LMFDB - Embedded newform 720.2.u.a.179.8

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			179.8
Character	$\chi$	$=$	720.179
Dual form			720.2.u.a.539.8

$q$-expansion

$f(q)$	$=$	$q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-0.419806 + 2.19631i) q^{5} -0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +O(q^{10})$	\(q+(-1.23687 + 0.685679i) q^{2} +(1.05969 - 1.69619i) q^{4} +(-0.419806 + 2.19631i) q^{5} -0.263783i q^{7} +(-0.147653 + 2.82457i) q^{8} +(-0.986717 - 3.00440i) q^{10} +(-0.913594 + 0.913594i) q^{11} +(-1.49018 + 1.49018i) q^{13} +(0.180870 + 0.326265i) q^{14} +(-1.75412 - 3.59487i) q^{16} -2.90538 q^{17} +(-0.296217 + 0.296217i) q^{19} +(3.28049 + 3.03947i) q^{20} +(0.503563 - 1.75643i) q^{22} +3.14640 q^{23} +(-4.64753 - 1.84404i) q^{25} +(0.821369 - 2.86493i) q^{26} +(-0.447426 - 0.279528i) q^{28} +(-2.43765 + 2.43765i) q^{29} +2.53546i q^{31} +(4.63454 + 3.24361i) q^{32} +(3.59358 - 1.99216i) q^{34} +(0.579348 + 0.110738i) q^{35} +(-1.53556 - 1.53556i) q^{37} +(0.163272 - 0.569491i) q^{38} +(-6.14164 - 1.51006i) q^{40} -10.7792 q^{41} +(-4.51269 + 4.51269i) q^{43} +(0.581504 + 2.51775i) q^{44} +(-3.89169 + 2.15742i) q^{46} -6.67809i q^{47} +6.93042 q^{49} +(7.01280 - 0.905871i) q^{50} +(0.948500 + 4.10674i) q^{52} +(-2.95356 + 2.95356i) q^{53} +(-1.62300 - 2.39006i) q^{55} +(0.745073 + 0.0389483i) q^{56} +(1.34361 - 4.68649i) q^{58} +(-9.76773 + 9.76773i) q^{59} +(-1.02388 - 1.02388i) q^{61} +(-1.73851 - 3.13603i) q^{62} +(-7.95640 - 0.834111i) q^{64} +(-2.64730 - 3.89847i) q^{65} +(3.67191 + 3.67191i) q^{67} +(-3.07880 + 4.92808i) q^{68} +(-0.792508 + 0.260279i) q^{70} -7.85546i q^{71} -12.4323 q^{73} +(2.95219 + 0.846384i) q^{74} +(0.188543 + 0.816337i) q^{76} +(0.240990 + 0.240990i) q^{77} +10.7196i q^{79} +(8.63182 - 2.34344i) q^{80} +(13.3324 - 7.39107i) q^{82} +(3.50410 - 3.50410i) q^{83} +(1.21970 - 6.38111i) q^{85} +(2.48735 - 8.67586i) q^{86} +(-2.44561 - 2.71540i) q^{88} -13.2383 q^{89} +(0.393083 + 0.393083i) q^{91} +(3.33421 - 5.33690i) q^{92} +(4.57903 + 8.25992i) q^{94} +(-0.526229 - 0.774936i) q^{95} -11.1057i q^{97} +(-8.57202 + 4.75204i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.23687	+	0.685679i	−0.874598	+	0.484848i
$2$	−1.23687	+	0.685679i	−0.874598	+	0.484848i
$3$		0			0
$3$		0			0
$4$	1.05969	−	1.69619i	0.529844	−	0.848095i
$5$	−0.419806	+	2.19631i	−0.187743	+	0.982218i
$5$	−0.419806	+	2.19631i	−0.187743	+	0.982218i
$6$		0			0
$7$		−	0.263783i		−	0.0997006i	−0.998757	−	0.0498503i	$-0.984126\pi$
$7$		−	0.263783i		−	0.0997006i	0.998757	−	0.0498503i	$-0.0158744\pi$
$8$	−0.147653	+	2.82457i	−0.0522031	+	0.998636i
$9$		0			0
$10$	−0.986717	−	3.00440i	−0.312027	−	0.950073i
$11$	−0.913594	+	0.913594i	−0.275459	+	0.275459i	−0.831293	−	0.555834i	$-0.812399\pi$
$11$	−0.913594	+	0.913594i	−0.275459	+	0.275459i	0.555834	+	0.831293i	$0.312399\pi$
$12$		0			0
$13$	−1.49018	+	1.49018i	−0.413300	+	0.413300i	−0.882887	−	0.469586i	$-0.844403\pi$
$13$	−1.49018	+	1.49018i	−0.413300	+	0.413300i	0.469586	+	0.882887i	$0.344403\pi$
$14$	0.180870	+	0.326265i	0.0483397	+	0.0871979i
$15$		0			0
$16$	−1.75412	−	3.59487i	−0.438531	−	0.898716i
$17$	−2.90538			−0.704659			−0.352329	−	0.935876i	$-0.614610\pi$
$17$	−2.90538			−0.704659			−0.352329	+	0.935876i	$0.614610\pi$
$18$		0			0
$19$	−0.296217	+	0.296217i	−0.0679568	+	0.0679568i	−0.740268	−	0.672312i	$-0.765302\pi$
$19$	−0.296217	+	0.296217i	−0.0679568	+	0.0679568i	0.672312	+	0.740268i	$0.265302\pi$
$20$	3.28049	+	3.03947i	0.733540	+	0.679646i
$21$		0			0
$22$	0.503563	−	1.75643i	0.107360	−	0.374472i
$23$	3.14640			0.656070			0.328035	−	0.944666i	$-0.393614\pi$
$23$	3.14640			0.656070			0.328035	+	0.944666i	$0.393614\pi$
$24$		0			0
$25$	−4.64753	−	1.84404i	−0.929505	−	0.368809i
$26$	0.821369	−	2.86493i	0.161084	−	0.561860i
$27$		0			0
$28$	−0.447426	−	0.279528i	−0.0845556	−	0.0528258i
$29$	−2.43765	+	2.43765i	−0.452660	+	0.452660i	−0.896236	−	0.443577i	$-0.853709\pi$
$29$	−2.43765	+	2.43765i	−0.452660	+	0.452660i	0.443577	+	0.896236i	$0.353709\pi$
$30$		0			0
$31$			2.53546i			0.455382i	0.973733	+	0.227691i	$0.0731177\pi$
$31$			2.53546i			0.455382i	−0.973733	+	0.227691i	$0.926882\pi$
$32$	4.63454	+	3.24361i	0.819279	+	0.573395i
$33$		0			0
$34$	3.59358	−	1.99216i	0.616293	−	0.341653i
$35$	0.579348	+	0.110738i	0.0979277	+	0.0187181i
$36$		0			0
$37$	−1.53556	−	1.53556i	−0.252444	−	0.252444i	0.569528	−	0.821972i	$-0.307126\pi$
$37$	−1.53556	−	1.53556i	−0.252444	−	0.252444i	−0.821972	+	0.569528i	$0.807126\pi$
$38$	0.163272	−	0.569491i	0.0264861	−	0.0923836i
$39$		0			0
$40$	−6.14164	−	1.51006i	−0.971078	−	0.238762i
$41$	−10.7792			−1.68343			−0.841713	−	0.539925i	$-0.818453\pi$
$41$	−10.7792			−1.68343			−0.841713	+	0.539925i	$0.818453\pi$
$42$		0			0
$43$	−4.51269	+	4.51269i	−0.688178	+	0.688178i	−0.961829	−	0.273651i	$-0.911769\pi$
$43$	−4.51269	+	4.51269i	−0.688178	+	0.688178i	0.273651	+	0.961829i	$0.411769\pi$
$44$	0.581504	+	2.51775i	0.0876651	+	0.379566i
$45$		0			0
$46$	−3.89169	+	2.15742i	−0.573798	+	0.318095i
$47$		−	6.67809i		−	0.974100i	−0.873374	−	0.487050i	$-0.838073\pi$
$47$		−	6.67809i		−	0.974100i	0.873374	−	0.487050i	$-0.161927\pi$
$48$		0			0
$49$	6.93042			0.990060
$50$	7.01280	−	0.905871i	0.991760	−	0.128109i
$51$		0			0
$52$	0.948500	+	4.10674i	0.131533	+	0.569503i
$53$	−2.95356	+	2.95356i	−0.405703	+	0.405703i	−0.880237	−	0.474534i	$-0.842617\pi$
$53$	−2.95356	+	2.95356i	−0.405703	+	0.405703i	0.474534	+	0.880237i	$0.342617\pi$
$54$		0			0
$55$	−1.62300	−	2.39006i	−0.218845	−	0.322276i
$56$	0.745073	+	0.0389483i	0.0995646	+	0.00520468i
$57$		0			0
$58$	1.34361	−	4.68649i	0.176424	−	0.615367i
$59$	−9.76773	+	9.76773i	−1.27165	+	1.27165i	−0.326428	+	0.945222i	$0.605845\pi$
$59$	−9.76773	+	9.76773i	−1.27165	+	1.27165i	−0.945222	+	0.326428i	$0.894155\pi$
$60$		0			0
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	0.638515	−	0.769610i	$-0.279549\pi$
$61$	−1.02388	−	1.02388i	−0.131095	−	0.131095i	−0.769610	+	0.638515i	$0.779549\pi$
$62$	−1.73851	−	3.13603i	−0.220791	−	0.398277i
$63$		0			0
$64$	−7.95640	−	0.834111i	−0.994550	−	0.104264i
$65$	−2.64730	−	3.89847i	−0.328357	−	0.483545i
$66$		0			0
$67$	3.67191	+	3.67191i	0.448595	+	0.448595i	0.894887	−	0.446292i	$-0.147256\pi$
$67$	3.67191	+	3.67191i	0.448595	+	0.448595i	−0.446292	+	0.894887i	$0.647256\pi$
$68$	−3.07880	+	4.92808i	−0.373359	+	0.597618i
$69$		0			0
$70$	−0.792508	+	0.260279i	−0.0947228	+	0.0311093i
$71$		−	7.85546i		−	0.932272i	−0.884713	−	0.466136i	$-0.845646\pi$
$71$		−	7.85546i		−	0.932272i	0.884713	−	0.466136i	$-0.154354\pi$
$72$		0			0
$73$	−12.4323			−1.45509			−0.727543	−	0.686062i	$-0.759338\pi$
$73$	−12.4323			−1.45509			−0.727543	+	0.686062i	$0.759338\pi$
$74$	2.95219	+	0.846384i	0.343185	+	0.0983901i
$75$		0			0
$76$	0.188543	+	0.816337i	0.0216273	+	0.0936403i
$77$	0.240990	+	0.240990i	0.0274634	+	0.0274634i
$78$		0			0
$79$			10.7196i			1.20605i	0.797724	+	0.603023i	$0.206037\pi$
$79$			10.7196i			1.20605i	−0.797724	+	0.603023i	$0.793963\pi$
$80$	8.63182	−	2.34344i	0.965066	−	0.262005i
$81$		0			0
$82$	13.3324	−	7.39107i	1.47232	−	0.816207i
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	−0.488140	−	0.872765i	$-0.662325\pi$
$83$	3.50410	−	3.50410i	0.384625	−	0.384625i	0.872765	+	0.488140i	$0.162325\pi$
$84$		0			0
$85$	1.21970	−	6.38111i	0.132295	−	0.692129i
$86$	2.48735	−	8.67586i	0.268217	−	0.935542i
$87$		0			0
$88$	−2.44561	−	2.71540i	−0.260703	−	0.289463i
$89$	−13.2383			−1.40326			−0.701629	−	0.712542i	$-0.747544\pi$
$89$	−13.2383			−1.40326			−0.701629	+	0.712542i	$0.747544\pi$
$90$		0			0
$91$	0.393083	+	0.393083i	0.0412063	+	0.0412063i
$92$	3.33421	−	5.33690i	0.347615	−	0.556410i
$93$		0			0
$94$	4.57903	+	8.25992i	0.472291	+	0.851946i
$95$	−0.526229	−	0.774936i	−0.0539900	−	0.0795068i
$96$		0			0
$97$		−	11.1057i		−	1.12761i	−0.825908	−	0.563804i	$-0.809337\pi$
$97$		−	11.1057i		−	1.12761i	0.825908	−	0.563804i	$-0.190663\pi$
$98$	−8.57202	+	4.75204i	−0.865905	+	0.480029i
$99$		0			0
$100$	−8.05278	+	5.92898i	−0.805278	+	0.592898i
$101$	−0.625096	−	0.625096i	−0.0621994	−	0.0621994i	0.675323	−	0.737522i	$-0.264004\pi$
$101$	−0.625096	−	0.625096i	−0.0621994	−	0.0621994i	−0.737522	+	0.675323i	$0.764004\pi$
$102$		0			0
$103$			7.47669i			0.736701i	0.929687	+	0.368350i	$0.120077\pi$
$103$			7.47669i			0.736701i	−0.929687	+	0.368350i	$0.879923\pi$
$104$	−3.98908	−	4.42914i	−0.391161	−	0.434312i
$105$		0			0
$106$	1.62797	−	5.67837i	0.158123	−	0.551532i
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.999015	−	0.0443705i	$-0.985872\pi$
$107$	−10.7929	−	10.7929i	−1.04339	−	1.04339i	−0.0443705	−	0.999015i	$-0.514128\pi$
$108$		0			0
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	0.694499	−	0.719493i	$-0.255626\pi$
$109$	−0.260948	−	0.260948i	−0.0249942	−	0.0249942i	−0.719493	+	0.694499i	$0.755626\pi$
$110$	3.64625	+	1.84334i	0.347657	+	0.175755i
$111$		0			0
$112$	−0.948264	+	0.462707i	−0.0896025	+	0.0437217i
$113$	3.88893			0.365839			0.182920	−	0.983128i	$-0.441445\pi$
$113$	3.88893			0.365839			0.182920	+	0.983128i	$0.441445\pi$
$114$		0			0
$115$	−1.32088	+	6.91046i	−0.123173	+	0.644404i
$116$	1.55157	+	6.71786i	0.144059	+	0.623738i
$117$		0			0
$118$	5.38387	−	18.7789i	0.495625	−	1.72874i
$119$			0.766390i			0.0702549i
$120$		0			0
$121$			9.33069i			0.848245i
$122$	1.96846	+	0.564353i	0.178216	+	0.0510942i
$123$		0			0
$124$	4.30063	+	2.68680i	0.386208	+	0.241282i
$125$	6.00115	−	9.43325i	0.536759	−	0.843736i
$126$		0			0
$127$	18.1176			1.60768			0.803840	−	0.594846i	$-0.202787\pi$
$127$	18.1176			1.60768			0.803840	+	0.594846i	$0.202787\pi$
$128$	10.4130	−	4.42385i	0.920384	−	0.391017i
$129$		0			0
$130$	5.94746	+	3.00670i	0.521627	+	0.263705i
$131$	14.0610	+	14.0610i	1.22851	+	1.22851i	0.964526	+	0.263988i	$0.0850378\pi$
$131$	14.0610	+	14.0610i	1.22851	+	1.22851i	0.263988	+	0.964526i	$0.414962\pi$
$132$		0			0
$133$	0.0781369	+	0.0781369i	0.00677533	+	0.00677533i
$134$	−7.05942	−	2.02392i	−0.609841	−	0.174840i
$135$		0			0
$136$	0.428988	−	8.20646i	0.0367854	−	0.703698i
$137$		−	10.3404i		−	0.883440i	−0.897153	−	0.441720i	$-0.854368\pi$
$137$		−	10.3404i		−	0.883440i	0.897153	−	0.441720i	$-0.145632\pi$
$138$		0			0
$139$	11.8106	+	11.8106i	1.00176	+	1.00176i	0.999998	+	0.00176137i	$0.000560663\pi$
$139$	11.8106	+	11.8106i	1.00176	+	1.00176i	0.00176137	+	0.999998i	$0.499439\pi$
$140$	0.801760	−	0.865337i	0.0677611	−	0.0731344i
$141$		0			0
$142$	5.38633	+	9.71618i	0.452011	+	0.815363i
$143$		−	2.72283i		−	0.227695i
$144$		0			0
$145$	−4.33048	−	6.37716i	−0.359627	−	0.529594i
$146$	15.3771	−	8.52454i	1.27262	−	0.705496i
$147$		0			0
$148$	−4.23181	+	0.977386i	−0.347853	+	0.0803407i
$149$	5.72046	+	5.72046i	0.468639	+	0.468639i	0.901473	−	0.432835i	$-0.142487\pi$
$149$	5.72046	+	5.72046i	0.468639	+	0.468639i	−0.432835	+	0.901473i	$0.642487\pi$
$150$		0			0
$151$	−14.9974			−1.22047			−0.610234	−	0.792221i	$-0.708925\pi$
$151$	−14.9974			−1.22047			−0.610234	+	0.792221i	$0.708925\pi$
$152$	−0.792948	−	0.880422i	−0.0643166	−	0.0714117i
$153$		0			0
$154$	−0.463316	−	0.132831i	−0.0373350	−	0.0107039i
$155$	−5.56865	−	1.06440i	−0.447285	−	0.0854948i
$156$		0			0
$157$	0.0261720	−	0.0261720i	0.00208875	−	0.00208875i	−0.706062	−	0.708150i	$-0.749530\pi$
$157$	0.0261720	−	0.0261720i	0.00208875	−	0.00208875i	0.708150	+	0.706062i	$0.249530\pi$
$158$	−7.35019	−	13.2587i	−0.584750	−	1.05481i
$159$		0			0
$160$	−9.06957	+	8.81719i	−0.717013	+	0.697060i
$161$		−	0.829967i		−	0.0654106i
$162$		0			0
$163$	17.1126	+	17.1126i	1.34036	+	1.34036i	0.895700	+	0.444659i	$0.146675\pi$
$163$	17.1126	+	17.1126i	1.34036	+	1.34036i	0.444659	+	0.895700i	$0.353325\pi$
$164$	−11.4226	+	18.2836i	−0.891953	+	1.42771i
$165$		0			0
$166$	−1.93142	+	6.73680i	−0.149907	+	0.522877i
$167$	19.4611			1.50594			0.752971	−	0.658053i	$-0.228620\pi$
$167$	19.4611			1.50594			0.752971	+	0.658053i	$0.228620\pi$
$168$		0			0
$169$			8.55875i			0.658365i
$170$	2.86679	+	8.72892i	0.219873	+	0.669477i
$171$		0			0
$172$	2.87233	+	12.4364i	0.219013	+	0.948268i
$173$	11.3427	+	11.3427i	0.862367	+	0.862367i	0.991613	−	0.129245i	$-0.0412555\pi$
$173$	11.3427	+	11.3427i	0.862367	+	0.862367i	−0.129245	+	0.991613i	$0.541256\pi$
$174$		0			0
$175$	−0.486428	+	1.22594i	−0.0367705	+	0.0926722i
$176$	4.88680	+	1.68169i	0.368356	+	0.126762i
$177$		0			0
$178$	16.3741	−	9.07724i	1.22729	−	0.680368i
$179$	4.50621	+	4.50621i	0.336810	+	0.336810i	0.855165	−	0.518356i	$-0.173456\pi$
$179$	4.50621	+	4.50621i	0.336810	+	0.336810i	−0.518356	+	0.855165i	$0.673456\pi$
$180$		0			0
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	−0.224062	−	0.974575i	$-0.571932\pi$
$181$	10.0971	−	10.0971i	0.750512	−	0.750512i	0.974575	+	0.224062i	$0.0719320\pi$
$182$	−0.755721	−	0.216663i	−0.0560178	−	0.0160601i
$183$		0			0
$184$	−0.464575	+	8.88723i	−0.0342489	+	0.655176i
$185$	4.01719	−	2.72792i	0.295350	−	0.200561i
$186$		0			0
$187$	2.65434	−	2.65434i	0.194104	−	0.194104i
$188$	−11.3273	−	7.07669i	−0.826129	−	0.516121i
$189$		0			0
$190$	1.18223	+	0.597670i	0.0857683	+	0.0433595i
$191$	23.8545			1.72605			0.863025	−	0.505161i	$-0.168567\pi$
$191$	23.8545			1.72605			0.863025	+	0.505161i	$0.168567\pi$
$192$		0			0
$193$			13.8585i			0.997560i	0.866729	+	0.498780i	$0.166218\pi$
$193$			13.8585i			0.997560i	−0.866729	+	0.498780i	$0.833782\pi$
$194$	7.61492	+	13.7362i	0.546719	+	0.986205i
$195$		0			0
$196$	7.34408	−	11.7553i	0.524577	−	0.839665i
$197$	−11.9818	+	11.9818i	−0.853664	+	0.853664i	−0.990582	−	0.136918i	$-0.956280\pi$
$197$	−11.9818	+	11.9818i	−0.853664	+	0.853664i	0.136918	+	0.990582i	$0.456280\pi$
$198$		0			0
$199$	−11.4336			−0.810507			−0.405253	−	0.914204i	$-0.632817\pi$
$199$	−11.4336			−0.810507			−0.405253	+	0.914204i	$0.632817\pi$
$200$	5.89485	−	12.8550i	0.416829	−	0.908985i
$201$		0			0
$202$	1.20178	+	0.344546i	0.0845567	+	0.0242422i
$203$	0.643010	+	0.643010i	0.0451304	+	0.0451304i
$204$		0			0
$205$	4.52517	−	23.6744i	0.316051	−	1.65349i
$206$	−5.12661	−	9.24769i	−0.357188	−	0.644317i
$207$		0			0
$208$	7.97093	+	2.74303i	0.552685	+	0.190195i
$209$		−	0.541243i		−	0.0374386i
$210$		0			0
$211$	6.45820	−	6.45820i	0.444601	−	0.444601i	−0.448954	−	0.893555i	$-0.648203\pi$
$211$	6.45820	−	6.45820i	0.444601	−	0.444601i	0.893555	+	0.448954i	$0.148203\pi$
$212$	1.87995	+	8.13966i	0.129115	+	0.559034i
$213$		0			0
$214$	20.7498	+	5.94891i	1.41843	+	0.406659i
$215$	−8.01679	−	11.8057i	−0.546741	−	0.805142i
$216$		0			0
$217$	0.668811			0.0454019
$218$	0.501684	+	0.143832i	0.0339783	+	0.00974150i
$219$		0			0
$220$	−5.77388	+	0.220194i	−0.389275	+	0.0148455i
$221$	4.32953	−	4.32953i	0.291236	−	0.291236i
$222$		0			0
$223$	−0.620487			−0.0415509			−0.0207754	−	0.999784i	$-0.506614\pi$
$223$	−0.620487			−0.0415509			−0.0207754	+	0.999784i	$0.506614\pi$
$224$	0.855609	−	1.22251i	0.0571678	−	0.0816826i
$225$		0			0
$226$	−4.81009	+	2.66656i	−0.319962	+	0.177377i
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	−0.957152	−	0.289588i	$-0.906482\pi$
$227$	−10.0579	+	10.0579i	−0.667564	+	0.667564i	0.289588	+	0.957152i	$0.406482\pi$
$228$		0			0
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	−0.00983872	−	0.999952i	$-0.503132\pi$
$229$	14.9831	−	14.9831i	0.990113	−	0.990113i	0.999952	+	0.00983872i	$0.00313181\pi$
$230$	−3.10461	−	9.45304i	−0.204712	−	0.623315i
$231$		0			0
$232$	−6.52538	−	7.24523i	−0.428412	−	0.475673i
$233$			2.07914i			0.136209i	0.997678	+	0.0681046i	$0.0216952\pi$
$233$			2.07914i			0.136209i	−0.997678	+	0.0681046i	$0.978305\pi$
$234$		0			0
$235$	14.6671	+	2.80350i	0.956779	+	0.182880i
$236$	6.21718	+	26.9187i	0.404704	+	1.75226i
$237$		0			0
$238$	−0.525498	−	0.947924i	−0.0340630	−	0.0614448i
$239$	−13.2816			−0.859113			−0.429557	−	0.903040i	$-0.641330\pi$
$239$	−13.2816			−0.859113			−0.429557	+	0.903040i	$0.641330\pi$
$240$		0			0
$241$	−3.84064			−0.247397			−0.123699	−	0.992320i	$-0.539476\pi$
$241$	−3.84064			−0.247397			−0.123699	+	0.992320i	$0.539476\pi$
$242$	−6.39786	−	11.5408i	−0.411270	−	0.741873i
$243$		0			0
$244$	−2.82170	+	0.651704i	−0.180641	+	0.0417210i
$245$	−2.90943	+	15.2213i	−0.185877	+	0.972455i
$246$		0			0
$247$		−	0.882830i		−	0.0561731i
$248$	−7.16159	−	0.374368i	−0.454761	−	0.0237724i
$249$		0			0
$250$	−0.954446	+	15.7826i	−0.0603645	+	0.998176i
$251$	10.6627	−	10.6627i	0.673022	−	0.673022i	−0.285389	−	0.958412i	$-0.592123\pi$
$251$	10.6627	−	10.6627i	0.673022	−	0.673022i	0.958412	+	0.285389i	$0.0921229\pi$
$252$		0			0
$253$	−2.87453	+	2.87453i	−0.180720	+	0.180720i
$254$	−22.4091	+	12.4229i	−1.40607	+	0.779481i
$255$		0			0
$256$	−9.84611	+	12.6117i	−0.615382	+	0.788229i
$257$	−11.6239			−0.725081			−0.362540	−	0.931968i	$-0.618090\pi$
$257$	−11.6239			−0.725081			−0.362540	+	0.931968i	$0.618090\pi$
$258$		0			0
$259$	−0.405054	+	0.405054i	−0.0251688	+	0.0251688i
$260$	−9.41785	+	0.359162i	−0.584071	+	0.0222743i
$261$		0			0
$262$	−27.0329	−	7.75027i	−1.67010	−	0.478813i
$263$	29.3422			1.80932			0.904658	−	0.426138i	$-0.140126\pi$
$263$	29.3422			1.80932			0.904658	+	0.426138i	$0.140126\pi$
$264$		0			0
$265$	−5.24701	−	7.72685i	−0.322321	−	0.474657i
$266$	−0.150222	−	0.0430682i	−0.00921070	−	0.00264068i
$267$		0			0
$268$	10.1193	−	2.33718i	0.618137	−	0.142766i
$269$	8.91793	−	8.91793i	0.543736	−	0.543736i	−0.380886	−	0.924622i	$-0.624381\pi$
$269$	8.91793	−	8.91793i	0.543736	−	0.543736i	0.924622	+	0.380886i	$0.124381\pi$
$270$		0			0
$271$		−	31.2790i		−	1.90007i	−0.312150	−	0.950033i	$-0.601049\pi$
$271$		−	31.2790i		−	1.90007i	0.312150	−	0.950033i	$-0.398951\pi$
$272$	5.09640	+	10.4445i	0.309014	+	0.633288i
$273$		0			0
$274$	7.09020	+	12.7897i	0.428335	+	0.772655i
$275$	5.93066	−	2.56124i	0.357632	−	0.154449i
$276$		0			0
$277$	−4.04579	−	4.04579i	−0.243088	−	0.243088i	0.575038	−	0.818126i	$-0.304987\pi$
$277$	−4.04579	−	4.04579i	−0.243088	−	0.243088i	−0.818126	+	0.575038i	$0.804987\pi$
$278$	−22.7064	−	6.50986i	−1.36184	−	0.390436i
$279$		0			0
$280$	−0.398329	+	1.62006i	−0.0238047	+	0.0968170i
$281$	−19.2114			−1.14606			−0.573029	−	0.819535i	$-0.694232\pi$
$281$	−19.2114			−1.14606			−0.573029	+	0.819535i	$0.694232\pi$
$282$		0			0
$283$	−10.0809	+	10.0809i	−0.599247	+	0.599247i	−0.940112	−	0.340865i	$-0.889280\pi$
$283$	−10.0809	+	10.0809i	−0.599247	+	0.599247i	0.340865	+	0.940112i	$0.389280\pi$
$284$	−13.3244	−	8.32434i	−0.790655	−	0.493959i
$285$		0			0
$286$	1.86699	+	3.36778i	0.110397	+	0.199141i
$287$			2.84337i			0.167839i
$288$		0			0
$289$	−8.55875			−0.503456
$290$	9.72892	+	4.91839i	0.571302	+	0.288818i
$291$		0			0
$292$	−13.1743	+	21.0875i	−0.770969	+	1.23405i
$293$	−4.81368	+	4.81368i	−0.281218	+	0.281218i	−0.833595	−	0.552376i	$-0.813721\pi$
$293$	−4.81368	+	4.81368i	−0.281218	+	0.281218i	0.552376	+	0.833595i	$0.313721\pi$
$294$		0			0
$295$	−17.3524	−	25.5535i	−1.01029	−	1.48778i
$296$	4.56402	−	4.11056i	0.265278	−	0.238922i
$297$		0			0
$298$	−10.9979	−	3.15306i	−0.637089	−	0.182652i
$299$	−4.68869	+	4.68869i	−0.271154	+	0.271154i
$300$		0			0
$301$	1.19037	+	1.19037i	0.0686118	+	0.0686118i
$302$	18.5498	−	10.2834i	1.06742	−	0.591742i
$303$		0			0
$304$	1.58446	+	0.545259i	0.0908750	+	0.0312727i
$305$	2.67859	−	1.81893i	0.153376	−	0.104152i
$306$		0			0
$307$	−17.1791	−	17.1791i	−0.980465	−	0.980465i	0.0193480	−	0.999813i	$-0.493841\pi$
$307$	−17.1791	−	17.1791i	−0.980465	−	0.980465i	−0.999813	+	0.0193480i	$0.993841\pi$
$308$	0.664140	−	0.153391i	0.0378429	−	0.00874026i
$309$		0			0
$310$	7.61753	−	2.50178i	0.432647	−	0.142092i
$311$		−	16.6032i		−	0.941479i	−0.882272	−	0.470740i	$-0.843987\pi$
$311$		−	16.6032i		−	0.941479i	0.882272	−	0.470740i	$-0.156013\pi$
$312$		0			0
$313$	−10.8345			−0.612404			−0.306202	−	0.951967i	$-0.599058\pi$
$313$	−10.8345			−0.612404			−0.306202	+	0.951967i	$0.599058\pi$
$314$	−0.0144257	+	0.0503169i	−0.000814090	+	0.00283954i
$315$		0			0
$316$	18.1824	+	11.3594i	1.02284	+	0.639017i
$317$	15.3464	+	15.3464i	0.861942	+	0.861942i	0.991564	−	0.129621i	$-0.0413762\pi$
$317$	15.3464	+	15.3464i	0.861942	+	0.861942i	−0.129621	+	0.991564i	$0.541376\pi$
$318$		0			0
$319$		−	4.45404i		−	0.249378i
$320$	5.17211	−	17.1245i	0.289129	−	0.957290i
$321$		0			0
$322$	0.569091	+	1.02656i	0.0317142	+	0.0572080i
$323$	0.860623	−	0.860623i	0.0478863	−	0.0478863i
$324$		0			0
$325$	9.67358	−	4.17768i	0.536594	−	0.231736i
$326$	−32.8997	−	9.43226i	−1.82215	−	0.522405i
$327$		0			0
$328$	1.59158	−	30.4466i	0.0878801	−	1.68113i
$329$	−1.76157			−0.0971183
$330$		0			0
$331$	−6.23806	−	6.23806i	−0.342875	−	0.342875i	0.514572	−	0.857447i	$-0.327951\pi$
$331$	−6.23806	−	6.23806i	−0.342875	−	0.342875i	−0.857447	+	0.514572i	$0.827951\pi$
$332$	−2.23037	−	9.65687i	−0.122407	−	0.529990i
$333$		0			0
$334$	−24.0708	+	13.3440i	−1.31709	+	0.730154i
$335$	−9.60613	+	6.52315i	−0.524839	+	0.356398i
$336$		0			0
$337$		−	8.87003i		−	0.483181i	−0.970378	−	0.241591i	$-0.922331\pi$
$337$		−	8.87003i		−	0.483181i	0.970378	−	0.241591i	$-0.0776691\pi$
$338$	−5.86856	−	10.5861i	−0.319207	−	0.575805i
$339$		0			0
$340$	−9.53108	−	8.83083i	−0.516895	−	0.478919i
$341$	−2.31638	−	2.31638i	−0.125439	−	0.125439i
$342$		0			0
$343$		−	3.67461i		−	0.198410i
$344$	−12.0801	−	13.4127i	−0.651315	−	0.723165i
$345$		0			0
$346$	−21.8068	−	6.25196i	−1.17234	−	0.336107i
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	0.943449	−	0.331517i	$-0.107560\pi$
$347$	11.3990	+	11.3990i	0.611932	+	0.611932i	−0.331517	+	0.943449i	$0.607560\pi$
$348$		0			0
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	0.327393	−	0.944888i	$-0.393830\pi$
$349$	−11.5358	−	11.5358i	−0.617496	−	0.617496i	−0.944888	+	0.327393i	$0.893830\pi$
$350$	−0.238953	−	1.84986i	−0.0127726	−	0.0988790i
$351$		0			0
$352$	−7.19743	+	1.27075i	−0.383624	+	0.0677310i
$353$	20.5642			1.09452			0.547260	−	0.836963i	$-0.315671\pi$
$353$	20.5642			1.09452			0.547260	+	0.836963i	$0.315671\pi$
$354$		0			0
$355$	17.2530	+	3.29777i	0.915695	+	0.175027i
$356$	−14.0285	+	22.4547i	−0.743508	+	1.19010i
$357$		0			0
$358$	−8.66339	−	2.48377i	−0.457875	−	0.131271i
$359$		−	18.8141i		−	0.992972i	−0.868045	−	0.496486i	$-0.834623\pi$
$359$		−	18.8141i		−	0.992972i	0.868045	−	0.496486i	$-0.165377\pi$
$360$		0			0
$361$			18.8245i			0.990764i
$362$	−5.56542	+	19.4122i	−0.292512	+	1.02028i
$363$		0			0
$364$	1.08329	−	0.250198i	0.0567798	−	0.0131139i
$365$	5.21914	−	27.3051i	0.273182	−	1.42921i
$366$		0			0
$367$	−12.1654			−0.635031			−0.317515	−	0.948253i	$-0.602849\pi$
$367$	−12.1654			−0.635031			−0.317515	+	0.948253i	$0.602849\pi$
$368$	−5.51917	−	11.3109i	−0.287707	−	0.589621i
$369$		0			0
$370$	−3.09826	+	6.12859i	−0.161071	+	0.318610i
$371$	0.779099	+	0.779099i	0.0404488	+	0.0404488i
$372$		0			0
$373$	14.7424	+	14.7424i	0.763330	+	0.763330i	0.976923	−	0.213592i	$-0.0685164\pi$
$373$	14.7424	+	14.7424i	0.763330	+	0.763330i	−0.213592	+	0.976923i	$0.568516\pi$
$374$	−1.46304	+	5.10309i	−0.0756522	+	0.263875i
$375$		0			0
$376$	18.8627	+	0.986038i	0.972772	+	0.0508510i
$377$		−	7.26505i		−	0.374169i
$378$		0			0
$379$	1.59803	+	1.59803i	0.0820853	+	0.0820853i	0.746957	−	0.664872i	$-0.231514\pi$
$379$	1.59803	+	1.59803i	0.0820853	+	0.0820853i	−0.664872	+	0.746957i	$0.731514\pi$
$380$	−1.87208	+	0.0713941i	−0.0960356	+	0.00366244i
$381$		0			0
$382$	−29.5049	+	16.3565i	−1.50960	+	0.836873i
$383$			24.9035i			1.27251i	0.771479	+	0.636255i	$0.219517\pi$
$383$			24.9035i			1.27251i	−0.771479	+	0.636255i	$0.780483\pi$
$384$		0			0
$385$	−0.630458	+	0.428120i	−0.0321311	+	0.0218190i
$386$	−9.50252	−	17.1412i	−0.483665	−	0.872464i
$387$		0			0
$388$	−18.8373	−	11.7685i	−0.956319	−	0.597457i
$389$	11.9793	+	11.9793i	0.607375	+	0.607375i	0.942259	−	0.334884i	$-0.108697\pi$
$389$	11.9793	+	11.9793i	0.607375	+	0.607375i	−0.334884	+	0.942259i	$0.608697\pi$
$390$		0			0
$391$	−9.14150			−0.462306
$392$	−1.02329	+	19.5755i	−0.0516842	+	0.988710i
$393$		0			0
$394$	6.60422	−	23.0355i	0.332716	−	1.16051i
$395$	−23.5435	−	4.50014i	−1.18460	−	0.226427i
$396$		0			0
$397$	−16.0845	+	16.0845i	−0.807258	+	0.807258i	−0.984218	−	0.176960i	$-0.943374\pi$
$397$	−16.0845	+	16.0845i	−0.807258	+	0.807258i	0.176960	+	0.984218i	$0.443374\pi$
$398$	14.1419	−	7.83978i	0.708868	−	0.392973i
$399$		0			0
$400$	1.52324	+	19.9419i	0.0761618	+	0.997095i
$401$		−	3.56411i		−	0.177983i	−0.996032	−	0.0889915i	$-0.971636\pi$
$401$		−	3.56411i		−	0.177983i	0.996032	−	0.0889915i	$-0.0283644\pi$
$402$		0			0
$403$	−3.77828	−	3.77828i	−0.188210	−	0.188210i
$404$	−1.72269	+	0.397875i	−0.0857069	+	0.0197950i
$405$		0			0
$406$	−1.23622	−	0.354420i	−0.0613524	−	0.0175896i
$407$	2.80575			0.139076
$408$		0			0
$409$		−	0.455458i		−	0.0225209i	−0.999937	−	0.0112605i	$-0.996416\pi$
$409$		−	0.455458i		−	0.0225209i	0.999937	−	0.0112605i	$-0.00358439\pi$
$410$	10.6360	+	32.3849i	0.525275	+	1.59938i
$411$		0			0
$412$	12.6819	+	7.92296i	0.624792	+	0.390336i
$413$	2.57656	+	2.57656i	0.126784	+	0.126784i
$414$		0			0
$415$	6.22503	+	9.16712i	0.305575	+	0.449996i
$416$	−11.7398	+	2.07273i	−0.575593	+	0.101624i
$417$		0			0
$418$	0.371119	+	0.669447i	0.0181520	+	0.0327437i
$419$	7.20612	+	7.20612i	0.352042	+	0.352042i	0.860869	−	0.508827i	$-0.169921\pi$
$419$	7.20612	+	7.20612i	0.352042	+	0.352042i	−0.508827	+	0.860869i	$0.669921\pi$
$420$		0			0
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	−0.959574	−	0.281455i	$-0.909183\pi$
$421$	−13.9138	+	13.9138i	−0.678119	+	0.678119i	0.281455	+	0.959574i	$0.409183\pi$
$422$	−3.55969	+	12.4162i	−0.173283	+	0.604411i
$423$		0			0
$424$	−7.90645	−	8.77865i	−0.383971	−	0.426329i
$425$	13.5028	+	5.35766i	0.654984	+	0.259885i
$426$		0			0
$427$	−0.270083	+	0.270083i	−0.0130702	+	0.0130702i
$428$	−29.7438	+	6.86968i	−1.43772	+	0.332059i
$429$		0			0
$430$	18.0106	+	9.10515i	0.868550	+	0.439089i
$431$	20.2896			0.977314			0.488657	−	0.872476i	$-0.337487\pi$
$431$	20.2896			0.977314			0.488657	+	0.872476i	$0.337487\pi$
$432$		0			0
$433$			13.2049i			0.634587i	0.948327	+	0.317294i	$0.102774\pi$
$433$			13.2049i			0.634587i	−0.948327	+	0.317294i	$0.897226\pi$
$434$	−0.827232	+	0.458590i	−0.0397084	+	0.0220130i
$435$		0			0
$436$	−0.719140	+	0.166094i	−0.0344406	+	0.00795445i
$437$	−0.932017	+	0.932017i	−0.0445844	+	0.0445844i
$438$		0			0
$439$	4.81740			0.229922			0.114961	−	0.993370i	$-0.463326\pi$
$439$	4.81740			0.229922			0.114961	+	0.993370i	$0.463326\pi$
$440$	6.99054	−	4.23138i	0.333261	−	0.201723i
$441$		0			0
$442$	−2.38639	+	8.32373i	−0.113509	+	0.395920i
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	0.890463	−	0.455055i	$-0.150380\pi$
$443$	9.16428	+	9.16428i	0.435408	+	0.435408i	−0.455055	+	0.890463i	$0.650380\pi$
$444$		0			0
$445$	5.55752	−	29.0754i	0.263452	−	1.37831i
$446$	0.767461	−	0.425455i	0.0363403	−	0.0201459i
$447$		0			0
$448$	−0.220024	+	2.09876i	−0.0103952	+	0.0991572i
$449$			3.67981i			0.173661i	0.996223	+	0.0868305i	$0.0276739\pi$
$449$			3.67981i			0.173661i	−0.996223	+	0.0868305i	$0.972326\pi$
$450$		0			0
$451$	9.84780	−	9.84780i	0.463715	−	0.463715i
$452$	4.12105	−	6.59636i	0.193838	−	0.310267i
$453$		0			0
$454$	5.54379	−	19.3367i	0.260183	−	0.907517i
$455$	−1.02835	+	0.698312i	−0.0482098	+	0.0327374i
$456$		0			0
$457$	18.1968			0.851212			0.425606	−	0.904908i	$-0.360061\pi$
$457$	18.1968			0.851212			0.425606	+	0.904908i	$0.360061\pi$
$458$	−8.25854	+	28.8058i	−0.385896	+	1.34601i
$459$		0			0
$460$	10.3217	+	9.56340i	0.481254	+	0.445896i
$461$	−20.4826	+	20.4826i	−0.953971	+	0.953971i	−0.998986	−	0.0450155i	$-0.985666\pi$
$461$	−20.4826	+	20.4826i	−0.953971	+	0.953971i	0.0450155	+	0.998986i	$0.485666\pi$
$462$		0			0
$463$	−22.5416			−1.04760			−0.523799	−	0.851842i	$-0.675486\pi$
$463$	−22.5416			−1.04760			−0.523799	+	0.851842i	$0.675486\pi$
$464$	13.0389	+	4.48708i	0.605318	+	0.208308i
$465$		0			0
$466$	−1.42562	−	2.57163i	−0.0660408	−	0.119128i
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.246507	+	0.969141i	$0.579283\pi$
$467$	−26.2704	+	26.2704i	−1.21565	+	1.21565i	−0.969141	+	0.246507i	$0.920717\pi$
$468$		0			0
$469$	0.968587	−	0.968587i	0.0447252	−	0.0447252i
$470$	−20.0636	+	6.58939i	−0.925466	+	0.303946i
$471$		0			0
$472$	−26.1474	−	29.0319i	−1.20353	−	1.33630i
$473$		−	8.24552i		−	0.379130i
$474$		0			0
$475$	1.92291	−	0.830438i	0.0882292	−	0.0381031i
$476$	1.29994	+	0.812135i	0.0595828	+	0.0372241i
$477$		0			0
$478$	16.4276	−	9.10690i	0.751379	−	0.416540i
$479$	0.723719			0.0330676			0.0165338	−	0.999863i	$-0.494737\pi$
$479$	0.723719			0.0330676			0.0165338	+	0.999863i	$0.494737\pi$
$480$		0			0
$481$	4.57651			0.208671
$482$	4.75036	−	2.63344i	0.216373	−	0.119950i
$483$		0			0
$484$	15.8266	+	9.88762i	0.719392	+	0.449437i
$485$	24.3914	+	4.66222i	1.10756	+	0.211701i
$486$		0			0
$487$			15.0222i			0.680719i	0.940295	+	0.340360i	$0.110549\pi$
$487$			15.0222i			0.680719i	−0.940295	+	0.340360i	$0.889451\pi$
$488$	3.04321	−	2.74085i	0.137760	−	0.124072i
$489$		0			0
$490$	−6.83836	−	20.8217i	−0.308926	−	0.940629i
$491$	−3.04102	+	3.04102i	−0.137239	+	0.137239i	−0.772389	−	0.635150i	$-0.780938\pi$
$491$	−3.04102	+	3.04102i	−0.137239	+	0.137239i	0.635150	+	0.772389i	$0.280938\pi$
$492$		0			0
$493$	7.08230	−	7.08230i	0.318971	−	0.318971i
$494$	0.605338	+	1.09194i	0.0272355	+	0.0491289i
$495$		0			0
$496$	9.11464	−	4.44751i	0.409260	−	0.199699i
$497$	−2.07214			−0.0929481
$498$		0			0
$499$	11.3545	−	11.3545i	0.508298	−	0.508298i	−0.405706	−	0.914004i	$-0.632974\pi$
$499$	11.3545	−	11.3545i	0.508298	−	0.508298i	0.914004	+	0.405706i	$0.132974\pi$
$500$	−9.64124	−	20.1754i	−0.431170	−	0.902271i
$501$		0			0
$502$	−5.87716	+	20.4995i	−0.262310	+	0.914938i
$503$	−24.8256			−1.10692			−0.553459	−	0.832876i	$-0.686692\pi$
$503$	−24.8256			−1.10692			−0.553459	+	0.832876i	$0.686692\pi$
$504$		0			0
$505$	1.63532	−	1.11048i	0.0727708	−	0.0494159i
$506$	1.58441	−	5.52643i	0.0704357	−	0.245680i
$507$		0			0
$508$	19.1990	−	30.7309i	0.851820	−	1.36347i
$509$	22.3544	−	22.3544i	0.990841	−	0.990841i	−0.00911778	−	0.999958i	$-0.502902\pi$
$509$	22.3544	−	22.3544i	0.990841	−	0.990841i	0.999958	+	0.00911778i	$0.00290232\pi$
$510$		0			0
$511$			3.27942i			0.145073i
$512$	3.53079	−	22.3502i	0.156040	−	0.987751i
$513$		0			0
$514$	14.3773	−	7.97029i	0.634154	−	0.351554i
$515$	−16.4211	−	3.13876i	−0.723601	−	0.138310i
$516$		0			0
$517$	6.10106	+	6.10106i	0.268324	+	0.268324i
$518$	0.223262	−	0.778736i	0.00980955	−	0.0342157i
$519$		0			0
$520$	11.4024	−	6.90186i	0.500027	−	0.302667i
$521$	−30.7334			−1.34646			−0.673228	−	0.739435i	$-0.735093\pi$
$521$	−30.7334			−1.34646			−0.673228	+	0.739435i	$0.735093\pi$
$522$		0			0
$523$	−12.6215	+	12.6215i	−0.551898	+	0.551898i	−0.926988	−	0.375090i	$-0.877612\pi$
$523$	−12.6215	+	12.6215i	−0.551898	+	0.551898i	0.375090	+	0.926988i	$0.377612\pi$
$524$	38.7504	−	8.94984i	1.69282	−	0.390976i
$525$		0			0
$526$	−36.2924	+	20.1193i	−1.58242	+	0.877244i
$527$		−	7.36649i		−	0.320889i
$528$		0			0
$529$	−13.1002			−0.569572
$530$	11.7880	+	5.95934i	0.512038	+	0.258857i
$531$		0			0
$532$	0.215336	−	0.0497343i	0.00933599	−	0.00215626i
$533$	16.0629	−	16.0629i	0.695761	−	0.695761i
$534$		0			0
$535$	28.2353	−	19.1735i	1.22072	−	0.828944i
$536$	−10.9137	+	9.82940i	−0.471402	+	0.424566i
$537$		0			0
$538$	−4.91547	+	17.1451i	−0.211921	+	0.739180i
$539$	−6.33159	+	6.33159i	−0.272721	+	0.272721i
$540$		0			0
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	0.978990	−	0.203909i	$-0.0653645\pi$
$541$	18.0279	+	18.0279i	0.775081	+	0.775081i	−0.203909	+	0.978990i	$0.565365\pi$
$542$	21.4474	+	38.6880i	0.921244	+	1.66179i
$543$		0			0
$544$	−13.4651	−	9.42393i	−0.577312	−	0.404048i
$545$	0.682668	−	0.463574i	0.0292423	−	0.0198573i
$546$		0			0
$547$	−26.0749	−	26.0749i	−1.11488	−	1.11488i	−0.992480	−	0.122403i	$-0.960940\pi$
$547$	−26.0749	−	26.0749i	−1.11488	−	1.11488i	−0.122403	−	0.992480i	$-0.539060\pi$
$548$	−17.5393	−	10.9576i	−0.749241	−	0.468086i
$549$		0			0
$550$	−5.57925	+	7.23445i	−0.237900	+	0.308478i
$551$		−	1.44414i		−	0.0615226i
$552$		0			0
$553$	2.82764			0.120244
$554$	7.77823	+	2.23000i	0.330465	+	0.0947435i
$555$		0			0
$556$	32.5485	−	7.51745i	1.38036	−	0.318811i
$557$	23.2849	+	23.2849i	0.986612	+	0.986612i	0.999912	−	0.0132999i	$-0.00423361\pi$
$557$	23.2849	+	23.2849i	0.986612	+	0.986612i	−0.0132999	+	0.999912i	$0.504234\pi$
$558$		0			0
$559$		−	13.4494i		−	0.568849i
$560$	−0.618161	−	2.27693i	−0.0261221	−	0.0962177i
$561$		0			0
$562$	23.7620	−	13.1729i	1.00234	−	0.555664i
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	−0.749619	−	0.661870i	$-0.769763\pi$
$563$	−2.08207	+	2.08207i	−0.0877489	+	0.0877489i	0.661870	+	0.749619i	$0.269763\pi$
$564$		0			0
$565$	−1.63259	+	8.54127i	−0.0686837	+	0.359334i
$566$	5.55648	−	19.3810i	0.233556	−	0.814644i
$567$		0			0
$568$	22.1883	+	1.15988i	0.931001	+	0.0486675i
$569$	22.4930			0.942957			0.471478	−	0.881878i	$-0.343721\pi$
$569$	22.4930			0.942957			0.471478	+	0.881878i	$0.343721\pi$
$570$		0			0
$571$	−17.5867	−	17.5867i	−0.735979	−	0.735979i	0.235818	−	0.971797i	$-0.424223\pi$
$571$	−17.5867	−	17.5867i	−0.735979	−	0.735979i	−0.971797	+	0.235818i	$0.924223\pi$
$572$	−4.61844	−	2.88535i	−0.193107	−	0.120643i
$573$		0			0
$574$	−1.94964	−	3.51687i	−0.0813763	−	0.146791i
$575$	−14.6230	−	5.80211i	−0.609821	−	0.241965i
$576$		0			0
$577$		−	24.8497i		−	1.03450i	−0.855833	−	0.517252i	$-0.826955\pi$
$577$		−	24.8497i		−	1.03450i	0.855833	−	0.517252i	$-0.173045\pi$
$578$	10.5861	−	5.86856i	0.440322	−	0.244100i
$579$		0			0
$580$	−15.4058	+	0.587521i	−0.639693	+	0.0243955i
$581$	−0.924321	−	0.924321i	−0.0383473	−	0.0383473i
$582$		0			0
$583$		−	5.39671i		−	0.223509i
$584$	1.83566	−	35.1158i	0.0759600	−	1.45310i
$585$		0			0
$586$	2.65325	−	9.25454i	0.109605	−	0.382301i
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	0.0537988	−	0.998552i	$-0.482867\pi$
$587$	−22.8896	−	22.8896i	−0.944753	−	0.944753i	−0.998552	+	0.0537988i	$0.982867\pi$
$588$		0			0
$589$	−0.751046	−	0.751046i	−0.0309463	−	0.0309463i
$590$	38.9841	+	19.7081i	1.60495	+	0.811371i
$591$		0			0
$592$	−2.82657	+	8.21368i	−0.116171	+	0.337580i
$593$	13.3090			0.546536			0.273268	−	0.961938i	$-0.411895\pi$
$593$	13.3090			0.546536			0.273268	+	0.961938i	$0.411895\pi$
$594$		0			0
$595$	−1.68323	−	0.321735i	−0.0690056	−	0.0131899i
$596$	15.7649	−	3.64109i	0.645756	−	0.149145i
$597$		0			0
$598$	2.58436	−	9.01424i	0.105682	−	0.368620i
$599$		−	7.33982i		−	0.299897i	−0.988694	−	0.149948i	$-0.952089\pi$
$599$		−	7.33982i		−	0.299897i	0.988694	−	0.149948i	$-0.0479108\pi$
$600$		0			0
$601$			27.4748i			1.12072i	0.828250	+	0.560359i	$0.189337\pi$
$601$			27.4748i			1.12072i	−0.828250	+	0.560359i	$0.810663\pi$
$602$	−2.28854	−	0.656119i	−0.0932740	−	0.0267414i
$603$		0			0
$604$	−15.8925	+	25.4384i	−0.646658	+	1.03507i
$605$	−20.4931	−	3.91708i	−0.833162	−	0.159252i
$606$		0			0
$607$	27.4473			1.11405			0.557026	−	0.830495i	$-0.311942\pi$
$607$	27.4473			1.11405			0.557026	+	0.830495i	$0.311942\pi$
$608$	−2.33364	+	0.412017i	−0.0946416	+	0.0167095i
$609$		0			0
$610$	−2.06587	+	4.08643i	−0.0836445	+	0.165455i
$611$	9.95153	+	9.95153i	0.402596	+	0.402596i
$612$		0			0
$613$	17.6219	+	17.6219i	0.711742	+	0.711742i	0.966899	−	0.255158i	$-0.0821274\pi$
$613$	17.6219	+	17.6219i	0.711742	+	0.711742i	−0.255158	+	0.966899i	$0.582127\pi$
$614$	33.0277	+	9.46896i	1.33289	+	0.382136i
$615$		0			0
$616$	−0.716277	+	0.645111i	−0.0288596	+	0.0259923i
$617$		−	41.8102i		−	1.68322i	−0.540088	−	0.841608i	$-0.681609\pi$
$617$		−	41.8102i		−	1.68322i	0.540088	−	0.841608i	$-0.318391\pi$
$618$		0			0
$619$	1.39925	+	1.39925i	0.0562406	+	0.0562406i	0.734668	−	0.678427i	$-0.237338\pi$
$619$	1.39925	+	1.39925i	0.0562406	+	0.0562406i	−0.678427	+	0.734668i	$0.737338\pi$
$620$	−7.70646	+	8.31756i	−0.309499	+	0.334041i
$621$		0			0
$622$	11.3844	+	20.5359i	0.456475	+	0.823416i
$623$			3.49204i			0.139906i
$624$		0			0
$625$	18.1990	+	17.1405i	0.727960	+	0.685620i
$626$	13.4009	−	7.42901i	0.535607	−	0.296923i
$627$		0			0
$628$	−0.0166585	−	0.0721267i	−0.000664747	−	0.00287817i
$629$	4.46139	+	4.46139i	0.177887	+	0.177887i
$630$		0			0
$631$	33.0559			1.31593			0.657967	−	0.753047i	$-0.271417\pi$
$631$	33.0559			1.31593			0.657967	+	0.753047i	$0.271417\pi$
$632$	−30.2782	−	1.58277i	−1.20440	−	0.0629594i
$633$		0			0
$634$	−29.5043	−	8.45880i	−1.17176	−	0.335942i
$635$	−7.60589	+	39.7919i	−0.301830	+	1.57909i
$636$		0			0
$637$	−10.3275	+	10.3275i	−0.409192	+	0.409192i
$638$	3.05404	+	5.50906i	0.120911	+	0.218106i
$639$		0			0
$640$	5.34471	+	24.7272i	0.211268	+	0.977428i
$641$			8.31451i			0.328404i	0.986427	+	0.164202i	$0.0525048\pi$
$641$			8.31451i			0.328404i	−0.986427	+	0.164202i	$0.947495\pi$
$642$		0			0
$643$	17.1504	+	17.1504i	0.676344	+	0.676344i	0.959171	−	0.282827i	$-0.0912722\pi$
$643$	17.1504	+	17.1504i	0.676344	+	0.676344i	−0.282827	+	0.959171i	$0.591272\pi$
$644$	−1.40778	−	0.879506i	−0.0554744	−	0.0346574i
$645$		0			0
$646$	−0.474366	+	1.65459i	−0.0186637	+	0.0650989i
$647$	−5.95293			−0.234034			−0.117017	−	0.993130i	$-0.537333\pi$
$647$	−5.95293			−0.234034			−0.117017	+	0.993130i	$0.537333\pi$
$648$		0			0
$649$		−	17.8475i		−	0.700575i
$650$	−9.10040	+	11.8002i	−0.356947	+	0.462843i
$651$		0			0
$652$	47.1601	−	10.8922i	1.84693	−	0.426571i
$653$	−24.1739	−	24.1739i	−0.945997	−	0.945997i	0.0526174	−	0.998615i	$-0.483244\pi$
$653$	−24.1739	−	24.1739i	−0.945997	−	0.945997i	−0.998615	+	0.0526174i	$0.983244\pi$
$654$		0			0
$655$	−36.7851	+	24.9793i	−1.43731	+	0.976024i
$656$	18.9080	+	38.7497i	0.738234	+	1.51292i
$657$		0			0
$658$	2.17883	−	1.20787i	0.0849395	−	0.0470877i
$659$	−25.0108	−	25.0108i	−0.974284	−	0.974284i	0.0253938	−	0.999678i	$-0.491916\pi$
$659$	−25.0108	−	25.0108i	−0.974284	−	0.974284i	−0.999678	+	0.0253938i	$0.991916\pi$
$660$		0			0
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.132061	+	0.991242i	$0.542159\pi$
$661$	−28.8800	+	28.8800i	−1.12330	+	1.12330i	−0.991242	+	0.132061i	$0.957841\pi$
$662$	11.9930	+	3.43835i	0.466120	+	0.133635i
$663$		0			0
$664$	9.38018	+	10.4150i	0.364022	+	0.404179i
$665$	−0.204415	+	0.138810i	−0.00792687	+	0.00538283i
$666$		0			0
$667$	−7.66982	+	7.66982i	−0.296977	+	0.296977i
$668$	20.6227	−	33.0097i	0.797915	−	1.27718i
$669$		0			0
$670$	7.40873	−	14.6550i	0.286224	−	0.566172i
$671$	1.87083			0.0722224
$672$		0			0
$673$			26.0623i			1.00463i	0.864685	+	0.502315i	$0.167518\pi$
$673$			26.0623i			1.00463i	−0.864685	+	0.502315i	$0.832482\pi$
$674$	6.08199	+	10.9711i	0.234270	+	0.422589i
$675$		0			0
$676$	14.5173	+	9.06961i	0.558357	+	0.348831i
$677$	9.70043	−	9.70043i	0.372818	−	0.372818i	−0.495685	−	0.868503i	$-0.665083\pi$
$677$	9.70043	−	9.70043i	0.372818	−	0.372818i	0.868503	+	0.495685i	$0.165083\pi$
$678$		0			0
$679$	−2.92948			−0.112423
$680$	17.8438	+	4.38731i	0.684279	+	0.168246i
$681$		0			0
$682$	4.45335	+	1.27677i	0.170528	+	0.0488899i
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	0.528635	−	0.848849i	$-0.322704\pi$
$683$	−8.36855	−	8.36855i	−0.320214	−	0.320214i	−0.848849	+	0.528635i	$0.822704\pi$
$684$		0			0
$685$	22.7107	+	4.34096i	0.867731	+	0.165860i
$686$	2.51960	+	4.54501i	0.0961988	+	0.173529i
$687$		0			0
$688$	24.1383	+	8.30670i	0.920264	+	0.316690i
$689$		−	8.80266i		−	0.335355i
$690$		0			0
$691$	16.7998	−	16.7998i	0.639095	−	0.639095i	−0.311237	−	0.950332i	$-0.600743\pi$
$691$	16.7998	−	16.7998i	0.639095	−	0.639095i	0.950332	+	0.311237i	$0.100743\pi$
$692$	31.2590	−	7.21963i	1.18829	−	0.274449i
$693$		0			0
$694$	−21.9152	−	6.28303i	−0.831889	−	0.238501i
$695$	−30.8978	+	20.9815i	−1.17202	+	0.795873i
$696$		0			0
$697$	31.3177			1.18624
$698$	22.1781	+	6.35840i	0.839452	+	0.240669i
$699$		0			0
$700$	1.56396	+	2.12419i	0.0591122	+	0.0802867i
$701$	−26.5344	+	26.5344i	−1.00219	+	1.00219i	−0.00219271	+	0.999998i	$0.500698\pi$
$701$	−26.5344	+	26.5344i	−1.00219	+	1.00219i	−0.999998	+	0.00219271i	$0.999302\pi$
$702$		0			0
$703$	0.909716			0.0343106
$704$	8.03095	−	6.50688i	0.302678	−	0.245237i
$705$		0			0
$706$	−25.4352	+	14.1004i	−0.957265	+	0.530676i
$707$	−0.164890	+	0.164890i	−0.00620131	+	0.00620131i
$708$		0			0
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.249840	+	0.968287i	$0.580378\pi$
$709$	−32.4351	+	32.4351i	−1.21813	+	1.21813i	−0.968287	+	0.249840i	$0.919622\pi$
$710$	−23.6009	+	7.75112i	−0.885727	+	0.290894i
$711$		0			0
$712$	1.95467	−	37.3925i	0.0732545	−	1.40135i
$713$			7.97758i			0.298763i
$714$		0			0
$715$	5.98017	+	1.14306i	0.223646	+	0.0427480i
$716$	12.4186	−	2.86821i	0.464103	−	0.107190i
$717$		0			0
$718$	12.9005	+	23.2706i	0.481441	+	0.868452i
$719$	−8.81868			−0.328881			−0.164441	−	0.986387i	$-0.552582\pi$
$719$	−8.81868			−0.328881			−0.164441	+	0.986387i	$0.552582\pi$
$720$		0			0
$721$	1.97222			0.0734495
$722$	−12.9076	−	23.2834i	−0.480370	−	0.866520i
$723$		0			0
$724$	−6.42683	−	27.8264i	−0.238851	−	1.03416i
$725$	15.8242	−	6.83390i	0.587695	−	0.253805i
$726$		0			0
$727$			10.5815i			0.392448i	0.980559	+	0.196224i	$0.0628679\pi$
$727$			10.5815i			0.392448i	−0.980559	+	0.196224i	$0.937132\pi$
$728$	−1.16833	+	1.05225i	−0.0433012	+	0.0389990i
$729$		0			0
$730$	12.2671	+	37.3514i	0.454027	+	1.38244i
$731$	13.1111	−	13.1111i	0.484931	−	0.484931i
$732$		0			0
$733$	−0.891694	+	0.891694i	−0.0329355	+	0.0329355i	−0.723383	−	0.690447i	$-0.757414\pi$
$733$	−0.891694	+	0.891694i	−0.0329355	+	0.0329355i	0.690447	+	0.723383i	$0.257414\pi$
$734$	15.0471	−	8.34159i	0.555397	−	0.307894i
$735$		0			0
$736$	14.5821	+	10.2057i	0.537505	+	0.376187i
$737$	−6.70927			−0.247139
$738$		0			0
$739$	−22.1859	+	22.1859i	−0.816120	+	0.816120i	−0.985543	−	0.169423i	$-0.945810\pi$
$739$	−22.1859	+	22.1859i	−0.816120	+	0.816120i	0.169423	+	0.985543i	$0.445810\pi$
$740$	−0.370100	−	9.70467i	−0.0136052	−	0.356751i
$741$		0			0
$742$	−1.49786	−	0.429431i	−0.0549880	−	0.0157649i
$743$	7.89487			0.289635			0.144817	−	0.989458i	$-0.453741\pi$
$743$	7.89487			0.289635			0.144817	+	0.989458i	$0.453741\pi$
$744$		0			0
$745$	−14.9654	+	10.1624i	−0.548289	+	0.372322i
$746$	−28.3429	−	8.12583i	−1.03771	−	0.297508i
$747$		0			0
$748$	−1.68949	−	7.31504i	−0.0617740	−	0.267464i
$749$	−2.84697	+	2.84697i	−0.104026	+	0.104026i
$750$		0			0
$751$		−	4.43117i		−	0.161696i	−0.996726	−	0.0808478i	$-0.974237\pi$
$751$		−	4.43117i		−	0.161696i	0.996726	−	0.0808478i	$-0.0257628\pi$
$752$	−24.0068	+	11.7142i	−0.875439	+	0.427173i
$753$		0			0
$754$	4.98149	+	8.98591i	0.181415	+	0.327248i
$755$	6.29598	−	32.9388i	0.229134	−	1.19877i
$756$		0			0
$757$	22.8329	+	22.8329i	0.829876	+	0.829876i	0.987499	−	0.157623i	$-0.0503832\pi$
$757$	22.8329	+	22.8329i	0.829876	+	0.829876i	−0.157623	+	0.987499i	$0.550383\pi$
$758$	−3.07229	−	0.880817i	−0.111591	−	0.0319927i
$759$		0			0
$760$	2.26656	−	1.37195i	0.0822168	−	0.0497659i
$761$	−18.3941			−0.666784			−0.333392	−	0.942788i	$-0.608193\pi$
$761$	−18.3941			−0.666784			−0.333392	+	0.942788i	$0.608193\pi$
$762$		0			0
$763$	−0.0688335	+	0.0688335i	−0.00249194	+	0.00249194i
$764$	25.2783	−	40.4617i	0.914537	−	1.46385i
$765$		0			0
$766$	−17.0758	−	30.8024i	−0.616975	−	1.11294i
$767$		−	29.1113i		−	1.05115i
$768$		0			0
$769$	12.2959			0.443402			0.221701	−	0.975115i	$-0.428839\pi$
$769$	12.2959			0.443402			0.221701	+	0.975115i	$0.428839\pi$
$770$	0.486241	−	0.961820i	0.0175229	−	0.0346616i
$771$		0			0
$772$	23.5067	+	14.6857i	0.846026	+	0.528551i
$773$	16.8697	−	16.8697i	0.606762	−	0.606762i	−0.335337	−	0.942098i	$-0.608850\pi$
$773$	16.8697	−	16.8697i	0.606762	−	0.606762i	0.942098	+	0.335337i	$0.108850\pi$
$774$		0			0
$775$	4.67551	−	11.7836i	0.167949	−	0.423280i
$776$	31.3687	+	1.63978i	1.12607	+	0.0588647i
$777$		0			0
$778$	−23.0308	−	6.60287i	−0.825694	−	0.236724i
$779$	3.19298	−	3.19298i	0.114400	−	0.114400i
$780$		0			0
$781$	7.17670	+	7.17670i	0.256803	+	0.256803i
$782$	11.3068	−	6.26814i	0.404332	−	0.224148i
$783$		0			0
$784$	−12.1568	−	24.9139i	−0.434171	−	0.889783i
$785$	0.0464945	+	0.0684688i	0.00165946	+	0.00244376i
$786$		0			0
$787$	−32.0462	−	32.0462i	−1.14232	−	1.14232i	−0.988024	−	0.154299i	$-0.950688\pi$
$787$	−32.0462	−	32.0462i	−1.14232	−	1.14232i	−0.154299	−	0.988024i	$-0.549312\pi$
$788$	7.62641	+	33.0203i	0.271680	+	1.17630i
$789$		0			0
$790$	32.2058	−	10.5772i	1.14583	−	0.376319i
$791$		−	1.02583i		−

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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