0.972996	−	0.230821i	$-0.0741411\pi$
$131$	8.49459	+	8.49459i	0.742175	+	0.742175i	−0.230821	+	0.972996i	$0.574141\pi$
$132$		0			0
$133$	−4.88754	−	4.88754i	−0.423803	−	0.423803i
$134$	−14.4690	−	13.7285i	−1.24993	−	1.18596i
$135$		0			0
$136$	−8.90224	+	0.702639i	−0.763361	+	0.0602508i
$137$			15.1013i			1.29019i	0.764102	+	0.645096i	$0.223182\pi$
$137$			15.1013i			1.29019i	−0.764102	+	0.645096i	$0.776818\pi$
$138$		0			0
$139$	−11.6635	−	11.6635i	−0.989286	−	0.989286i	0.0106573	−	0.999943i	$-0.496608\pi$
$139$	−11.6635	−	11.6635i	−0.989286	−	0.989286i	−0.999943	+	0.0106573i	$0.996608\pi$
$140$	4.89258	−	3.95636i	0.413499	−	0.334374i
$141$		0			0
$142$	0.00353239	+	0.134511i	0.000296432	+	0.0112879i
$143$			0.608476i			0.0508833i
$144$		0			0
$145$	−8.18351	−	1.30317i	−0.679604	−	0.108223i
$146$	11.2974	−	0.296682i	0.934983	−	0.0245536i
$147$		0			0
$148$	12.0356	+	10.8337i	0.989324	+	0.890522i
$149$	−11.1281	−	11.1281i	−0.911646	−	0.911646i	0.0847561	−	0.996402i	$-0.472989\pi$
$149$	−11.1281	−	11.1281i	−0.911646	−	0.911646i	−0.996402	+	0.0847561i	$0.972989\pi$
$150$		0			0
$151$	−21.8766			−1.78030			−0.890148	−	0.455672i	$-0.849399\pi$
$151$	−21.8766			−1.78030			−0.890148	+	0.455672i	$0.849399\pi$
$152$	−9.02197	+	10.5682i	−0.731778	+	0.857193i
$153$		0			0
$154$	−0.359516	−	0.341116i	−0.0289706	−	0.0274879i
$155$	10.7791	−	7.81768i	0.865798	−	0.627931i
$156$		0			0
$157$	15.3928	−	15.3928i	1.22848	−	1.22848i	0.263935	−	0.964541i	$-0.414980\pi$
$157$	15.3928	−	15.3928i	1.22848	−	1.22848i	0.964541	−	0.263935i	$-0.0850204\pi$
$158$	0.210363	+	8.01045i	0.0167356	+	0.637277i
$159$		0			0
$160$	−8.70283	−	9.17937i	−0.688019	−	0.725693i
$161$		−	2.78032i		−	0.219120i
$162$		0			0
$163$	−4.90113	−	4.90113i	−0.383886	−	0.383886i	0.488614	−	0.872500i	$-0.337503\pi$
$163$	−4.90113	−	4.90113i	−0.383886	−	0.383886i	−0.872500	+	0.488614i	$0.837503\pi$
$164$	−0.318499	+	0.0167398i	−0.0248706	+	0.00130716i
$165$		0			0
$166$	−16.8870	+	17.7979i	−1.31069	+	1.38138i
$167$	−17.4380			−1.34939			−0.674695	−	0.738097i	$-0.735725\pi$
$167$	−17.4380			−1.34939			−0.674695	+	0.738097i	$0.735725\pi$
$168$		0			0
$169$			7.03205i			0.540927i
$170$	−6.07180	−	7.92544i	−0.465686	−	0.607854i
$171$		0			0
$172$	−12.5469	+	13.9389i	−0.956688	+	1.06283i
$173$	−17.4288	−	17.4288i	−1.32509	−	1.32509i	−0.909598	−	0.415490i	$-0.863610\pi$
$173$	−17.4288	−	17.4288i	−1.32509	−	1.32509i	−0.415490	−	0.909598i	$-0.636390\pi$
$174$		0			0
$175$	6.68679	+	2.18507i	0.505474	+	0.165176i
$176$	−0.626761	+	0.774460i	−0.0472439	+	0.0583771i
$177$		0			0
$178$	15.4519	−	0.405783i	1.15817	−	0.0304147i
$179$	−12.4635	−	12.4635i	−0.931565	−	0.931565i	0.0662383	−	0.997804i	$-0.478900\pi$
$179$	−12.4635	−	12.4635i	−0.931565	−	0.931565i	−0.997804	+	0.0662383i	$0.978900\pi$
$180$		0			0
$181$	−7.07994	+	7.07994i	−0.526248	+	0.526248i	−0.919451	−	0.393203i	$-0.871367\pi$
$181$	−7.07994	+	7.07994i	−0.526248	+	0.526248i	0.393203	+	0.919451i	$0.371367\pi$
$182$	3.52614	+	3.34568i	0.261375	+	0.247998i
$183$		0			0
$184$	−5.57202	+	0.439790i	−0.410775	+	0.0324218i
$185$	−2.84719	+	17.8795i	−0.209330	+	1.31452i
$186$		0			0
$187$	−0.556057	+	0.556057i	−0.0406629	+	0.0406629i
$188$	0.120951	+	2.30128i	0.00882127	+	0.167838i
$189$		0			0
$190$	−15.4011	−	2.03955i	−1.11731	−	0.147964i
$191$	12.6011			0.911781			0.455891	−	0.890036i	$-0.349321\pi$
$191$	12.6011			0.911781			0.455891	+	0.890036i	$0.349321\pi$
$192$		0			0
$193$		−	5.15723i		−	0.371226i	−0.982623	−	0.185613i	$-0.940573\pi$
$193$		−	5.15723i		−	0.371226i	0.982623	−	0.185613i	$-0.0594270\pi$
$194$	−0.387649	−	14.7614i	−0.0278316	−	1.05981i
$195$		0			0
$196$	10.0271	−	0.527010i	0.716225	−	0.0376436i
$197$	3.59790	−	3.59790i	0.256340	−	0.256340i	−0.567224	−	0.823564i	$-0.691983\pi$
$197$	3.59790	−	3.59790i	0.256340	−	0.256340i	0.823564	+	0.567224i	$0.191983\pi$
$198$		0			0
$199$	7.58554			0.537725			0.268862	−	0.963179i	$-0.413352\pi$
$199$	7.58554			0.537725			0.268862	+	0.963179i	$0.413352\pi$
$200$	3.32137	−	13.7466i	0.234856	−	0.972030i
$201$		0			0
$202$	6.59458	+	6.25708i	0.463993	+	0.440247i
$203$	3.68686	+	3.68686i	0.258767	+	0.258767i
$204$		0			0
$205$	−0.209353	−	0.288659i	−0.0146219	−	0.0201608i
$206$	0.284266	+	10.8246i	0.0198057	+	0.754187i
$207$		0			0
$208$	6.14728	−	7.59593i	0.426237	−	0.526683i
$209$			1.22365i			0.0846417i
$210$		0			0
$211$	0.605008	−	0.605008i	0.0416505	−	0.0416505i	−0.685975	−	0.727625i	$-0.740624\pi$
$211$	0.605008	−	0.605008i	0.0416505	−	0.0416505i	0.727625	+	0.685975i	$0.240624\pi$
$212$	10.1253	−	11.2487i	0.695409	−	0.772563i
$213$		0			0
$214$	−6.16881	−	5.85310i	−0.421691	−	0.400110i
$215$	−20.7068	−	3.29743i	−1.41219	−	0.224883i
$216$		0			0
$217$	−8.37827			−0.568754
$218$	−0.262363	−	0.248936i	−0.0177695	−	0.0168601i
$219$		0			0
$220$	−1.10772	−	0.117196i	−0.0746823	−	0.00790138i
$221$	5.45382	−	5.45382i	0.366863	−	0.366863i
$222$		0			0
$223$	−25.2652			−1.69188			−0.845940	−	0.533278i	$-0.820960\pi$
$223$	−25.2652			−1.69188			−0.845940	+	0.533278i	$0.820960\pi$
$224$	1.04181	+	7.89043i	0.0696087	+	0.527202i
$225$		0			0
$226$	−9.73870	+	0.255748i	−0.647809	+	0.0170121i
$227$	6.61823	−	6.61823i	0.439267	−	0.439267i	−0.452498	−	0.891765i	$-0.649467\pi$
$227$	6.61823	−	6.61823i	0.439267	−	0.439267i	0.891765	+	0.452498i	$0.149467\pi$
$228$		0			0
$229$	−0.0446899	+	0.0446899i	−0.00295319	+	0.00295319i	−0.708582	−	0.705629i	$-0.750665\pi$
$229$	−0.0446899	+	0.0446899i	−0.00295319	+	0.00295319i	0.705629	+	0.708582i	$0.250665\pi$
$230$	−3.80042	−	4.96063i	−0.250592	−	0.327094i
$231$		0			0
$232$	6.80562	−	7.97199i	0.446811	−	0.523387i
$233$			13.5011i			0.884488i	0.896895	+	0.442244i	$0.145817\pi$
$233$			13.5011i			0.884488i	−0.896895	+	0.442244i	$0.854183\pi$
$234$		0			0
$235$	−2.08566	+	1.51265i	−0.136054	+	0.0986747i
$236$	8.48774	−	9.42943i	0.552505	−	0.613804i
$237$		0			0
$238$	0.164914	+	6.27982i	0.0106898	+	0.407060i
$239$	−5.58106			−0.361009			−0.180504	−	0.983574i	$-0.557773\pi$
$239$	−5.58106			−0.361009			−0.180504	+	0.983574i	$0.557773\pi$
$240$		0			0
$241$	15.7677			1.01569			0.507845	−	0.861449i	$-0.330442\pi$
$241$	15.7677			1.01569			0.507845	+	0.861449i	$0.330442\pi$
$242$	−0.406082	−	15.4633i	−0.0261039	−	0.994017i
$243$		0			0
$244$	14.3101	+	12.8810i	0.916113	+	0.824623i
$245$	6.59096	+	9.08768i	0.421081	+	0.580591i
$246$		0			0
$247$		−	12.0016i		−	0.763643i
$248$	1.32527	+	16.7908i	0.0841548	+	1.06622i
$249$		0			0
$250$	14.9173	−	5.24158i	0.943453	−	0.331506i
$251$	−10.5401	+	10.5401i	−0.665287	+	0.665287i	−0.956621	−	0.291334i	$-0.905901\pi$
$251$	−10.5401	+	10.5401i	−0.665287	+	0.665287i	0.291334	+	0.956621i	$0.405901\pi$
$252$		0			0
$253$	−0.348043	+	0.348043i	−0.0218812	+	0.0218812i
$254$	4.49727	−	0.118103i	0.282184	−	0.00741044i
$255$		0			0
$256$	15.6484	−	3.33598i	0.978023	−	0.208499i
$257$	−20.0698			−1.25192			−0.625959	−	0.779856i	$-0.715292\pi$
$257$	−20.0698			−1.25192			−0.625959	+	0.779856i	$0.715292\pi$
$258$		0			0
$259$	8.05510	−	8.05510i	0.500520	−	0.500520i
$260$	10.8645	+	1.14946i	0.673789	+	0.0712868i
$261$		0			0
$262$	−12.3244	−	11.6937i	−0.761403	−	0.722436i
$263$	−28.6944			−1.76937			−0.884687	−	0.466185i	$-0.845628\pi$
$263$	−28.6944			−1.76937			−0.884687	+	0.466185i	$0.845628\pi$
$264$		0			0
$265$	16.7104	+	2.66103i	1.02651	+	0.163466i
$266$	7.09109	+	6.72818i	0.434783	+	0.412531i
$267$		0			0
$268$	20.9649	+	18.8712i	1.28064	+	1.15274i
$269$	−13.7007	+	13.7007i	−0.835349	+	0.835349i	−0.988243	−	0.152894i	$-0.951141\pi$
$269$	−13.7007	+	13.7007i	−0.835349	+	0.835349i	0.152894	+	0.988243i	$0.451141\pi$
$270$		0			0
$271$		−	6.47842i		−	0.393536i	−0.980450	−	0.196768i	$-0.936955\pi$
$271$		−	6.47842i		−	0.393536i	0.980450	−	0.196768i	$-0.0630445\pi$
$272$	12.5592	−	1.32384i	0.761516	−	0.0802697i
$273$		0			0
$274$	−0.560650	−	21.3491i	−0.0338701	−	1.28975i
$275$	−0.563529	−	1.11059i	−0.0339821	−	0.0669708i
$276$		0			0
$277$	−10.7023	−	10.7023i	−0.643041	−	0.643041i	0.308261	−	0.951302i	$-0.400253\pi$
$277$	−10.7023	−	10.7023i	−0.643041	−	0.643041i	−0.951302	+	0.308261i	$0.900253\pi$
$278$	16.9220	+	16.0560i	1.01492	+	0.962974i
$279$		0			0
$280$	−6.76989	+	5.77486i	−0.404578	+	0.345114i
$281$	23.3237			1.39138			0.695688	−	0.718344i	$-0.255100\pi$
$281$	23.3237			1.39138			0.695688	+	0.718344i	$0.255100\pi$
$282$		0			0
$283$	7.39967	−	7.39967i	0.439865	−	0.439865i	−0.452102	−	0.891966i	$-0.649326\pi$
$283$	7.39967	−	7.39967i	0.439865	−	0.439865i	0.891966	+	0.452102i	$0.149326\pi$
$284$	−0.00998767	−	0.190030i	−0.000592659	−	0.0112762i
$285$		0			0
$286$	−0.0225902	−	0.860219i	−0.00133579	−	0.0508658i
$287$			0.224366i			0.0132439i
$288$		0			0
$289$	−7.03205			−0.413650
$290$	11.6176	+	1.53851i	0.682210	+	0.0903444i
$291$		0			0
$292$	−15.9605	+	0.838855i	−0.934016	+	0.0490903i
$293$	5.94867	−	5.94867i	0.347525	−	0.347525i	−0.511662	−	0.859187i	$-0.670970\pi$
$293$	5.94867	−	5.94867i	0.347525	−	0.347525i	0.859187	+	0.511662i	$0.170970\pi$
$294$		0			0
$295$	14.0078	+	2.23066i	0.815567	+	0.129874i
$296$	−17.4173	−	14.8690i	−1.01236	−	0.864244i
$297$		0			0
$298$	16.1452	+	15.3189i	0.935264	+	0.887399i
$299$	3.41361	−	3.41361i	0.197414	−	0.197414i
$300$		0			0
$301$	9.32889	+	9.32889i	0.537708	+	0.537708i
$302$	30.9276	−	0.812190i	1.77968	−	0.0467363i
$303$		0			0
$304$	12.3622	−	15.2755i	0.709023	−	0.876108i
$305$	−3.38526	+	21.2583i	−0.193839	+	1.21725i
$306$		0			0
$307$	12.0570	+	12.0570i	0.688130	+	0.688130i	0.961818	−	0.273689i	$-0.0882437\pi$
$307$	12.0570	+	12.0570i	0.688130	+	0.688130i	−0.273689	+	0.961818i	$0.588244\pi$
$308$	0.520921	+	0.468898i	0.0296822	+	0.0267179i
$309$		0			0
$310$	−14.9485	+	11.4522i	−0.849016	+	0.650444i
$311$			31.3243i			1.77624i	0.459615	+	0.888118i	$0.347988\pi$
$311$			31.3243i			1.77624i	−0.459615	+	0.888118i	$0.652012\pi$
$312$		0			0
$313$	−24.0690			−1.36046			−0.680230	−	0.732999i	$-0.738120\pi$
$313$	−24.0690			−1.36046			−0.680230	+	0.732999i	$0.738120\pi$
$314$	−21.1897	+	22.3326i	−1.19580	+	1.26030i
$315$		0			0
$316$	−0.594790	−	11.3168i	−0.0334596	−	0.636618i
$317$	−10.2657	−	10.2657i	−0.576579	−	0.576579i	0.357380	−	0.933959i	$-0.383670\pi$
$317$	−10.2657	−	10.2657i	−0.576579	−	0.576579i	−0.933959	+	0.357380i	$0.883670\pi$
$318$		0			0
$319$		−	0.923046i		−	0.0516807i
$320$	12.6442	+	12.6540i	0.706833	+	0.707381i
$321$		0			0
$322$	0.103222	+	3.93061i	0.00575233	+	0.219044i
$323$	10.9677	−	10.9677i	0.610257	−	0.610257i
$324$		0			0
$325$	5.52710	+	10.8927i	0.306589	+	0.604216i
$326$	7.11082	+	6.74690i	0.393832	+	0.373676i
$327$		0			0
$328$	0.449649	−	0.0354901i	0.0248277	−	0.00195961i
$329$	1.62112			0.0893755
$330$		0			0
$331$	−12.7608	−	12.7608i	−0.701395	−	0.701395i	0.263315	−	0.964710i	$-0.415184\pi$
$331$	−12.7608	−	12.7608i	−0.701395	−	0.701395i	−0.964710	+	0.263315i	$0.915184\pi$
$332$	23.2129	−	25.7883i	1.27397	−	1.41532i
$333$		0			0
$334$	24.6525	−	0.647400i	1.34892	−	0.0354242i
$335$	−4.95953	+	31.1443i	−0.270968	+	1.70159i
$336$		0			0
$337$			17.3967i			0.947660i	0.880616	+	0.473830i	$0.157129\pi$
$337$			17.3967i			0.947660i	−0.880616	+	0.473830i	$0.842871\pi$
$338$	−0.261071	−	9.94139i	−0.0142004	−	0.540741i
$339$		0			0
$340$	8.87811	+	10.9790i	0.481483	+	0.595419i
$341$	1.04880	+	1.04880i	0.0567956	+	0.0567956i
$342$		0			0
$343$		−	16.9122i		−	0.913175i
$344$	17.2203	−	20.1716i	0.928457	−	1.08758i
$345$		0			0
$346$	25.2866	+	23.9925i	1.35942	+	1.28984i
$347$	9.64234	+	9.64234i	0.517628	+	0.517628i	0.916853	−	0.399225i	$-0.130721\pi$
$347$	9.64234	+	9.64234i	0.517628	+	0.517628i	−0.399225	+	0.916853i	$0.630721\pi$
$348$		0			0
$349$	−3.66120	−	3.66120i	−0.195980	−	0.195980i	0.602294	−	0.798274i	$-0.294253\pi$
$349$	−3.66120	−	3.66120i	−0.195980	−	0.195980i	−0.798274	+	0.602294i	$0.794253\pi$
$350$	−9.53441	−	2.84084i	−0.509636	−	0.151849i
$351$		0			0
$352$	0.857315	−	1.11814i	0.0456951	−	0.0595973i
$353$	18.9960			1.01106			0.505528	−	0.862810i	$-0.331298\pi$
$353$	18.9960			1.01106			0.505528	+	0.862810i	$0.331298\pi$
$354$		0			0
$355$	0.172226	−	0.124909i	0.00914081	−	0.00662949i
$356$	−21.8297	+	1.14733i	−1.15697	+	0.0608084i
$357$		0			0
$358$	18.0827	+	17.1573i	0.955700	+	0.906789i
$359$		−	8.71770i		−	0.460103i	−0.973178	−	0.230051i	$-0.926111\pi$
$359$		−	8.71770i		−	0.460103i	0.973178	−	0.230051i	$-0.0738894\pi$
$360$		0			0
$361$		−	5.13530i		−	0.270279i
$362$	9.74625	−	10.2719i	0.512252	−	0.539882i
$363$		0			0
$364$	−5.10921	−	4.59896i	−0.267795	−	0.241051i
$365$	−10.4910	−	14.4651i	−0.549124	−	0.757138i
$366$		0			0
$367$	−28.0501			−1.46420			−0.732101	−	0.681196i	$-0.761460\pi$
$367$	−28.0501			−1.46420			−0.732101	+	0.681196i	$0.761460\pi$
$368$	7.86098	−	0.828609i	0.409782	−	0.0431942i
$369$		0			0
$370$	3.36136	−	25.3824i	0.174749	−	1.31957i
$371$	−7.52841	−	7.52841i	−0.390856	−	0.390856i
$372$		0			0
$373$	−4.90740	−	4.90740i	−0.254096	−	0.254096i	0.568552	−	0.822647i	$-0.307504\pi$
$373$	−4.90740	−	4.90740i	−0.254096	−	0.254096i	−0.822647	+	0.568552i	$0.807504\pi$
$374$	0.765468	−	0.806756i	0.0395814	−	0.0417163i
$375$		0			0
$376$	−0.256429	−	3.24888i	−0.0132243	−	0.167548i
$377$			9.05326i			0.466267i
$378$		0			0
$379$	26.0620	+	26.0620i	1.33872	+	1.33872i	0.897305	+	0.441412i	$0.145522\pi$
$379$	26.0620	+	26.0620i	1.33872	+	1.33872i	0.441412	+	0.897305i	$0.354478\pi$
$380$	21.8486	+	2.31158i	1.12081	+	0.118582i
$381$		0			0
$382$	−17.8145	+	0.467826i	−0.911467	+	0.0239361i
$383$		−	6.91314i		−	0.353245i	−0.984279	−	0.176623i	$-0.943483\pi$
$383$		−	6.91314i		−	0.353245i	0.984279	−	0.176623i	$-0.0565172\pi$
$384$		0			0
$385$	−0.123231	+	0.773850i	−0.00628042	+	0.0394391i
$386$	0.191467	+	7.29091i	0.00974541	+	0.371098i
$387$		0			0
$388$	1.09606	+	20.8542i	0.0556440	+	1.05871i
$389$	14.5222	+	14.5222i	0.736302	+	0.736302i	0.971860	−	0.235558i	$-0.0756918\pi$
$389$	14.5222	+	14.5222i	0.736302	+	0.736302i	−0.235558	+	0.971860i	$0.575692\pi$
$390$		0			0
$391$	6.23906			0.315523
$392$	−14.1561	+	1.11731i	−0.714989	+	0.0564329i
$393$		0			0
$394$	−4.95287	+	5.22002i	−0.249522	+	0.262981i
$395$	10.2565	−	7.43864i	0.516060	−	0.374279i
$396$		0			0
$397$	18.3367	−	18.3367i	0.920291	−	0.920291i	−0.0767588	−	0.997050i	$-0.524457\pi$
$397$	18.3367	−	18.3367i	0.920291	−	0.920291i	0.997050	+	0.0767588i	$0.0244571\pi$
$398$	−10.7239	+	0.281620i	−0.537540	+	0.0141163i
$399$		0			0
$400$	−4.18515	+	19.5572i	−0.209257	+	0.977861i
$401$		−	33.5380i		−	1.67481i	−0.546585	−	0.837404i	$-0.684073\pi$
$401$		−	33.5380i		−	1.67481i	0.546585	−	0.837404i	$-0.315927\pi$
$402$		0			0
$403$	−10.2866	−	10.2866i	−0.512414	−	0.512414i
$404$	−9.55523	−	8.60097i	−0.475391	−	0.427914i
$405$		0			0
$406$	−5.34908	−	5.07533i	−0.265471	−	0.251884i
$407$	−2.01669			−0.0999634
$408$		0			0
$409$		−	18.0044i		−	0.890260i	−0.895466	−	0.445130i	$-0.853158\pi$
$409$		−	18.0044i		−	0.890260i	0.895466	−	0.445130i	$-0.146842\pi$
$410$	0.306685	+	0.400312i	0.0151461	+	0.0197700i
$411$		0			0
$412$	−0.803748	−	15.2925i	−0.0395978	−	0.753407i
$413$	−6.31084	−	6.31084i	−0.310536	−	0.310536i
$414$		0			0
$415$	38.3096	+	6.10056i	1.88054	+	0.299465i
$416$	−8.40857	+	10.9668i	−0.412264	+	0.537691i
$417$		0			0
$418$	−0.0454291	−	1.72991i	−0.00222201	−	0.0846125i
$419$	16.7671	+	16.7671i	0.819126	+	0.819126i	0.985981	−	0.166856i	$-0.0533614\pi$
$419$	16.7671	+	16.7671i	0.819126	+	0.819126i	−0.166856	+	0.985981i	$0.553361\pi$
$420$		0			0
$421$	9.17528	−	9.17528i	0.447176	−	0.447176i	−0.447239	−	0.894415i	$-0.647593\pi$
$421$	9.17528	−	9.17528i	0.447176	−	0.447176i	0.894415	+	0.447239i	$0.147593\pi$
$422$	−0.832854	+	0.877777i	−0.0405427	+	0.0427295i
$423$		0			0
$424$	−13.8968	+	16.2785i	−0.674888	+	0.790553i
$425$	−4.90331	+	15.0052i	−0.237846	+	0.727859i
$426$		0			0
$427$	9.57736	−	9.57736i	0.463481	−	0.463481i
$428$	8.93831	+	8.04566i	0.432049	+	0.388902i
$429$		0			0
$430$	29.3962	+	3.89290i	1.41761	+	0.187733i
$431$	−36.6726			−1.76646			−0.883228	−	0.468943i	$-0.844635\pi$
$431$	−36.6726			−1.76646			−0.883228	+	0.468943i	$0.844635\pi$
$432$		0			0
$433$		−	28.1455i		−	1.35259i	−0.736633	−	0.676293i	$-0.763586\pi$
$433$		−	28.1455i		−	1.35259i	0.736633	−	0.676293i	$-0.236414\pi$
$434$	11.8446	−	0.311051i	0.568558	−	0.0149309i
$435$		0			0
$436$	0.380152	+	0.342187i	0.0182060	+	0.0163878i
$437$	6.86480	−	6.86480i	0.328388	−	0.328388i
$438$		0			0
$439$	−3.32665			−0.158772			−0.0793862	−	0.996844i	$-0.525296\pi$
$439$	−3.32665			−0.158772			−0.0793862	+	0.996844i	$0.525296\pi$
$440$	1.57036	+	0.124559i	0.0748640	+	0.00593810i
$441$		0			0
$442$	−7.50772	+	7.91268i	−0.357106	+	0.376368i
$443$	−6.03644	−	6.03644i	−0.286800	−	0.286800i	0.549013	−	0.835814i	$-0.315004\pi$
$443$	−6.03644	−	6.03644i	−0.286800	−	0.286800i	−0.835814	+	0.549013i	$0.815004\pi$
$444$		0			0
$445$	−14.3489	−	19.7844i	−0.680203	−	0.937871i
$446$	35.7180	−	0.937992i	1.69130	−	0.0444152i
$447$		0			0
$448$	−1.76577	−	11.1162i	−0.0834248	−	0.525193i
$449$			14.2691i			0.673402i	0.941612	+	0.336701i	$0.109311\pi$
$449$			14.2691i			0.673402i	−0.941612	+	0.336701i	$0.890689\pi$
$450$		0			0
$451$	0.0280862	−	0.0280862i	0.00132253	−	0.00132253i
$452$	13.7584	−	0.723116i	0.647139	−	0.0340125i
$453$		0			0
$454$	−9.11065	+	9.60207i	−0.427584	+	0.450647i
$455$	1.20865	−	7.58994i	0.0566624	−	0.355822i
$456$		0			0
$457$	−25.0611			−1.17231			−0.586154	−	0.810200i	$-0.699359\pi$
$457$	−25.0611			−1.17231			−0.586154	+	0.810200i	$0.699359\pi$
$458$	0.0615201	−	0.0648384i	0.00287464	−	0.00302970i
$459$		0			0
$460$	5.55692	+	6.87188i	0.259093	+	0.320403i
$461$	11.6030	−	11.6030i	0.540407	−	0.540407i	−0.383241	−	0.923648i	$-0.625192\pi$
$461$	11.6030	−	11.6030i	0.540407	−	0.540407i	0.923648	+	0.383241i	$0.125192\pi$
$462$		0			0
$463$	8.74913			0.406607			0.203303	−	0.979116i	$-0.434832\pi$
$463$	8.74913			0.406607			0.203303	+	0.979116i	$0.434832\pi$
$464$	−9.32531	+	11.5229i	−0.432917	+	0.534936i
$465$		0			0
$466$	−0.501241	−	19.0869i	−0.0232196	−	0.884183i
$467$	−19.3047	+	19.3047i	−0.893316	+	0.893316i	−0.994834	−	0.101518i	$-0.967630\pi$
$467$	−19.3047	+	19.3047i	−0.893316	+	0.893316i	0.101518	+	0.994834i	$0.467630\pi$
$468$		0			0
$469$	14.0312	−	14.0312i	0.647901	−	0.647901i
$470$	2.89240	−	2.21591i	0.133416	−	0.102212i
$471$		0			0
$472$	−11.6493	+	13.6458i	−0.536201	+	0.628097i
$473$		−	2.33559i		−	0.107391i
$474$		0			0
$475$	11.1150	+	21.9052i	0.509993	+	1.00508i
$476$	−0.466288	−	8.87182i	−0.0213723	−	0.406639i
$477$		0			0
$478$	7.89009	−	0.207202i	0.360884	−	0.00947719i
$479$	19.9695			0.912431			0.456215	−	0.889869i	$-0.349205\pi$
$479$	19.9695			0.912431			0.456215	+	0.889869i	$0.349205\pi$
$480$		0			0
$481$	19.7797			0.901877
$482$	−22.2913	+	0.585392i	−1.01534	+	0.0266639i
$483$		0			0
$484$	1.14818	+	21.8458i	0.0521899	+	0.992990i
$485$	−18.9003	+	13.7077i	−0.858219	+	0.622434i
$486$		0			0
$487$		−	34.8592i		−	1.57962i	−0.613351	−	0.789811i	$-0.710179\pi$
$487$		−	34.8592i		−	1.57962i	0.613351	−	0.789811i	$-0.289821\pi$
$488$	−20.7089	−	17.6790i	−0.937446	−	0.800289i
$489$		0			0
$490$	−9.65520	−	12.6028i	−0.436177	−	0.569336i
$491$	−21.4659	+	21.4659i	−0.968743	+	0.968743i	−0.999526	−	0.0307829i	$-0.990200\pi$
$491$	−21.4659	+	21.4659i	−0.968743	+	0.968743i	0.0307829	+	0.999526i	$0.490200\pi$
$492$		0			0
$493$	−8.27333	+	8.27333i	−0.372612	+	0.372612i
$494$	0.445570	+	16.9670i	0.0200471	+	0.763380i
$495$		0			0
$496$	−2.49695	−	23.6884i	−0.112116	−	1.06364i
$497$	−0.133866			−0.00600471
$498$		0			0
$499$	−18.0781	+	18.0781i	−0.809287	+	0.809287i	−0.984526	−	0.175239i	$-0.943930\pi$
$499$	−18.0781	+	18.0781i	−0.809287	+	0.809287i	0.175239	+	0.984526i	$0.443930\pi$
$500$	−20.8944	+	7.96397i	−0.934425	+	0.356160i
$501$		0			0
$502$	14.5095	−	15.2922i	0.647593	−	0.682523i
$503$	−3.90394			−0.174068			−0.0870341	−	0.996205i	$-0.527739\pi$
$503$	−3.90394			−0.174068			−0.0870341	+	0.996205i	$0.527739\pi$
$504$		0			0
$505$	2.26042	−	14.1947i	0.100587	−	0.631656i
$506$	0.479115	−	0.504958i	0.0212993	−	0.0224481i
$507$		0			0
$508$	−6.35353	+	0.333931i	−0.281892	+	0.0148158i
$509$	11.0778	−	11.0778i	0.491014	−	0.491014i	−0.417612	−	0.908626i	$-0.637133\pi$
$509$	11.0778	−	11.0778i	0.491014	−	0.491014i	0.908626	+	0.417612i	$0.137133\pi$
$510$		0			0
$511$			11.2433i			0.497374i
$512$	−21.9986	+	5.29713i	−0.972212	+	0.234102i
$513$		0			0
$514$	28.3731	−	0.745108i	1.25149	−	0.0328653i
$515$	13.8597	−	10.0519i	0.610732	−	0.442941i
$516$		0			0
$517$	−0.202933	−	0.202933i	−0.00892500	−	0.00892500i
$518$	−11.0887	+	11.6868i	−0.487207	+	0.513487i
$519$		0			0
$520$	−15.4021	−	1.22167i	−0.675428	−	0.0535739i
$521$	2.61052			0.114369			0.0571844	−	0.998364i	$-0.481788\pi$
$521$	2.61052			0.114369			0.0571844	+	0.998364i	$0.481788\pi$
$522$		0			0
$523$	−21.2735	+	21.2735i	−0.930226	+	0.930226i	−0.997720	−	0.0674935i	$-0.978500\pi$
$523$	−21.2735	+	21.2735i	−0.930226	+	0.930226i	0.0674935	+	0.997720i	$0.478500\pi$
$524$	17.8574	+	16.0741i	0.780106	+	0.702199i
$525$		0			0
$526$	40.5661	−	1.06531i	1.76876	−	0.0464496i
$527$		−	18.8009i		−	0.818980i
$528$		0			0
$529$	−19.0949			−0.830213
$530$	−23.7227	−	3.14157i	−1.03045	−	0.136461i
$531$		0			0
$532$	−10.2747	−	9.24855i	−0.445463	−	0.400975i
$533$	−0.275471	+	0.275471i	−0.0119320	+	0.0119320i
$534$		0			0
$535$	−2.11448	+	13.2782i	−0.0914168	+	0.574068i
$536$	−30.3393	−	25.9004i	−1.31046	−	1.11873i
$537$		0			0
$538$	18.8604	−	19.8777i	0.813132	−	0.856991i
$539$	−0.884224	+	0.884224i	−0.0380862	+	0.0380862i
$540$		0			0
$541$	−8.92150	−	8.92150i	−0.383565	−	0.383565i	0.488820	−	0.872385i	$-0.337428\pi$
$541$	−8.92150	−	8.92150i	−0.383565	−	0.383565i	−0.872385	+	0.488820i	$0.837428\pi$
$542$	0.240517	+	9.15871i	0.0103311	+	0.393400i
$543$		0			0
$544$	−17.7062	+	2.33782i	−0.759146	+	0.100233i
$545$	−0.0899300	+	0.564732i	−0.00385218	+	0.0241905i
$546$		0			0
$547$	24.0470	+	24.0470i	1.02818	+	1.02818i	0.999591	+	0.0285840i	$0.00909983\pi$
$547$	24.0470	+	24.0470i	1.02818	+	1.02818i	0.0285840	+	0.999591i	$0.490900\pi$
$548$	1.58521	+	30.1610i	0.0677168	+	1.28841i
$549$		0			0
$550$	0.837907	+	1.54914i	0.0357285	+	0.0660557i
$551$			18.2062i			0.775609i
$552$		0			0
$553$	−7.97205			−0.339006
$554$	15.5275	+	14.7328i	0.659701	+	0.625939i
$555$		0			0
$556$	−24.5192	−	22.0705i	−1.03985	−	0.935999i
$557$	17.5090	+	17.5090i	0.741879	+	0.741879i	0.972939	−	0.231060i	$-0.0742195\pi$
$557$	17.5090	+	17.5090i	0.741879	+	0.741879i	−0.231060	+	0.972939i	$0.574220\pi$
$558$		0			0
$559$			22.9076i			0.968886i
$560$	9.35637	−	8.41540i	0.395379	−	0.355616i
$561$		0			0
$562$	−32.9733	+	0.865914i	−1.39090	+	0.0365264i
$563$	11.2032	−	11.2032i	0.472157	−	0.472157i	−0.430455	−	0.902612i	$-0.641647\pi$
$563$	11.2032	−	11.2032i	0.472157	−	0.472157i	0.902612	+	0.430455i	$0.141647\pi$
$564$		0			0
$565$	9.04353	+	12.4693i	0.380464	+	0.524588i
$566$	−10.1864	+	10.7358i	−0.428166	+	0.451260i
$567$		0			0
$568$	0.0211749	+	0.268280i	0.000888478	+	0.0112568i
$569$	4.83805			0.202821			0.101411	−	0.994845i	$-0.467664\pi$
$569$	4.83805			0.202821			0.101411	+	0.994845i	$0.467664\pi$
$570$		0			0
$571$	9.64695	+	9.64695i	0.403712	+	0.403712i	0.879539	−	0.475827i	$-0.157851\pi$
$571$	9.64695	+	9.64695i	0.403712	+	0.403712i	−0.475827	+	0.879539i	$0.657851\pi$
$572$	0.0638728	+	1.21528i	0.00267066	+	0.0508132i
$573$		0			0
$574$	−0.00832978	−	0.317192i	−0.000347678	−	0.0132393i
$575$	−3.06904	+	9.39194i	−0.127988	+	0.391671i
$576$		0			0
$577$			18.0261i			0.750438i	0.926936	+	0.375219i	$0.122432\pi$
$577$			18.0261i			0.750438i	−0.926936	+	0.375219i	$0.877568\pi$
$578$	9.94139	−	0.261071i	0.413508	−	0.0108591i
$579$		0			0
$580$	−16.4813	−	1.74372i	−0.684347	−	0.0724039i
$581$	−17.2593	−	17.2593i	−0.716038	−	0.716038i
$582$		0			0
$583$			1.88482i			0.0780614i
$584$	22.5326	−	1.77846i	0.932405	−	0.0735932i
$585$		0			0
$586$	−8.18894	+	8.63064i	−0.338282	+	0.356528i
$587$	−5.25140	−	5.25140i	−0.216749	−	0.216749i	0.590378	−	0.807127i	$-0.298979\pi$
$587$	−5.25140	−	5.25140i	−0.216749	−	0.216749i	−0.807127	+	0.590378i	$0.798979\pi$
$588$		0			0
$589$	−20.6865	−	20.6865i	−0.852373	−	0.852373i
$590$	−19.8860	−	2.63349i	−0.818695	−	0.108419i
$591$		0			0
$592$	25.1753	+	20.3741i	1.03470	+	0.837369i
$593$	−0.0811054			−0.00333060			−0.00166530	−	0.999999i	$-0.500530\pi$
$593$	−0.0811054			−0.00333060			−0.00166530	+	0.999999i	$0.500530\pi$
$594$		0			0
$595$	8.04060	−	5.83155i	0.329632	−	0.239070i
$596$	−23.3936	−	21.0573i	−0.958238	−	0.862541i
$597$		0			0
$598$	−4.69918	+	4.95264i	−0.192164	+	0.202529i
$599$			8.29253i			0.338824i	0.985545	+	0.169412i	$0.0541868\pi$
$599$			8.29253i			0.338824i	−0.985545	+	0.169412i	$0.945813\pi$
$600$		0			0
$601$		−	5.82196i		−	0.237483i	−0.992925	−	0.118741i	$-0.962114\pi$
$601$		−	5.82196i		−	0.237483i	0.992925	−	0.118741i	$-0.0378859\pi$
$602$	−13.5348	−	12.8422i	−0.551639	−	0.523407i
$603$		0			0
$604$	−43.6930	+	2.29643i	−1.77784	+	0.0934404i
$605$	−19.7990	+	14.3595i	−0.804944	+	0.583796i
$606$		0			0
$607$	−22.0548			−0.895178			−0.447589	−	0.894239i	$-0.647717\pi$
$607$	−22.0548			−0.895178			−0.447589	+	0.894239i	$0.647717\pi$
$608$	−16.9097	+	22.0543i	−0.685779	+	0.894419i
$609$		0			0
$610$	3.99659	−	30.1791i	0.161817	−	1.22192i
$611$	1.99038	+	1.99038i	0.0805220	+	0.0805220i
$612$		0			0
$613$	14.9250	+	14.9250i	0.602816	+	0.602816i	0.941059	−	0.338243i	$-0.109832\pi$
$613$	14.9250	+	14.9250i	0.602816	+	0.602816i	−0.338243	+	0.941059i	$0.609832\pi$
$614$	−17.4929	−	16.5977i	−0.705957	−	0.669828i
$615$		0			0
$616$	−0.753848	−	0.643553i	−0.0303734	−	0.0259295i
$617$		−	31.5403i		−	1.26976i	−0.772609	−	0.634882i	$-0.781049\pi$
$617$		−	31.5403i		−	1.26976i	0.772609	−	0.634882i	$-0.218951\pi$
$618$		0			0
$619$	6.89013	+	6.89013i	0.276938	+	0.276938i	0.831885	−	0.554947i	$-0.187262\pi$
$619$	6.89013	+	6.89013i	0.276938	+	0.276938i	−0.554947	+	0.831885i	$0.687262\pi$
$620$	20.7079	−	16.7453i	0.831647	−	0.672508i
$621$		0			0
$622$	−1.16294	−	44.2840i	−0.0466297	−	1.77562i
$623$			15.3778i			0.616100i
$624$		0			0
$625$	−20.1760	−	14.7624i	−0.807042	−	0.590494i
$626$	34.0270	−	0.893583i	1.35999	−	0.0357148i
$627$		0			0
$628$	29.1273	−	32.3589i	1.16230	−	1.29126i
$629$	18.0757	+	18.0757i	0.720725	+	0.720725i
$630$		0			0
$631$	−32.9043			−1.30990			−0.654950	−	0.755672i	$-0.727310\pi$
$631$	−32.9043			−1.30990			−0.654950	+	0.755672i	$0.727310\pi$
$632$	1.26102	+	15.9767i	0.0501605	+	0.635520i
$633$		0			0
$634$	14.8940	+	14.1318i	0.591517	+	0.561244i
$635$	−4.17625	−	5.75825i	−0.165729	−	0.228509i
$636$		0			0
$637$	8.67249	−	8.67249i	0.343617	−	0.343617i
$638$	0.0342689	+	1.30493i	0.00135672	+	0.0516629i
$639$		0			0
$640$	−18.3452	−	17.4199i	−0.725159	−	0.688581i
$641$		−	28.3921i		−	1.12142i	−0.828013	−	0.560710i	$-0.810528\pi$
$641$		−	28.3921i		−	1.12142i	0.828013	−	0.560710i	$-0.189472\pi$
$642$		0			0
$643$	−2.71547	−	2.71547i	−0.107088	−	0.107088i	0.651533	−	0.758621i	$-0.274126\pi$
$643$	−2.71547	−	2.71547i	−0.107088	−	0.107088i	−0.758621	+	0.651533i	$0.774126\pi$
$644$	−0.291855	−	5.55298i	−0.0115007	−	0.218818i
$645$		0			0
$646$	−15.0981	+	15.9125i	−0.594027	+	0.626067i
$647$	33.2882			1.30869			0.654346	−	0.756195i	$-0.272944\pi$
$647$	33.2882			1.30869			0.654346	+	0.756195i	$0.272944\pi$
$648$		0			0
$649$			1.57999i			0.0620200i
$650$	−8.21821	−	15.1940i	−0.322345	−	0.595959i
$651$		0			0
$652$	−10.3032	−	9.27427i	−0.403506	−	0.363208i
$653$	4.82719	+	4.82719i	0.188902	+	0.188902i	0.795221	−	0.606319i	$-0.207355\pi$
$653$	4.82719	+	4.82719i	0.188902	+	0.188902i	−0.606319	+	0.795221i	$0.707355\pi$
$654$		0			0
$655$	−4.22442	+	26.5280i	−0.165062	+	1.03653i
$656$	−0.634364	+	0.0668669i	−0.0247677	+	0.00261071i
$657$		0			0
$658$	−2.29183	+	0.0601857i	−0.0893447	+	0.00234628i
$659$	−22.5484	−	22.5484i	−0.878359	−	0.878359i	0.115005	−	0.993365i	$-0.463311\pi$
$659$	−22.5484	−	22.5484i	−0.878359	−	0.878359i	−0.993365	+	0.115005i	$0.963311\pi$
$660$		0			0
$661$	17.3551	−	17.3551i	0.675035	−	0.675035i	−0.283838	−	0.958872i	$-0.591608\pi$
$661$	17.3551	−	17.3551i	0.675035	−	0.675035i	0.958872	+	0.283838i	$0.0916077\pi$
$662$	18.5140	+	17.5665i	0.719567	+	0.682741i
$663$		0			0
$664$	−31.8592	+	37.3194i	−1.23638	+	1.44827i
$665$	2.43061	−	15.2634i	0.0942548	−	0.591890i
$666$		0			0
$667$	−5.17838	+	5.17838i	−0.200508	+	0.200508i
$668$	−34.8278	+	1.83049i	−1.34753	+	0.0708239i
$669$		0			0
$670$	5.85516	−	44.2136i	0.226205	−	1.70812i
$671$	−2.39780			−0.0925661
$672$		0			0
$673$			20.2889i			0.782080i	0.920374	+	0.391040i	$0.127885\pi$
$673$			20.2889i			0.782080i	−0.920374	+	0.391040i	$0.872115\pi$
$674$	−0.645869	−	24.5942i	−0.0248780	−	0.947334i
$675$		0			0
$676$	0.738167	+	14.0447i	0.0283910	+	0.540181i
$677$	−0.349388	+	0.349388i	−0.0134281	+	0.0134281i	−0.713789	−	0.700361i	$-0.753022\pi$
$677$	−0.349388	+	0.349388i	−0.0134281	+	0.0134281i	0.700361	+	0.713789i	$0.253022\pi$
$678$		0			0
$679$	14.6906			0.563775
$680$	−12.9588	−	15.1917i	−0.496948	−	0.582574i
$681$		0			0
$682$	−1.52165	−	1.44378i	−0.0582670	−	0.0552850i
$683$	−4.40464	−	4.40464i	−0.168539	−	0.168539i	0.617798	−	0.786337i	$-0.288025\pi$
$683$	−4.40464	−	4.40464i	−0.168539	−	0.168539i	−0.786337	+	0.617798i	$0.788025\pi$
$684$		0			0
$685$	−27.3351	+	19.8252i	−1.04442	+	0.757480i
$686$	0.627882	+	23.9093i	0.0239726	+	0.912860i
$687$		0			0
$688$	−23.5959	+	29.1564i	−0.899586	+	1.11158i
$689$		−	18.4864i		−	0.704276i
$690$		0			0
$691$	−22.7615	+	22.7615i	−0.865890	+	0.865890i	−0.992014	−	0.126125i	$-0.959746\pi$
$691$	−22.7615	+	22.7615i	−0.865890	+	0.865890i	0.126125	+	0.992014i	$0.459746\pi$
$692$	−36.6391	−	32.9800i	−1.39281	−	1.25371i
$693$		0			0
$694$	−13.9896	−	13.2736i	−0.531038	−	0.503861i
$695$	5.80034	−	36.4243i	0.220020	−	1.38165i
$696$		0			0
$697$	−0.503478			−0.0190706
$698$	5.31186	+	5.04001i	0.201057	+	0.190767i
$699$		0			0
$700$	13.5845	+	3.66219i	0.513447	+	0.138418i
$701$	34.9589	−	34.9589i	1.32038	−	1.32038i	0.406913	−	0.913467i	$-0.366605\pi$
$701$	34.9589	−	34.9589i	1.32038	−	1.32038i	0.913467	−	0.406913i	$-0.133395\pi$
$702$		0			0
$703$	39.7771			1.50022
$704$	−1.17050	+	1.61258i	−0.0441148	+	0.0607763i
$705$		0			0
$706$	−26.8552	+	0.705245i	−1.01071	+	0.0265422i
$707$	−6.39503	+	6.39503i	−0.240510	+	0.240510i
$708$		0			0
$709$	−20.7652	+	20.7652i	−0.779854	+	0.779854i	−0.979806	−	0.199952i	$-0.935922\pi$
$709$	−20.7652	+	20.7652i	−0.779854	+	0.779854i	0.199952	+	0.979806i	$0.435922\pi$
$710$	−0.238843	+	0.182981i	−0.00896362	+	0.00686716i
$711$		0			0
$712$	30.8186	−	2.43246i	1.15498	−	0.0911602i
$713$		−	11.7677i		−	0.440704i
$714$		0			0
$715$	−1.10141	+	0.798814i	−0.0411905	+	0.0298740i
$716$	−26.2010	−	23.5843i	−0.979175	−	0.881387i
$717$		0			0
$718$	0.323653	+	12.3244i	0.0120786	+	0.459944i
$719$	−9.48453			−0.353713			−0.176857	−	0.984237i	$-0.556593\pi$
$719$	−9.48453			−0.353713			−0.176857	+	0.984237i	$0.556593\pi$
$720$		0			0
$721$	−10.7727			−0.401198
$722$	0.190653	+	7.25991i	0.00709536	+	0.270186i
$723$		0			0
$724$	−13.3972	+	14.8836i	−0.497902	+	0.553143i
$725$	−8.38451	−	16.5239i	−0.311393	−	0.613684i
$726$		0			0
$727$			29.4631i			1.09272i	0.837549	+	0.546362i	$0.183988\pi$
$727$			29.4631i			1.09272i	−0.837549	+	0.546362i	$0.816012\pi$
$728$	7.39376	+	6.31199i	0.274031	+	0.233938i
$729$		0			0
$730$	15.3684	+	20.0602i	0.568811	+	0.742462i
$731$	−20.9341	+	20.9341i	−0.774275	+	0.774275i
$732$		0			0
$733$	−13.5703	+	13.5703i	−0.501231	+	0.501231i	−0.911820	−	0.410590i	$-0.865323\pi$
$733$	−13.5703	+	13.5703i	−0.501231	+	0.501231i	0.410590	+	0.911820i	$0.365323\pi$
$734$	39.6551	−	1.04138i	1.46370	−	0.0384382i
$735$		0			0
$736$	−11.0825	+	1.46327i	−0.408507	+	0.0539369i
$737$	−3.51287			−0.129398
$738$		0			0
$739$	−1.19592	+	1.19592i	−0.0439927	+	0.0439927i	−0.728761	−	0.684768i	$-0.759903\pi$
$739$	−1.19592	+	1.19592i	−0.0439927	+	0.0439927i	0.684768	+	0.728761i	$0.259903\pi$
$740$	−3.80970	+	36.0085i	−0.140047	+	1.32370i
$741$		0			0
$742$	10.9226	+	10.3636i	0.400982	+	0.380460i
$743$	48.8695			1.79285			0.896424	−	0.443197i	$-0.146156\pi$
$743$	48.8695			1.79285			0.896424	+	0.443197i	$0.146156\pi$
$744$		0			0
$745$	5.53406	−	34.7521i	0.202752	−	1.27322i
$746$	7.11991	+	6.75553i	0.260679	+	0.247338i
$747$		0			0
$748$	−1.05221	+	1.16895i	−0.0384726	+	0.0427411i
$749$	5.98214	−	5.98214i	0.218583	−	0.218583i
$750$		0			0
$751$			17.8326i			0.650721i	0.945590	+	0.325360i	$0.105486\pi$
$751$			17.8326i			0.650721i	−0.945590	+	0.325360i	$0.894514\pi$
$752$	0.483138	+	4.58351i	0.0176182	+	0.167143i
$753$		0			0
$754$	−0.336111	−	12.7988i	−0.0122404	−	0.466106i
$755$	−28.7199	−	39.5993i	−1.04522	−	1.44117i
$756$		0			0
$757$	19.7676	+	19.7676i	0.718467	+	0.718467i	0.968291	−	0.249824i	$-0.0803728\pi$
$757$	19.7676	+	19.7676i	0.718467	+	0.718467i	−0.249824	+	0.968291i	$0.580373\pi$
$758$	−37.8121	−	35.8770i	−1.37340	−	1.30311i
$759$		0			0
$760$	−30.9738	−	2.45680i	−1.12354	−	0.0891173i
$761$	3.72357			0.134979			0.0674896	−	0.997720i	$-0.478501\pi$
$761$	3.72357			0.134979			0.0674896	+	0.997720i	$0.478501\pi$
$762$		0			0
$763$	0.254425	−	0.254425i	0.00921079	−	0.00921079i
$764$	25.1674	−	1.32276i	0.910524	−	0.0478556i
$765$		0			0
$766$	0.256657	+	9.77329i	0.00927339	+	0.353123i
$767$		−	15.4966i		−	0.559549i
$768$		0			0
$769$	−17.9937			−0.648868			−0.324434	−	0.945908i	$-0.605174\pi$
$769$	−17.9937			−0.648868			−0.324434	+	0.945908i	$0.605174\pi$
$770$	0.145485	−	1.09859i	0.00524290	−	0.0395903i
$771$		0			0
$772$	−0.541363	−	10.3002i	−0.0194841	−	0.370714i
$773$	14.5506	−	14.5506i	0.523350	−	0.523350i	−0.395232	−	0.918582i	$-0.629336\pi$
$773$	14.5506	−	14.5506i	0.523350	−	0.523350i	0.918582	+	0.395232i	$0.129336\pi$
$774$		0			0
$775$	28.3019	+	9.24831i	1.01663	+	0.332209i
$776$	−2.32376	−	29.4414i	−0.0834181	−	1.05688i
$777$		0			0
$778$	−21.0695	−	19.9912i	−0.755378	−	0.716719i
$779$	−0.553973	+	0.553973i	−0.0198482	+	0.0198482i
$780$		0			0
$781$	0.0167574	+	0.0167574i	0.000599629	+	0.000599629i
$782$	−8.82032	+	0.231631i	−0.315414	+	0.00828310i
$783$		0			0
$784$	19.9713	−	2.10513i	0.713262	−	0.0751833i
$785$	48.0705	+	7.65492i	1.71571	+	0.273216i
$786$		0			0
$787$	27.4478	+	27.4478i	0.978410	+	0.978410i	0.999772	−	0.0213618i	$-0.00680019\pi$
$787$	27.4478	+	27.4478i	0.978410	+	0.978410i	−0.0213618	+	0.999772i	$0.506800\pi$
$788$	6.80820	−	7.56356i	0.242532	−	0.269441i
$789$		0			0
$790$	−14.2237	+	10.8970i	−0.506056	+	0.387697i
$791$		−

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

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