LMFDB - Embedded newform 552.2.q.b.121.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(25,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 0, 2]))

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

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

chi := DirichletCharacter("552.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			121.2
Character	$\chi$	$=$	552.121
Dual form			552.2.q.b.73.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.959493 - 0.281733i) q^{3} +(-2.20233 + 1.41535i) q^{5} +(-0.514962 + 3.58164i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})$	\(q+(-0.959493 - 0.281733i) q^{3} +(-2.20233 + 1.41535i) q^{5} +(-0.514962 + 3.58164i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-2.22711 - 4.87669i) q^{11} +(-0.416071 - 2.89384i) q^{13} +(2.51187 - 0.737551i) q^{15} +(5.05879 - 5.83815i) q^{17} +(-0.423471 - 0.488712i) q^{19} +(1.50317 - 3.29148i) q^{21} +(-0.961254 - 4.69851i) q^{23} +(0.769957 - 1.68597i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-2.40378 + 2.77411i) q^{29} +(-5.05280 + 1.48364i) q^{31} +(0.762975 + 5.30660i) q^{33} +(-3.93516 - 8.61679i) q^{35} +(-2.76087 - 1.77431i) q^{37} +(-0.416071 + 2.89384i) q^{39} +(10.4326 - 6.70460i) q^{41} +(-6.82789 - 2.00485i) q^{43} -2.61791 q^{45} -10.1303 q^{47} +(-5.84650 - 1.71669i) q^{49} +(-6.49867 + 4.17644i) q^{51} +(-0.257234 + 1.78910i) q^{53} +(11.8071 + 7.58794i) q^{55} +(0.268632 + 0.588221i) q^{57} +(0.444147 + 3.08911i) q^{59} +(5.55347 - 1.63065i) q^{61} +(-2.36959 + 2.73466i) q^{63} +(5.01212 + 5.78429i) q^{65} +(5.49914 - 12.0414i) q^{67} +(-0.401406 + 4.77900i) q^{69} +(1.62989 - 3.56895i) q^{71} +(4.29657 + 4.95851i) q^{73} +(-1.21376 + 1.40075i) q^{75} +(18.6134 - 5.46540i) q^{77} +(1.44201 + 10.0294i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-2.72723 - 1.75269i) q^{83} +(-2.87808 + 20.0175i) q^{85} +(3.08797 - 1.98452i) q^{87} +(-12.3708 - 3.63240i) q^{89} +10.5789 q^{91} +5.26611 q^{93} +(1.62432 + 0.476944i) q^{95} +(-7.03916 + 4.52380i) q^{97} +(0.762975 - 5.30660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) $ 30 * q - 3 * q^3 - 3 * q^9	$ 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) $ 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{9}{11}\right)$	$1$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$3$	−0.959493	−	0.281733i	−0.553964	−	0.162658i
$4$		0			0
$5$	−2.20233	+	1.41535i	−0.984911	+	0.632964i	−0.930784	−	0.365570i	$-0.880874\pi$
$5$	−2.20233	+	1.41535i	−0.984911	+	0.632964i	−0.0541272	+	0.998534i	$0.517238\pi$
$6$		0			0
$7$	−0.514962	+	3.58164i	−0.194637	+	1.35373i	0.624899	+	0.780705i	$0.285140\pi$
$7$	−0.514962	+	3.58164i	−0.194637	+	1.35373i	−0.819537	+	0.573027i	$0.805769\pi$
$8$		0			0
$9$	0.841254	+	0.540641i	0.280418	+	0.180214i
$10$		0			0
$11$	−2.22711	−	4.87669i	−0.671500	−	1.47038i	−0.871405	−	0.490564i	$-0.836791\pi$
$11$	−2.22711	−	4.87669i	−0.671500	−	1.47038i	0.199906	−	0.979815i	$-0.435936\pi$
$12$		0			0
$13$	−0.416071	−	2.89384i	−0.115397	−	0.802606i	−0.962520	−	0.271209i	$-0.912576\pi$
$13$	−0.416071	−	2.89384i	−0.115397	−	0.802606i	0.847123	−	0.531397i	$-0.178333\pi$
$14$		0			0
$15$	2.51187	−	0.737551i	0.648562	−	0.190435i
$16$		0			0
$17$	5.05879	−	5.83815i	1.22694	−	1.41596i	0.349040	−	0.937108i	$-0.386508\pi$
$17$	5.05879	−	5.83815i	1.22694	−	1.41596i	0.877896	−	0.478851i	$-0.158947\pi$
$18$		0			0
$19$	−0.423471	−	0.488712i	−0.0971510	−	0.112118i	0.705092	−	0.709116i	$-0.250906\pi$
$19$	−0.423471	−	0.488712i	−0.0971510	−	0.112118i	−0.802243	+	0.596998i	$0.796360\pi$
$20$		0			0
$21$	1.50317	−	3.29148i	0.328018	−	0.718259i
$22$		0			0
$23$	−0.961254	−	4.69851i	−0.200435	−	0.979707i
$23$	−0.961254	−	4.69851i	−0.200435	−	0.979707i
$24$		0			0
$25$	0.769957	−	1.68597i	0.153991	−	0.337194i
$26$		0			0
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$		0			0
$29$	−2.40378	+	2.77411i	−0.446371	+	0.515140i	−0.933689	−	0.358085i	$-0.883430\pi$
$29$	−2.40378	+	2.77411i	−0.446371	+	0.515140i	0.487318	+	0.873225i	$0.337975\pi$
$30$		0			0
$31$	−5.05280	+	1.48364i	−0.907510	+	0.266469i	−0.701992	−	0.712185i	$-0.747706\pi$
$31$	−5.05280	+	1.48364i	−0.907510	+	0.266469i	−0.205517	+	0.978653i	$0.565888\pi$
$32$		0			0
$33$	0.762975	+	5.30660i	0.132817	+	0.923761i
$34$		0			0
$35$	−3.93516	−	8.61679i	−0.665163	−	1.45650i
$36$		0			0
$37$	−2.76087	−	1.77431i	−0.453885	−	0.291694i	0.293654	−	0.955912i	$-0.405129\pi$
$37$	−2.76087	−	1.77431i	−0.453885	−	0.291694i	−0.747539	+	0.664218i	$0.768765\pi$
$38$		0			0
$39$	−0.416071	+	2.89384i	−0.0666247	+	0.463385i
$40$		0			0
$41$	10.4326	−	6.70460i	1.62929	−	1.04708i	0.679750	−	0.733444i	$-0.262088\pi$
$41$	10.4326	−	6.70460i	1.62929	−	1.04708i	0.949543	−	0.313638i	$-0.101548\pi$
$42$		0			0
$43$	−6.82789	−	2.00485i	−1.04124	−	0.305736i	−0.283969	−	0.958834i	$-0.591651\pi$
$43$	−6.82789	−	2.00485i	−1.04124	−	0.305736i	−0.757274	+	0.653097i	$0.773469\pi$
$44$		0			0
$45$	−2.61791			−0.390255
$46$		0			0
$47$	−10.1303			−1.47766			−0.738828	−	0.673894i	$-0.764621\pi$
$47$	−10.1303			−1.47766			−0.738828	+	0.673894i	$0.764621\pi$
$48$		0			0
$49$	−5.84650	−	1.71669i	−0.835215	−	0.245241i
$50$		0			0
$51$	−6.49867	+	4.17644i	−0.909995	+	0.584818i
$52$		0			0
$53$	−0.257234	+	1.78910i	−0.0353338	+	0.245752i	−0.999832	−	0.0183382i	$-0.994162\pi$
$53$	−0.257234	+	1.78910i	−0.0353338	+	0.245752i	0.964498	+	0.264090i	$0.0850715\pi$
$54$		0			0
$55$	11.8071	+	7.58794i	1.59206	+	1.02316i
$56$		0			0
$57$	0.268632	+	0.588221i	0.0355811	+	0.0779118i
$58$		0			0
$59$	0.444147	+	3.08911i	0.0578230	+	0.402168i	0.998092	+	0.0617366i	$0.0196639\pi$
$59$	0.444147	+	3.08911i	0.0578230	+	0.402168i	−0.940270	+	0.340431i	$0.889427\pi$
$60$		0			0
$61$	5.55347	−	1.63065i	0.711050	−	0.208783i	0.0938463	−	0.995587i	$-0.470084\pi$
$61$	5.55347	−	1.63065i	0.711050	−	0.208783i	0.617203	+	0.786804i	$0.288266\pi$
$62$		0			0
$63$	−2.36959	+	2.73466i	−0.298541	+	0.344534i
$64$		0			0
$65$	5.01212	+	5.78429i	0.621676	+	0.717453i
$66$		0			0
$67$	5.49914	−	12.0414i	0.671826	−	1.47109i	−0.199251	−	0.979949i	$-0.563851\pi$
$67$	5.49914	−	12.0414i	0.671826	−	1.47109i	0.871077	−	0.491146i	$-0.163422\pi$
$68$		0			0
$69$	−0.401406	+	4.77900i	−0.0483237	+	0.575324i
$70$		0			0
$71$	1.62989	−	3.56895i	0.193432	−	0.423557i	−0.787920	−	0.615778i	$-0.788842\pi$
$71$	1.62989	−	3.56895i	0.193432	−	0.423557i	0.981352	+	0.192221i	$0.0615691\pi$
$72$		0			0
$73$	4.29657	+	4.95851i	0.502876	+	0.580349i	0.949260	−	0.314492i	$-0.101834\pi$
$73$	4.29657	+	4.95851i	0.502876	+	0.580349i	−0.446385	+	0.894841i	$0.647289\pi$
$74$		0			0
$75$	−1.21376	+	1.40075i	−0.140153	+	0.161745i
$76$		0			0
$77$	18.6134	−	5.46540i	2.12120	−	0.622840i
$78$		0			0
$79$	1.44201	+	10.0294i	0.162238	+	1.12839i	0.894402	+	0.447264i	$0.147601\pi$
$79$	1.44201	+	10.0294i	0.162238	+	1.12839i	−0.732164	+	0.681129i	$0.761489\pi$
$80$		0			0
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$		0			0
$83$	−2.72723	−	1.75269i	−0.299353	−	0.192382i	0.382338	−	0.924022i	$-0.375119\pi$
$83$	−2.72723	−	1.75269i	−0.299353	−	0.192382i	−0.681691	+	0.731640i	$0.738755\pi$
$84$		0			0
$85$	−2.87808	+	20.0175i	−0.312171	+	2.17120i
$86$		0			0
$87$	3.08797	−	1.98452i	0.331065	−	0.212763i
$88$		0			0
$89$	−12.3708	−	3.63240i	−1.31130	−	0.385033i	−0.449956	−	0.893051i	$-0.648560\pi$
$89$	−12.3708	−	3.63240i	−1.31130	−	0.385033i	−0.861347	+	0.508017i	$0.830379\pi$
$90$		0			0
$91$	10.5789			1.10897
$92$		0			0
$93$	5.26611			0.546071
$94$		0			0
$95$	1.62432	+	0.476944i	0.166652	+	0.0489334i
$96$		0			0
$97$	−7.03916	+	4.52380i	−0.714719	+	0.459322i	−0.846796	−	0.531918i	$-0.821472\pi$
$97$	−7.03916	+	4.52380i	−0.714719	+	0.459322i	0.132077	+	0.991239i	$0.457835\pi$
$98$		0			0
$99$	0.762975	−	5.30660i	0.0766818	−	0.533334i
$100$		0			0
$101$	−13.8122	−	8.87656i	−1.37436	−	0.883251i	−0.375318	−	0.926896i	$-0.622466\pi$
$101$	−13.8122	−	8.87656i	−1.37436	−	0.883251i	−0.999047	+	0.0436454i	$0.986103\pi$
$102$		0			0
$103$	−6.00799	−	13.1557i	−0.591985	−	1.29627i	−0.934235	−	0.356657i	$-0.883916\pi$
$103$	−6.00799	−	13.1557i	−0.591985	−	1.29627i	0.342251	−	0.939609i	$-0.388811\pi$
$104$		0			0
$105$	1.34813	+	9.37642i	0.131564	+	0.915045i
$106$		0			0
$107$	−6.89690	+	2.02511i	−0.666748	+	0.195775i	−0.597555	−	0.801828i	$-0.703861\pi$
$107$	−6.89690	+	2.02511i	−0.666748	+	0.195775i	−0.0691938	+	0.997603i	$0.522043\pi$
$108$		0			0
$109$	7.10690	−	8.20180i	0.680717	−	0.785590i	−0.305296	−	0.952258i	$-0.598755\pi$
$109$	7.10690	−	8.20180i	0.680717	−	0.785590i	0.986013	+	0.166668i	$0.0533008\pi$
$110$		0			0
$111$	2.14916	+	2.48026i	0.203989	+	0.235416i
$112$		0			0
$113$	−2.01632	+	4.41512i	−0.189679	+	0.415340i	−0.980449	−	0.196774i	$-0.936953\pi$
$113$	−2.01632	+	4.41512i	−0.189679	+	0.415340i	0.790770	+	0.612114i	$0.209681\pi$
$114$		0			0
$115$	8.76703	+	8.98715i	0.817530	+	0.838056i
$116$		0			0
$117$	1.21450	−	2.65939i	0.112281	−	0.245861i
$118$		0			0
$119$	18.3051	+	21.1252i	1.67802	+	1.93654i
$120$		0			0
$121$	−11.6187	+	13.4086i	−1.05624	+	1.21897i
$122$		0			0
$123$	−11.8989	+	3.49382i	−1.07289	+	0.315027i
$124$		0			0
$125$	−1.17230	−	8.15351i	−0.104854	−	0.729272i
$126$		0			0
$127$	2.09225	+	4.58140i	0.185658	+	0.406533i	0.979459	−	0.201644i	$-0.0646283\pi$
$127$	2.09225	+	4.58140i	0.185658	+	0.406533i	−0.793801	+	0.608177i	$0.791901\pi$
$128$		0			0
$129$	5.98648	+	3.84728i	0.527080	+	0.338734i
$130$		0			0
$131$	0.108047	−	0.751482i	0.00944009	−	0.0656573i	−0.984557	−	0.175065i	$-0.943986\pi$
$131$	0.108047	−	0.751482i	0.00944009	−	0.0656573i	0.993997	+	0.109408i	$0.0348955\pi$
$132$		0			0
$133$	1.96846	−	1.26505i	0.170687	−	0.109694i
$134$		0			0
$135$	2.51187	+	0.737551i	0.216187	+	0.0634783i
$136$		0			0
$137$	−14.9771			−1.27958			−0.639789	−	0.768550i	$-0.720978\pi$
$137$	−14.9771			−1.27958			−0.639789	+	0.768550i	$0.720978\pi$
$138$		0			0
$139$	7.52320			0.638110			0.319055	−	0.947736i	$-0.396635\pi$
$139$	7.52320			0.638110			0.319055	+	0.947736i	$0.396635\pi$
$140$		0			0
$141$	9.71996	+	2.85404i	0.818568	+	0.240353i
$142$		0			0
$143$	−13.1857	+	8.47395i	−1.10265	+	0.708627i
$144$		0			0
$145$	1.36758	−	9.51171i	0.113571	−	0.789904i
$146$		0			0
$147$	5.12603	+	3.29430i	0.422788	+	0.271709i
$148$		0			0
$149$	4.27249	+	9.35545i	0.350016	+	0.766429i	0.999979	+	0.00646263i	$0.00205713\pi$
$149$	4.27249	+	9.35545i	0.350016	+	0.766429i	−0.649963	+	0.759966i	$0.725216\pi$
$150$		0			0
$151$	2.99426	+	20.8255i	0.243669	+	1.69476i	0.633396	+	0.773828i	$0.281660\pi$
$151$	2.99426	+	20.8255i	0.243669	+	1.69476i	−0.389727	+	0.920931i	$0.627431\pi$
$152$		0			0
$153$	7.41206	−	2.17638i	0.599230	−	0.175950i
$154$		0			0
$155$	9.02806	−	10.4189i	0.725151	−	0.836869i
$156$		0			0
$157$	−9.92056	−	11.4489i	−0.791747	−	0.913725i	0.206152	−	0.978520i	$-0.433906\pi$
$157$	−9.92056	−	11.4489i	−0.791747	−	0.913725i	−0.997899	+	0.0647955i	$0.979360\pi$
$158$		0			0
$159$	0.750861	−	1.64416i	0.0595472	−	0.130390i
$160$		0			0
$161$	17.3234	−	1.02331i	1.36527	−	0.0806483i
$162$		0			0
$163$	−6.73194	+	14.7409i	−0.527286	+	1.15460i	0.439320	+	0.898331i	$0.355219\pi$
$163$	−6.73194	+	14.7409i	−0.527286	+	1.15460i	−0.966606	+	0.256265i	$0.917508\pi$
$164$		0			0
$165$	−9.19102	−	10.6070i	−0.715520	−	0.825754i
$166$		0			0
$167$	6.11506	−	7.05715i	0.473198	−	0.546099i	−0.468101	−	0.883675i	$-0.655062\pi$
$167$	6.11506	−	7.05715i	0.473198	−	0.546099i	0.941298	+	0.337576i	$0.109607\pi$
$168$		0			0
$169$	4.27223	−	1.25444i	0.328633	−	0.0964955i
$170$		0			0
$171$	−0.0920291	−	0.640076i	−0.00703764	−	0.0489479i
$172$		0			0
$173$	1.20927	+	2.64794i	0.0919393	+	0.201319i	0.950015	−	0.312204i	$-0.101067\pi$
$173$	1.20927	+	2.64794i	0.0919393	+	0.201319i	−0.858076	+	0.513523i	$0.828340\pi$
$174$		0			0
$175$	5.64204	+	3.62592i	0.426498	+	0.274094i
$176$		0			0
$177$	0.444147	−	3.08911i	0.0333841	−	0.232192i
$178$		0			0
$179$	−5.00570	+	3.21697i	−0.374144	+	0.240448i	−0.714176	−	0.699966i	$-0.753198\pi$
$179$	−5.00570	+	3.21697i	−0.374144	+	0.240448i	0.340032	+	0.940414i	$0.389562\pi$
$180$		0			0
$181$	−9.73775	−	2.85926i	−0.723802	−	0.212527i	−0.100977	−	0.994889i	$-0.532197\pi$
$181$	−9.73775	−	2.85926i	−0.723802	−	0.212527i	−0.622825	+	0.782361i	$0.714015\pi$
$182$		0			0
$183$	−5.78793			−0.427856
$184$		0			0
$185$	8.59161			0.631668
$186$		0			0
$187$	−39.7374	−	11.6679i	−2.90588	−	0.853244i
$188$		0			0
$189$	3.04405	−	1.95629i	0.221422	−	0.142299i
$190$		0			0
$191$	2.39491	−	16.6569i	0.173289	−	1.20525i	−0.698586	−	0.715526i	$-0.746187\pi$
$191$	2.39491	−	16.6569i	0.173289	−	1.20525i	0.871876	−	0.489728i	$-0.162904\pi$
$192$		0			0
$193$	−1.53778	−	0.988270i	−0.110692	−	0.0711373i	0.484124	−	0.875000i	$-0.339138\pi$
$193$	−1.53778	−	0.988270i	−0.110692	−	0.0711373i	−0.594815	+	0.803862i	$0.702775\pi$
$194$		0			0
$195$	−3.17947	−	6.96206i	−0.227686	−	0.498564i
$196$		0			0
$197$	2.19432	+	15.2618i	0.156339	+	1.08736i	0.905308	+	0.424755i	$0.139640\pi$
$197$	2.19432	+	15.2618i	0.156339	+	1.08736i	−0.748970	+	0.662604i	$0.769451\pi$
$198$		0			0
$199$	18.7628	−	5.50927i	1.33006	−	0.390542i	0.461948	−	0.886907i	$-0.347151\pi$
$199$	18.7628	−	5.50927i	1.33006	−	0.390542i	0.868114	+	0.496365i	$0.165332\pi$
$200$		0			0
$201$	−8.66884	+	10.0044i	−0.611453	+	0.705655i
$202$		0			0
$203$	−8.69802	−	10.0381i	−0.610481	−	0.704533i
$204$		0			0
$205$	−13.4866	+	29.5314i	−0.941942	+	2.06257i
$206$		0			0
$207$	1.73155	−	4.47233i	0.120351	−	0.310848i
$208$		0			0
$209$	−1.44018	+	3.15356i	−0.0996194	+	0.218136i
$210$		0			0
$211$	10.7321	+	12.3855i	0.738827	+	0.852652i	0.993436	−	0.114392i	$-0.0364920\pi$
$211$	10.7321	+	12.3855i	0.738827	+	0.852652i	−0.254608	+	0.967044i	$0.581947\pi$
$212$		0			0
$213$	−2.56936	+	2.96519i	−0.176049	+	0.203172i
$214$		0			0
$215$	17.8748	−	5.24852i	1.21905	−	0.357946i
$216$		0			0
$217$	−2.71185	−	18.8613i	−0.184092	−	1.28039i
$218$		0			0
$219$	−2.72556	−	5.96814i	−0.184176	−	0.403289i
$220$		0			0
$221$	−18.9995	−	12.2102i	−1.27804	−	0.821348i
$222$		0			0
$223$	1.00496	−	6.98967i	0.0672973	−	0.468063i	−0.928108	−	0.372311i	$-0.878565\pi$
$223$	1.00496	−	6.98967i	0.0672973	−	0.468063i	0.995405	−	0.0957518i	$-0.0305255\pi$
$224$		0			0
$225$	1.55923	−	1.00206i	0.103949	−	0.0668039i
$226$		0			0
$227$	6.16636	+	1.81061i	0.409276	+	0.120174i	0.479888	−	0.877330i	$-0.340677\pi$
$227$	6.16636	+	1.81061i	0.409276	+	0.120174i	−0.0706126	+	0.997504i	$0.522495\pi$
$228$		0			0
$229$	14.5667			0.962593			0.481296	−	0.876558i	$-0.340166\pi$
$229$	14.5667			0.962593			0.481296	+	0.876558i	$0.340166\pi$
$230$		0			0
$231$	−19.3992			−1.27638
$232$		0			0
$233$	−10.6308	−	3.12148i	−0.696446	−	0.204495i	−0.0856995	−	0.996321i	$-0.527312\pi$
$233$	−10.6308	−	3.12148i	−0.696446	−	0.204495i	−0.610747	+	0.791826i	$0.709131\pi$
$234$		0			0
$235$	22.3103	−	14.3379i	1.45536	−	0.935303i
$236$		0			0
$237$	1.44201	−	10.0294i	0.0936684	−	0.651478i
$238$		0			0
$239$	−1.64379	−	1.05640i	−0.106328	−	0.0683330i	0.486396	−	0.873738i	$-0.338311\pi$
$239$	−1.64379	−	1.05640i	−0.106328	−	0.0683330i	−0.592724	+	0.805405i	$0.701948\pi$
$240$		0			0
$241$	−6.71420	−	14.7020i	−0.432499	−	0.947042i	−0.992915	−	0.118830i	$-0.962086\pi$
$241$	−6.71420	−	14.7020i	−0.432499	−	0.947042i	0.560415	−	0.828212i	$-0.310642\pi$
$242$		0			0
$243$	−0.142315	−	0.989821i	−0.00912950	−	0.0634971i
$244$		0			0
$245$	15.3056	−	4.49414i	0.977841	−	0.287120i
$246$		0			0
$247$	−1.23806	+	1.42880i	−0.0787758	+	0.0909121i
$248$		0			0
$249$	2.12297	+	2.45004i	0.134538	+	0.155265i
$250$		0			0
$251$	−7.14133	+	15.6373i	−0.450757	+	0.987020i	0.538741	+	0.842471i	$0.318900\pi$
$251$	−7.14133	+	15.6373i	−0.450757	+	0.987020i	−0.989498	+	0.144548i	$0.953827\pi$
$252$		0			0
$253$	−20.7724	+	15.1518i	−1.30595	+	0.952589i
$254$		0			0
$255$	8.40107	−	18.3958i	0.526095	−	1.15199i
$256$		0			0
$257$	14.1768	+	16.3609i	0.884322	+	1.02056i	0.999629	+	0.0272326i	$0.00866946\pi$
$257$	14.1768	+	16.3609i	0.884322	+	1.02056i	−0.115307	+	0.993330i	$0.536785\pi$
$258$		0			0
$259$	7.77667	−	8.97475i	0.483219	−	0.557664i
$260$		0			0
$261$	−3.52199	+	1.03415i	−0.218006	+	0.0640123i
$262$		0			0
$263$	−1.95708	−	13.6118i	−0.120679	−	0.839339i	−0.956790	−	0.290779i	$-0.906086\pi$
$263$	−1.95708	−	13.6118i	−0.120679	−	0.839339i	0.836112	−	0.548559i	$-0.184824\pi$
$264$		0			0
$265$	−1.96569	−	4.30426i	−0.120751	−	0.264409i
$266$		0			0
$267$	10.8463	+	6.97052i	0.663785	+	0.426589i
$268$		0			0
$269$	2.50809	−	17.4442i	0.152921	−	1.06359i	−0.758370	−	0.651825i	$-0.774004\pi$
$269$	2.50809	−	17.4442i	0.152921	−	1.06359i	0.911291	−	0.411764i	$-0.135087\pi$
$270$		0			0
$271$	2.99388	−	1.92405i	0.181865	−	0.116878i	−0.446541	−	0.894763i	$-0.647344\pi$
$271$	2.99388	−	1.92405i	0.181865	−	0.116878i	0.628406	+	0.777886i	$0.283708\pi$
$272$		0			0
$273$	−10.1504	−	2.98043i	−0.614331	−	0.180384i
$274$		0			0
$275$	−9.93674			−0.599208
$276$		0			0
$277$	4.53860			0.272698			0.136349	−	0.990661i	$-0.456463\pi$
$277$	4.53860			0.272698			0.136349	+	0.990661i	$0.456463\pi$
$278$		0			0
$279$	−5.05280	−	1.48364i	−0.302503	−	0.0888230i
$280$		0			0
$281$	−13.4587	+	8.64941i	−0.802881	+	0.515980i	−0.876555	−	0.481302i	$-0.840164\pi$
$281$	−13.4587	+	8.64941i	−0.802881	+	0.515980i	0.0736737	+	0.997282i	$0.476528\pi$
$282$		0			0
$283$	3.23284	−	22.4849i	0.192172	−	1.33659i	−0.634072	−	0.773274i	$-0.718618\pi$
$283$	3.23284	−	22.4849i	0.192172	−	1.33659i	0.826244	−	0.563313i	$-0.190473\pi$
$284$		0			0
$285$	−1.42415	−	0.915248i	−0.0843596	−	0.0542146i
$286$		0			0
$287$	18.6411	+	40.8183i	1.10035	+	2.40943i
$288$		0			0
$289$	−6.07333	−	42.2409i	−0.357255	−	2.48476i
$290$		0			0
$291$	8.02853	−	2.35739i	0.470641	−	0.138193i
$292$		0			0
$293$	−13.0932	+	15.1104i	−0.764916	+	0.882760i	−0.995924	−	0.0901921i	$-0.971252\pi$
$293$	−13.0932	+	15.1104i	−0.764916	+	0.882760i	0.231009	+	0.972952i	$0.425797\pi$
$294$		0			0
$295$	−5.35033	−	6.17461i	−0.311508	−	0.359499i
$296$		0			0
$297$	−2.22711	+	4.87669i	−0.129230	+	0.282975i
$298$		0			0
$299$	−13.1968	+	4.73663i	−0.763189	+	0.273926i
$300$		0			0
$301$	10.6967	−	23.4226i	0.616550	−	1.35006i
$302$		0			0
$303$	10.7519	+	12.4083i	0.617680	+	0.712841i
$304$		0			0
$305$	−9.92264	+	11.4513i	−0.568168	+	0.655701i
$306$		0			0
$307$	−7.76735	+	2.28070i	−0.443306	+	0.130166i	−0.495765	−	0.868457i	$-0.665112\pi$
$307$	−7.76735	+	2.28070i	−0.443306	+	0.130166i	0.0524591	+	0.998623i	$0.483294\pi$
$308$		0			0
$309$	2.05825	+	14.3154i	0.117089	+	0.814375i
$310$		0			0
$311$	−7.55742	−	16.5484i	−0.428542	−	0.938376i	−0.993561	−	0.113298i	$-0.963858\pi$
$311$	−7.55742	−	16.5484i	−0.428542	−	0.938376i	0.565019	−	0.825078i	$-0.308869\pi$
$312$		0			0
$313$	−12.7983	−	8.22496i	−0.723402	−	0.464902i	0.126417	−	0.991977i	$-0.459652\pi$
$313$	−12.7983	−	8.22496i	−0.723402	−	0.464902i	−0.849819	+	0.527075i	$0.823289\pi$
$314$		0			0
$315$	1.34813	−	9.37642i	0.0759582	−	0.528301i
$316$		0			0
$317$	0.615622	−	0.395636i	0.0345768	−	0.0222211i	−0.523238	−	0.852186i	$-0.675276\pi$
$317$	0.615622	−	0.395636i	0.0345768	−	0.0222211i	0.557815	+	0.829965i	$0.311640\pi$
$318$		0			0
$319$	18.8820	+	5.54426i	1.05719	+	0.310419i
$320$		0			0
$321$	7.18807			0.401199
$322$		0			0
$323$	−4.99542			−0.277953
$324$		0			0
$325$	−5.19928	−	1.52665i	−0.288404	−	0.0846831i
$326$		0			0
$327$	−9.12973	+	5.86732i	−0.504875	+	0.324464i
$328$		0			0
$329$	5.21672	−	36.2831i	0.287607	−	2.00035i
$330$		0			0
$331$	8.26501	+	5.31160i	0.454286	+	0.291952i	0.747704	−	0.664032i	$-0.231156\pi$
$331$	8.26501	+	5.31160i	0.454286	+	0.291952i	−0.293418	+	0.955984i	$0.594793\pi$
$332$		0			0
$333$	−1.36333	−	2.98528i	−0.0747102	−	0.163592i
$334$		0			0
$335$	4.93194	+	34.3024i	0.269460	+	1.87414i
$336$		0			0
$337$	0.159410	−	0.0468069i	0.00868361	−	0.00254974i	−0.277388	−	0.960758i	$-0.589469\pi$
$337$	0.159410	−	0.0468069i	0.00868361	−	0.00254974i	0.286071	+	0.958208i	$0.407651\pi$
$338$		0			0
$339$	3.17853	−	3.66822i	0.172634	−	0.199230i
$340$		0			0
$341$	18.4884	+	21.3367i	1.00120	+	1.15545i
$342$		0			0
$343$	−1.36288	+	2.98430i	−0.0735888	+	0.161137i
$344$		0			0
$345$	−5.87993	−	11.0931i	−0.316565	−	0.597230i
$346$		0			0
$347$	1.92751	−	4.22066i	0.103474	−	0.226577i	−0.850813	−	0.525469i	$-0.823890\pi$
$347$	1.92751	−	4.22066i	0.103474	−	0.226577i	0.954287	+	0.298892i	$0.0966171\pi$
$348$		0			0
$349$	−1.81197	−	2.09113i	−0.0969926	−	0.111935i	0.705178	−	0.709030i	$-0.250867\pi$
$349$	−1.81197	−	2.09113i	−0.0969926	−	0.111935i	−0.802171	+	0.597095i	$0.796322\pi$
$350$		0			0
$351$	−1.91455	+	2.20951i	−0.102191	+	0.117935i
$352$		0			0
$353$	−10.8410	+	3.18321i	−0.577009	+	0.169425i	−0.557199	−	0.830379i	$-0.688124\pi$
$353$	−10.8410	+	3.18321i	−0.577009	+	0.169425i	−0.0198094	+	0.999804i	$0.506306\pi$
$354$		0			0
$355$	1.46178	+	10.1669i	0.0775830	+	0.539601i
$356$		0			0
$357$	−11.6119	−	25.4266i	−0.614569	−	1.34572i
$358$		0			0
$359$	11.0346	+	7.09148i	0.582381	+	0.374274i	0.798411	−	0.602113i	$-0.205674\pi$
$359$	11.0346	+	7.09148i	0.582381	+	0.374274i	−0.216029	+	0.976387i	$0.569311\pi$
$360$		0			0
$361$	2.64447	−	18.3927i	0.139183	−	0.968037i
$362$		0			0
$363$	14.9257	−	9.59215i	0.783395	−	0.503457i
$364$		0			0
$365$	−16.4805	−	4.83911i	−0.862628	−	0.253290i
$366$		0			0
$367$	21.1764			1.10540			0.552700	−	0.833380i	$-0.313597\pi$
$367$	21.1764			1.10540			0.552700	+	0.833380i	$0.313597\pi$
$368$		0			0
$369$	12.4012			0.645581
$370$		0			0
$371$	−6.27544	−	1.84264i	−0.325805	−	0.0956649i
$372$		0			0
$373$	−6.22348	+	3.99958i	−0.322239	+	0.207091i	−0.691752	−	0.722135i	$-0.743161\pi$
$373$	−6.22348	+	3.99958i	−0.322239	+	0.207091i	0.369513	+	0.929226i	$0.379525\pi$
$374$		0			0
$375$	−1.17230	+	8.15351i	−0.0605372	+	0.421046i
$376$		0			0
$377$	9.02798	+	5.80193i	0.464965	+	0.298815i
$378$		0			0
$379$	−10.1710	−	22.2714i	−0.522450	−	1.14401i	−0.968504	−	0.249000i	$-0.919898\pi$
$379$	−10.1710	−	22.2714i	−0.522450	−	1.14401i	0.446054	−	0.895006i	$-0.352829\pi$
$380$		0			0
$381$	−0.716774	−	4.98528i	−0.0367215	−	0.255403i
$382$		0			0
$383$	−10.4972	+	3.08224i	−0.536380	+	0.157495i	−0.538693	−	0.842502i	$-0.681082\pi$
$383$	−10.4972	+	3.08224i	−0.536380	+	0.157495i	0.00231337	+	0.999997i	$0.499264\pi$
$384$		0			0
$385$	−33.2574	+	38.3811i	−1.69496	+	1.95608i
$386$		0			0
$387$	−4.66008	−	5.37802i	−0.236885	−	0.273380i
$388$		0			0
$389$	−11.5367	+	25.2619i	−0.584936	+	1.28083i	0.353518	+	0.935428i	$0.384985\pi$
$389$	−11.5367	+	25.2619i	−0.584936	+	1.28083i	−0.938454	+	0.345404i	$0.887742\pi$
$390$		0			0
$391$	−32.2934	−	18.1568i	−1.63315	−	0.918229i
$392$		0			0
$393$	−0.315387	+	0.690601i	−0.0159092	+	0.0348362i
$394$		0			0
$395$	−17.3708	−	20.0470i	−0.874022	−	1.00868i
$396$		0			0
$397$	4.74690	−	5.47822i	0.238240	−	0.274944i	−0.624021	−	0.781408i	$-0.714502\pi$
$397$	4.74690	−	5.47822i	0.238240	−	0.274944i	0.862261	+	0.506464i	$0.169048\pi$
$398$		0			0
$399$	−2.24513	+	0.659230i	−0.112397	+	0.0330028i
$400$		0			0
$401$	4.40346	+	30.6268i	0.219898	+	1.52943i	0.738407	+	0.674355i	$0.235578\pi$
$401$	4.40346	+	30.6268i	0.219898	+	1.52943i	−0.518509	+	0.855072i	$0.673513\pi$
$402$		0			0
$403$	6.39572	+	14.0047i	0.318594	+	0.697623i
$404$		0			0
$405$	−2.20233	−	1.41535i	−0.109435	−	0.0703293i
$406$		0			0
$407$	−2.50397	+	17.4155i	−0.124117	+	0.863255i
$408$		0			0
$409$	29.1513	−	18.7344i	1.44144	−	0.926356i	0.441866	−	0.897081i	$-0.354317\pi$
$409$	29.1513	−	18.7344i	1.44144	−	0.926356i	0.999571	−	0.0292744i	$-0.00931967\pi$
$410$		0			0
$411$	14.3704	+	4.21953i	0.708840	+	0.208134i
$412$		0			0
$413$	−11.2928			−0.555682
$414$		0			0
$415$	8.48693			0.416607
$416$		0			0
$417$	−7.21846	−	2.11953i	−0.353490	−	0.103794i
$418$		0			0
$419$	33.3976	−	21.4633i	1.63158	−	1.04855i	0.683775	−	0.729693i	$-0.260337\pi$
$419$	33.3976	−	21.4633i	1.63158	−	1.04855i	0.947802	−	0.318859i	$-0.103300\pi$
$420$		0			0
$421$	−3.63478	+	25.2805i	−0.177148	+	1.23209i	0.686173	+	0.727439i	$0.259289\pi$
$421$	−3.63478	+	25.2805i	−0.177148	+	1.23209i	−0.863321	+	0.504655i	$0.831620\pi$
$422$		0			0
$423$	−8.52215	−	5.47686i	−0.414361	−	0.266294i
$424$		0			0
$425$	−5.94790	−	13.0241i	−0.288515	−	0.631761i
$426$		0			0
$427$	2.98056	+	20.7303i	0.144240	+	1.00321i
$428$		0			0
$429$	15.0390	−	4.41585i	0.726089	−	0.213199i
$430$		0			0
$431$	12.8112	−	14.7849i	0.617092	−	0.712162i	−0.358060	−	0.933699i	$-0.616562\pi$
$431$	12.8112	−	14.7849i	0.617092	−	0.712162i	0.975152	+	0.221536i	$0.0711071\pi$
$432$		0			0
$433$	−14.3737	−	16.5881i	−0.690756	−	0.797175i	0.296717	−	0.954966i	$-0.404108\pi$
$433$	−14.3737	−	16.5881i	−0.690756	−	0.797175i	−0.987473	+	0.157791i	$0.949563\pi$
$434$		0			0
$435$	−3.99194	+	8.74112i	−0.191399	+	0.419105i
$436$		0			0
$437$	−1.88915	+	2.45946i	−0.0903705	+	0.117652i
$438$		0			0
$439$	3.54226	−	7.75647i	0.169063	−	0.370196i	−0.806069	−	0.591822i	$-0.798409\pi$
$439$	3.54226	−	7.75647i	0.169063	−	0.370196i	0.975132	+	0.221626i	$0.0711363\pi$
$440$		0			0
$441$	−3.99028	−	4.60503i	−0.190013	−	0.219287i
$442$		0			0
$443$	4.43821	−	5.12197i	0.210866	−	0.243352i	−0.640457	−	0.767994i	$-0.721255\pi$
$443$	4.43821	−	5.12197i	0.210866	−	0.243352i	0.851323	+	0.524642i	$0.175801\pi$
$444$		0			0
$445$	32.3857	−	9.50929i	1.53523	−	0.450784i
$446$		0			0
$447$	−1.46369	−	10.1802i	−0.0692302	−	0.481507i
$448$		0			0
$449$	6.00448	+	13.1480i	0.283369	+	0.620492i	0.996774	−	0.0802604i	$-0.0255752\pi$
$449$	6.00448	+	13.1480i	0.283369	+	0.620492i	−0.713405	+	0.700752i	$0.752848\pi$
$450$		0			0
$451$	−55.9308	−	35.9445i	−2.63368	−	1.69256i
$452$		0			0
$453$	2.99426	−	20.8255i	0.140683	−	0.978469i
$454$		0			0
$455$	−23.2983	+	14.9729i	−1.09224	+	0.701940i
$456$		0			0
$457$	20.9510	+	6.15177i	0.980047	+	0.287768i	0.732244	−	0.681043i	$-0.238473\pi$
$457$	20.9510	+	6.15177i	0.980047	+	0.287768i	0.247803	+	0.968810i	$0.420291\pi$
$458$		0			0
$459$	−7.72498			−0.360571
$460$		0			0
$461$	29.6214			1.37960			0.689802	−	0.723998i	$-0.257698\pi$
$461$	29.6214			1.37960			0.689802	+	0.723998i	$0.257698\pi$
$462$		0			0
$463$	−12.0616	−	3.54161i	−0.560550	−	0.164592i	−0.0108303	−	0.999941i	$-0.503447\pi$
$463$	−12.0616	−	3.54161i	−0.560550	−	0.164592i	−0.549720	+	0.835349i	$0.685266\pi$
$464$		0			0
$465$	−11.5977	+	7.45340i	−0.537831	+	0.345643i
$466$		0			0
$467$	2.98424	−	20.7558i	0.138094	−	0.960465i	−0.796472	−	0.604675i	$-0.793303\pi$
$467$	2.98424	−	20.7558i	0.138094	−	0.960465i	0.934566	−	0.355790i	$-0.115788\pi$
$468$		0			0
$469$	40.2962	+	25.8968i	1.86071	+	1.19580i
$470$		0			0
$471$	6.29317	+	13.7801i	0.289974	+	0.634954i
$472$		0			0
$473$	5.42943	+	37.7625i	0.249646	+	1.73632i
$474$		0			0
$475$	−1.15001	+	0.337673i	−0.0527660	+	0.0154935i
$476$		0			0
$477$	−1.18366	+	1.36602i	−0.0541960	+	0.0625455i
$478$		0			0
$479$	−5.70744	−	6.58673i	−0.260779	−	0.300955i	0.610228	−	0.792226i	$-0.291078\pi$
$479$	−5.70744	−	6.58673i	−0.260779	−	0.300955i	−0.871007	+	0.491271i	$0.836533\pi$
$480$		0			0
$481$	−3.98583	+	8.72775i	−0.181738	+	0.397951i
$482$		0			0
$483$	−16.9100	−	3.89870i	−0.769430	−	0.177397i
$484$		0			0
$485$	9.09979	−	19.9258i	0.413200	−	0.904782i
$486$		0			0
$487$	8.98258	+	10.3665i	0.407040	+	0.469749i	0.921845	−	0.387558i	$-0.126681\pi$
$487$	8.98258	+	10.3665i	0.407040	+	0.469749i	−0.514806	+	0.857307i	$0.672136\pi$
$488$		0			0
$489$	10.6122	−	12.2472i	0.479902	−	0.553836i
$490$		0			0
$491$	−2.12398	+	0.623656i	−0.0958538	+	0.0281452i	−0.329308	−	0.944223i	$-0.606815\pi$
$491$	−2.12398	+	0.623656i	−0.0958538	+	0.0281452i	0.233454	+	0.972368i	$0.424997\pi$
$492$		0			0
$493$	4.03547	+	28.0673i	0.181748	+	1.26409i
$494$		0			0
$495$	5.83038	+	12.7668i	0.262056	+	0.573823i
$496$		0			0
$497$	11.9434	+	7.67554i	0.535734	+	0.344295i
$498$		0			0
$499$	−3.70770	+	25.7876i	−0.165980	+	1.15441i	0.721111	+	0.692819i	$0.243632\pi$
$499$	−3.70770	+	25.7876i	−0.165980	+	1.15441i	−0.887091	+	0.461594i	$0.847278\pi$
$500$		0			0
$501$	−7.85559	+	5.04848i	−0.350962	+	0.225549i
$502$		0			0
$503$	−10.4475	−	3.06766i	−0.465831	−	0.136780i	0.0403902	−	0.999184i	$-0.487140\pi$
$503$	−10.4475	−	3.06766i	−0.465831	−	0.136780i	−0.506221	+	0.862404i	$0.668958\pi$
$504$		0			0
$505$	42.9824			1.91269
$506$		0			0
$507$	−4.45260			−0.197747
$508$		0			0
$509$	5.92591	+	1.74000i	0.262661	+	0.0771243i	0.410412	−	0.911900i	$-0.365385\pi$
$509$	5.92591	+	1.74000i	0.262661	+	0.0771243i	−0.147750	+	0.989025i	$0.547203\pi$
$510$		0			0
$511$	−19.9722	+	12.8353i	−0.883516	+	0.567801i
$512$		0			0
$513$	−0.0920291	+	0.640076i	−0.00406318	+	0.0282601i
$514$		0			0
$515$	31.8514	+	20.4697i	1.40354	+	0.902001i
$516$		0			0
$517$	22.5613	+	49.4024i	0.992246	+	2.17272i
$518$		0			0
$519$	−0.414278	−	2.88137i	−0.0181848	−	0.126478i
$520$		0			0
$521$	22.0480	−	6.47386i	0.965938	−	0.283625i	0.239530	−	0.970889i	$-0.423007\pi$
$521$	22.0480	−	6.47386i	0.965938	−	0.283625i	0.726408	+	0.687264i	$0.241188\pi$
$522$		0			0
$523$	16.4643	−	19.0008i	0.719934	−	0.830848i	−0.271365	−	0.962477i	$-0.587475\pi$
$523$	16.4643	−	19.0008i	0.719934	−	0.830848i	0.991299	+	0.131628i	$0.0420205\pi$
$524$		0			0
$525$	−4.39196	−	5.06859i	−0.191681	−	0.221211i
$526$		0			0
$527$	−16.8993	+	37.0044i	−0.736147	+	1.61194i
$528$		0			0
$529$	−21.1520	+	9.03292i	−0.919651	+	0.392736i
$530$		0			0
$531$	−1.29646	+	2.83885i	−0.0562615	+	0.123195i
$532$		0			0
$533$	−23.7427	−	27.4005i	−1.02841	−	1.18685i
$534$		0			0
$535$	12.3230	−	14.2215i	0.532769	−	0.614849i
$536$		0			0
$537$	5.70926	−	1.67639i	0.246373	−	0.0723416i
$538$		0			0
$539$	4.64905	+	32.3349i	0.200249	+	1.39276i
$540$		0			0
$541$	−3.51018	−	7.68623i	−0.150915	−	0.330457i	0.819043	−	0.573733i	$-0.194505\pi$
$541$	−3.51018	−	7.68623i	−0.150915	−	0.330457i	−0.969957	+	0.243276i	$0.921778\pi$
$542$		0			0
$543$	8.53776	+	5.48688i	0.366390	+	0.235465i
$544$		0			0
$545$	−4.04330	+	28.1218i	−0.173196	+	1.20461i
$546$		0			0
$547$	−26.9316	+	17.3079i	−1.15151	+	0.740033i	−0.969940	−	0.243344i	$-0.921756\pi$
$547$	−26.9316	+	17.3079i	−1.15151	+	0.740033i	−0.181574	+	0.983377i	$0.558119\pi$
$548$		0			0
$549$	5.55347	+	1.63065i	0.237017	+	0.0695943i
$550$		0			0
$551$	2.37368			0.101122
$552$		0			0
$553$	−36.6642			−1.55912
$554$		0			0
$555$	−8.24359	−	2.42054i	−0.349921	−	0.102746i
$556$		0			0
$557$	15.5897	−	10.0189i	0.660558	−	0.424515i	−0.166953	−	0.985965i	$-0.553393\pi$
$557$	15.5897	−	10.0189i	0.660558	−	0.424515i	0.827511	+	0.561450i	$0.189756\pi$
$558$		0			0
$559$	−2.96082	+	20.5929i	−0.125229	+	0.870989i
$560$		0			0
$561$	34.8405	+	22.3906i	1.47097	+	0.945332i
$562$		0			0
$563$	13.3197	+	29.1661i	0.561358	+	1.22920i	0.951272	+	0.308352i	$0.0997775\pi$
$563$	13.3197	+	29.1661i	0.561358	+	1.22920i	−0.389914	+	0.920851i	$0.627495\pi$
$564$		0			0
$565$	−1.80835	−	12.5773i	−0.0760778	−	0.529133i
$566$		0			0
$567$	−3.47190	+	1.01944i	−0.145806	+	0.0428125i
$568$		0			0
$569$	8.23975	−	9.50917i	0.345428	−	0.398645i	−0.556277	−	0.830997i	$-0.687771\pi$
$569$	8.23975	−	9.50917i	0.345428	−	0.398645i	0.901705	+	0.432352i	$0.142316\pi$
$570$		0			0
$571$	2.91103	+	3.35951i	0.121823	+	0.140591i	0.813385	−	0.581726i	$-0.197623\pi$
$571$	2.91103	+	3.35951i	0.121823	+	0.140591i	−0.691562	+	0.722317i	$0.743077\pi$
$572$		0			0
$573$	−6.99070	+	15.3075i	−0.292041	+	0.639480i
$574$		0			0
$575$	−8.66167	−	1.99700i	−0.361217	−	0.0832808i
$576$		0			0
$577$	−8.39178	+	18.3754i	−0.349354	+	0.764979i	0.650630	+	0.759395i	$0.274505\pi$
$577$	−8.39178	+	18.3754i	−0.349354	+	0.764979i	−0.999984	+	0.00558426i	$0.998222\pi$
$578$		0			0
$579$	1.19706	+	1.38148i	0.0497481	+	0.0574124i
$580$		0			0
$581$	7.68192	−	8.86540i	0.318700	−	0.367799i
$582$		0			0
$583$	9.29778	−	2.73007i	0.385075	−	0.113068i
$584$		0			0
$585$	1.08924	+	7.57581i	0.0450344	+	0.313221i
$586$		0			0
$587$	17.7049	+	38.7684i	0.730760	+	1.60014i	0.798181	+	0.602417i	$0.205796\pi$
$587$	17.7049	+	38.7684i	0.730760	+	1.60014i	−0.0674209	+	0.997725i	$0.521477\pi$
$588$		0			0
$589$	2.86479	+	1.84109i	0.118041	+	0.0758606i
$590$		0			0
$591$	2.19432	−	15.2618i	0.0902621	−	0.627787i
$592$		0			0
$593$	20.3094	−	13.0520i	0.834006	−	0.535983i	−0.0525427	−	0.998619i	$-0.516733\pi$
$593$	20.3094	−	13.0520i	0.834006	−	0.535983i	0.886548	+	0.462636i	$0.153096\pi$
$594$		0			0
$595$	−70.2133	−	20.6165i	−2.87846	−	0.845193i
$596$		0			0
$597$	−19.5549			−0.800331
$598$		0			0
$599$	−23.1489			−0.945840			−0.472920	−	0.881105i	$-0.656800\pi$
$599$	−23.1489			−0.945840			−0.472920	+	0.881105i	$0.656800\pi$
$600$		0			0
$601$	4.83739	+	1.42038i	0.197321	+	0.0579387i	0.378900	−	0.925438i	$-0.376303\pi$
$601$	4.83739	+	1.42038i	0.197321	+	0.0579387i	−0.181579	+	0.983376i	$0.558121\pi$
$602$		0			0
$603$	11.1363	−	7.15684i	0.453503	−	0.291449i
$604$		0			0
$605$	6.61016	−	45.9747i	0.268741	−	1.86914i
$606$		0			0
$607$	−12.4607	−	8.00799i	−0.505763	−	0.325034i	0.262754	−	0.964863i	$-0.415369\pi$
$607$	−12.4607	−	8.00799i	−0.505763	−	0.325034i	−0.768518	+	0.639828i	$0.779005\pi$
$608$		0			0
$609$	5.51764	+	12.0820i	0.223586	+	0.489585i
$610$		0			0
$611$	4.21492	+	29.3154i	0.170518	+	1.18598i
$612$		0			0
$613$	−5.37427	+	1.57803i	−0.217065	+	0.0637360i	−0.388457	−	0.921467i	$-0.626992\pi$
$613$	−5.37427	+	1.57803i	−0.217065	+	0.0637360i	0.171392	+	0.985203i	$0.445174\pi$
$614$		0			0
$615$	21.2602	−	24.5356i	0.857295	−	0.989371i
$616$		0			0
$617$	0.0803270	+	0.0927023i	0.00323384	+	0.00373206i	0.757364	−	0.652993i	$-0.226487\pi$
$617$	0.0803270	+	0.0927023i	0.00323384	+	0.00373206i	−0.754130	+	0.656725i	$0.771941\pi$
$618$		0			0
$619$	−9.90368	+	21.6860i	−0.398063	+	0.871636i	0.599400	+	0.800449i	$0.295406\pi$
$619$	−9.90368	+	21.6860i	−0.398063	+	0.871636i	−0.997463	+	0.0711863i	$0.977322\pi$
$620$		0			0
$621$	−2.92141	+	3.80334i	−0.117232	+	0.152623i
$622$		0			0
$623$	19.3804	−	42.4372i	0.776460	−	1.70021i
$624$		0			0
$625$	20.1907	+	23.3013i	0.807626	+	0.932051i
$626$		0			0
$627$	2.27030	−	2.62007i	0.0906672	−	0.104635i
$628$		0			0
$629$	−24.3253	+	7.14256i	−0.969915	+	0.284793i
$630$		0			0
$631$	−0.858906	−	5.97383i	−0.0341925	−	0.237814i	0.965557	−	0.260191i	$-0.0837856\pi$
$631$	−0.858906	−	5.97383i	−0.0341925	−	0.237814i	−0.999750	+	0.0223771i	$0.992877\pi$
$632$		0			0
$633$	−6.80797	−	14.9074i	−0.270592	−	0.592515i
$634$		0			0
$635$	−11.0921	−	7.12847i	−0.440177	−	0.282885i
$636$		0			0
$637$	−2.53525	+	17.6331i	−0.100450	+	0.698648i
$638$		0			0
$639$	3.30067	−	2.12121i	0.130573	−	0.0839139i
$640$		0			0
$641$	−43.9553	−	12.9064i	−1.73613	−	0.509774i	−0.748041	−	0.663652i	$-0.769005\pi$
$641$	−43.9553	−	12.9064i	−1.73613	−	0.509774i	−0.988090	+	0.153878i	$0.950824\pi$
$642$		0			0
$643$	−21.8329			−0.861007			−0.430503	−	0.902589i	$-0.641664\pi$
$643$	−21.8329			−0.861007			−0.430503	+	0.902589i	$0.641664\pi$
$644$		0			0
$645$	−18.6294			−0.733533
$646$		0			0
$647$	−11.0088	−	3.23246i	−0.432799	−	0.127081i	0.0580743	−	0.998312i	$-0.481504\pi$
$647$	−11.0088	−	3.23246i	−0.432799	−	0.127081i	−0.490873	+	0.871231i	$0.663322\pi$
$648$		0			0
$649$	14.0755	−	9.04576i	0.552511	−	0.355077i
$650$		0			0
$651$	−2.71185	+	18.8613i	−0.106286	+	0.739234i
$652$		0			0
$653$	7.06814	+	4.54242i	0.276598	+	0.177758i	0.671584	−	0.740929i	$-0.265614\pi$
$653$	7.06814	+	4.54242i	0.276598	+	0.177758i	−0.394986	+	0.918687i	$0.629251\pi$
$654$		0			0
$655$	0.825655	+	1.80793i	0.0322610	+	0.0706418i
$656$		0			0
$657$	0.933734	+	6.49426i	0.0364284	+	0.253365i
$658$		0			0
$659$	22.1966	−	6.51752i	0.864658	−	0.253886i	0.180816	−	0.983517i	$-0.442126\pi$
$659$	22.1966	−	6.51752i	0.864658	−	0.253886i	0.683842	+	0.729631i	$0.260308\pi$
$660$		0			0
$661$	−0.128434	+	0.148220i	−0.00499549	+	0.00576510i	−0.758242	−	0.651973i	$-0.773941\pi$
$661$	−0.128434	+	0.148220i	−0.00499549	+	0.00576510i	0.753246	+	0.657739i	$0.228487\pi$
$662$		0			0
$663$	14.7898	+	17.0684i	0.574390	+	0.662881i
$664$		0			0
$665$	−2.54470	+	5.57212i	−0.0986794	+	0.216078i
$666$		0			0
$667$	15.3449	+	8.62757i	0.594155	+	0.334061i
$668$		0			0
$669$	−2.93347	+	6.42341i	−0.113415	+	0.248343i
$670$		0			0
$671$	−20.3204	−	23.4510i	−0.784460	−	0.905315i
$672$		0			0
$673$	22.7715	−	26.2797i	0.877776	−	1.01301i	−0.122014	−	0.992528i	$-0.538935\pi$
$673$	22.7715	−	26.2797i	0.877776	−	1.01301i	0.999790	−	0.0204792i	$-0.00651919\pi$
$674$		0			0
$675$	−1.77839	+	0.522181i	−0.0684501	+	0.0200988i
$676$		0			0
$677$	−3.55538	−	24.7282i	−0.136644	−	0.950383i	−0.936619	−	0.350349i	$-0.886063\pi$
$677$	−3.55538	−	24.7282i	−0.136644	−	0.950383i	0.799975	−	0.600034i	$-0.204846\pi$
$678$		0			0
$679$	−12.5777	−	27.5413i	−0.482688	−	1.05694i
$680$		0			0
$681$	−5.40647	−	3.47453i	−0.207176	−	0.133144i
$682$		0			0
$683$	0.172693	−	1.20111i	0.00660793	−	0.0459591i	−0.986251	−	0.165256i	$-0.947155\pi$
$683$	0.172693	−	1.20111i	0.00660793	−	0.0459591i	0.992859	+	0.119297i	$0.0380640\pi$
$684$		0			0
$685$	32.9845	−	21.1978i	1.26027	−	0.809927i
$686$		0			0
$687$	−13.9766	−	4.10391i	−0.533241	−	0.156574i
$688$		0			0
$689$	5.28439			0.201319
$690$		0			0
$691$	46.5527			1.77095			0.885475	−	0.464688i	$-0.153833\pi$
$691$	46.5527			1.77095			0.885475	+	0.464688i	$0.153833\pi$
$692$		0			0
$693$	18.6134	+	5.46540i	0.707066	+	0.207613i
$694$		0			0
$695$	−16.5686	+	10.6480i	−0.628481	+	0.403900i
$696$		0			0
$697$	13.6336	−	94.8240i	0.516411	−	3.59171i
$698$		0			0
$699$	9.32075	+	5.99008i	0.352543	+	0.226566i
$700$		0			0
$701$	−12.1759	−	26.6615i	−0.459877	−	1.00699i	−0.987516	−	0.157522i	$-0.949650\pi$
$701$	−12.1759	−	26.6615i	−0.459877	−	1.00699i	0.527638	−	0.849469i	$-0.323078\pi$
$702$		0			0
$703$	0.302026	+	2.10064i	0.0113911	+	0.0792271i
$704$		0			0
$705$	−25.4460	+	7.47162i	−0.958351	+	0.281397i
$706$		0			0
$707$	38.9054	−	44.8992i	1.46319	−	1.68861i
$708$		0			0
$709$	29.5681	+	34.1234i	1.11045	+	1.28153i	0.955947	+	0.293539i	$0.0948332\pi$
$709$	29.5681	+	34.1234i	1.11045	+	1.28153i	0.154506	+	0.987992i	$0.450621\pi$
$710$		0			0
$711$	−4.20920	+	9.21685i	−0.157857	+	0.345659i
$712$		0			0
$713$	11.8279	+	22.3145i	0.442958	+	0.835684i
$714$		0			0
$715$	17.0457	−	37.3248i	0.637472	−	1.39587i
$716$		0			0
$717$	1.27959	+	1.47672i	0.0477870	+	0.0551492i
$718$		0			0
$719$	24.4623	−	28.2310i	0.912291	−	1.05284i	−0.0861089	−	0.996286i	$-0.527443\pi$
$719$	24.4623	−	28.2310i	0.912291	−	1.05284i	0.998400	−	0.0565538i	$-0.0180112\pi$
$720$		0			0
$721$	50.2127	−	14.7438i	1.87002	−	0.549087i
$722$		0			0
$723$	2.30018	+	15.9981i	0.0855446	+	0.594976i
$724$		0			0
$725$	2.82626	+	6.18866i	0.104965	+	0.229841i
$726$		0			0
$727$	−31.0202	−	19.9355i	−1.15048	−	0.739367i	−0.180743	−	0.983530i	$-0.557850\pi$
$727$	−31.0202	−	19.9355i	−1.15048	−	0.739367i	−0.969734	+	0.244164i	$0.921487\pi$
$728$		0			0
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$		0			0
$731$	−46.2454	+	29.7201i	−1.71045	+	1.09924i
$732$		0			0
$733$	−4.06702	−	1.19418i	−0.150219	−	0.0441082i	0.205759	−	0.978603i	$-0.434034\pi$
$733$	−4.06702	−	1.19418i	−0.150219	−	0.0441082i	−0.355977	+	0.934495i	$0.615852\pi$
$734$		0			0
$735$	−15.9518			−0.588391
$736$		0			0
$737$	−70.9696			−2.61420
$738$		0			0
$739$	12.9139	+	3.79186i	0.475045	+	0.139486i	0.510486	−	0.859886i	$-0.329465\pi$
$739$	12.9139	+	3.79186i	0.475045	+	0.139486i	−0.0354412	+	0.999372i	$0.511284\pi$
$740$		0			0
$741$	1.59045	−	1.02212i	0.0584265	−	0.0375484i
$742$		0			0
$743$	−2.30477	+	16.0300i	−0.0845538	+	0.588085i	0.902861	+	0.429933i	$0.141463\pi$
$743$	−2.30477	+	16.0300i	−0.0845538	+	0.588085i	−0.987415	+	0.158152i	$0.949446\pi$
$744$		0			0
$745$	−22.6507	−	14.5567i	−0.829856	−	0.533316i
$746$		0			0
$747$	−1.34672	−	2.94891i	−0.0492740	−	0.107895i
$748$		0			0
$749$	−3.70158	−	25.7451i	−0.135253	−	0.940704i
$750$		0			0
$751$	16.1846	−	4.75223i	0.590585	−	0.173411i	0.0272340	−	0.999629i	$-0.491330\pi$
$751$	16.1846	−	4.75223i	0.590585	−	0.173411i	0.563351	+	0.826218i	$0.309512\pi$
$752$		0			0
$753$	11.2576	−	12.9920i	0.410250	−	0.473454i
$754$		0			0
$755$	−36.0698	−	41.6267i	−1.31271	−	1.51495i
$756$		0			0
$757$	12.3189	−	26.9746i	0.447737	−	0.980408i	−0.542376	−	0.840136i	$-0.682475\pi$
$757$	12.3189	−	26.9746i	0.447737	−	0.980408i	0.990113	−	0.140272i	$-0.0447976\pi$
$758$		0			0
$759$	24.1997	−	8.68584i	0.878394	−	0.315276i
$760$		0			0
$761$	−14.2523	+	31.2083i	−0.516647	+	1.13130i	0.454047	+	0.890978i	$0.349980\pi$
$761$	−14.2523	+	31.2083i	−0.516647	+	1.13130i	−0.970693	+	0.240321i	$0.922747\pi$
$762$		0			0
$763$	25.7161	+	29.6780i	0.930985	+	1.07441i
$764$		0			0
$765$	−13.2435	+	15.2838i	−0.478818	+	0.552586i
$766$		0			0
$767$	8.75458	−	2.57058i	0.316109	−	0.0928181i
$768$		0			0
$769$	6.53048	+	45.4205i	0.235495	+	1.63790i	0.673683	+	0.739021i	$0.264711\pi$
$769$	6.53048	+	45.4205i	0.235495	+	1.63790i	−0.438188	+	0.898884i	$0.644379\pi$
$770$		0			0
$771$	−8.99312	−	19.6922i	−0.323879	−	0.709197i
$772$		0			0
$773$	−35.1121	−	22.5651i	−1.26289	−	0.811612i	−0.274215	−	0.961668i	$-0.588418\pi$
$773$	−35.1121	−	22.5651i	−1.26289	−	0.811612i	−0.988677	+	0.150056i	$0.952055\pi$
$774$		0			0
$775$	−1.38907	+	9.66120i	−0.0498969	+	0.347041i
$776$		0			0
$777$	−9.99014	+	6.42027i	−0.358394	+	0.230326i
$778$		0			0
$779$	−7.69451	−	2.25931i	−0.275684	−	0.0809482i
$780$		0			0
$781$	−21.0346			−0.752679
$782$		0			0
$783$	3.67068			0.131179
$784$		0			0
$785$	38.0526	+	11.1732i	1.35815	+	0.398790i
$786$		0			0
$787$	−4.03864	+	2.59547i	−0.143962	+	0.0925186i	−0.610639	−	0.791909i	$-0.709087\pi$
$787$	−4.03864	+	2.59547i	−0.143962	+	0.0925186i	0.466677	+	0.884428i	$0.345451\pi$
$788$		0			0
$789$	−1.95708	+	13.6118i	−0.0696739	+	0.484592i
$790$		0			0
$791$	−14.7750	−	9.49535i	−0.525340	−	0.337616i
$792$		0			0
$793$	−7.02947	−	15.3924i	−0.249624	−	0.546600i
$794$		0			0
$795$	0.673415	+	4.68370i	0.0238836	+	0.166114i
$796$		0			0
$797$	−16.7250	+	4.91090i	−0.592430	+	0.173953i	−0.564186	−	0.825648i	$-0.690810\pi$
$797$	−16.7250	+	4.91090i	−0.592430	+	0.173953i	−0.0282443	+	0.999601i	$0.508992\pi$
$798$		0			0
$799$	−51.2470	+	59.1422i	−1.81299	+	2.09230i
$800$		0			0
$801$	−8.44316	−	9.74393i	−0.298324	−	0.344285i
$802$		0			0
$803$	14.6122	−	31.9962i	0.515653	−	1.12912i
$804$		0			0
$805$	−36.7034	+	26.7723i	−1.29363	+	0.943600i
$806$		0			0
$807$	−7.32108	+	16.0309i	−0.257714	+	0.564316i
$808$		0			0
$809$	−1.69255	−	1.95330i	−0.0595067	−	0.0686744i	0.725216	−	0.688522i	$-0.241740\pi$
$809$	−1.69255	−	1.95330i	−0.0595067	−	0.0686744i	−0.784722	+	0.619847i	$0.787195\pi$
$810$		0			0
$811$	0.869278	−	1.00320i	0.0305245	−	0.0352271i	−0.740282	−	0.672296i	$-0.765308\pi$
$811$	0.869278	−	1.00320i	0.0305245	−	0.0352271i	0.770807	+	0.637069i	$0.219853\pi$
$812$		0			0
$813$	−3.41467	+	1.00264i	−0.119758	+	0.0351640i
$814$		0			0
$815$	−6.03759	−	41.9923i	−0.211487	−	1.47093i
$816$		0			0
$817$	1.91162	+	4.18586i	0.0668791	+	0.146445i
$818$		0			0
$819$	8.89957	+	5.71941i	0.310976	+	0.199852i
$820$		0			0
$821$	4.58446	−	31.8856i	0.159999	−	1.11282i	−0.738632	−	0.674109i	$-0.764528\pi$
$821$	4.58446	−	31.8856i	0.159999	−	1.11282i	0.898630	−	0.438707i	$-0.144563\pi$
$822$		0			0
$823$	18.1228	−	11.6468i	0.631720	−	0.405982i	−0.185226	−	0.982696i	$-0.559302\pi$
$823$	18.1228	−	11.6468i	0.631720	−	0.405982i	0.816946	+	0.576714i	$0.195665\pi$
$824$		0			0
$825$	9.53423	+	2.79950i	0.331939	+	0.0974662i
$826$		0			0
$827$	13.8995			0.483333			0.241667	−	0.970359i	$-0.422306\pi$
$827$	13.8995			0.483333			0.241667	+	0.970359i	$0.422306\pi$
$828$		0			0
$829$	−28.7609			−0.998908			−0.499454	−	0.866340i	$-0.666466\pi$
$829$	−28.7609			−0.998908			−0.499454	+	0.866340i	$0.666466\pi$
$830$		0			0
$831$	−4.35475	−	1.27867i	−0.151065	−	0.0443566i
$832$		0			0
$833$	−39.5985	+	25.4484i	−1.37201	+	0.881735i
$834$		0			0
$835$	−3.47902	+	24.1971i	−0.120396	+	0.837376i
$836$		0			0
$837$	4.43014	+	2.84708i	0.153128	+	0.0984094i
$838$		0			0
$839$	−4.42075	−	9.68009i	−0.152621	−	0.334194i	0.817842	−	0.575443i	$-0.195170\pi$
$839$	−4.42075	−	9.68009i	−0.152621	−	0.334194i	−0.970463	+	0.241249i	$0.922443\pi$
$840$		0			0
$841$	2.20960	+	15.3681i	0.0761930	+	0.529934i
$842$		0			0
$843$	15.3504	−	4.50728i	0.528695	−	0.155239i
$844$		0			0
$845$	−7.63339	+	8.80940i	−0.262597	+	0.303053i
$846$		0			0
$847$	−42.0418	−	48.5188i	−1.44457	−	1.66713i
$848$		0			0
$849$	−9.43660	+	20.6633i	−0.323863	+	0.709162i
$850$		0			0
$851$	−5.68269	+	14.6776i	−0.194800	+	0.503140i
$852$		0			0
$853$	−14.9344	+	32.7018i	−0.511344	+	1.11969i	0.461269	+	0.887260i	$0.347394\pi$
$853$	−14.9344	+	32.7018i	−0.511344	+	1.11969i	−0.972614	+	0.232428i	$0.925333\pi$
$854$		0			0
$855$	1.10861	+	1.27940i	0.0379137	+	0.0437547i
$856$		0			0
$857$	20.9724	−	24.2034i	0.716404	−	0.826774i	−0.274466	−	0.961597i	$-0.588501\pi$
$857$	20.9724	−	24.2034i	0.716404	−	0.826774i	0.990870	+	0.134823i	$0.0430466\pi$
$858$		0			0
$859$	5.06620	−	1.48757i	0.172857	−	0.0507553i	−0.194159	−	0.980970i	$-0.562198\pi$
$859$	5.06620	−	1.48757i	0.172857	−	0.0507553i	0.367016	+	0.930215i	$0.380380\pi$
$860$		0			0
$861$	−6.38615	−	44.4167i	−0.217639	−	1.51372i
$862$		0			0
$863$	−4.70080	−	10.2933i	−0.160017	−	0.350388i	0.812593	−	0.582832i	$-0.198055\pi$
$863$	−4.70080	−	10.2933i	−0.160017	−	0.350388i	−0.972610	+	0.232443i	$0.925328\pi$
$864$		0			0
$865$	−6.41098	−	4.12008i	−0.217980	−	0.140087i
$866$		0			0
$867$	−6.07333	+	42.2409i	−0.206261	+	1.43458i
$868$		0			0
$869$	45.6987	−	29.3688i	1.55022	−	0.996267i
$870$		0			0
$871$	−37.1340	−	10.9035i	−1.25824	−	0.369451i
$872$		0			0
$873$	−8.36747			−0.283196
$874$		0			0
$875$	29.8066			1.00765
$876$		0			0
$877$	27.9335	+	8.20202i	0.943247	+	0.276962i	0.716973	−	0.697101i	$-0.245527\pi$
$877$	27.9335	+	8.20202i	0.943247	+	0.276962i	0.226275	+	0.974064i	$0.427345\pi$
$878$		0			0
$879$	16.8200	−	10.8095i	0.567324	−	0.364597i
$880$		0			0
$881$	0.827136	−	5.75286i	0.0278669	−	0.193819i	−0.971133	−	0.238540i	$-0.923331\pi$
$881$	0.827136	−	5.75286i	0.0278669	−	0.193819i	0.998999	+	0.0447218i	$0.0142401\pi$
$882$		0			0
$883$	0.972004	+	0.624669i	0.0327105	+	0.0210218i	0.556894	−	0.830584i	$-0.311993\pi$
$883$	0.972004	+	0.624669i	0.0327105	+	0.0210218i	−0.524183	+	0.851605i	$0.675629\pi$
$884$		0			0
$885$	3.39401	+	7.43185i	0.114088	+	0.249819i
$886$		0			0
$887$	−4.08725	−	28.4275i	−0.137237	−	0.954501i	−0.935785	−	0.352571i	$-0.885308\pi$
$887$	−4.08725	−	28.4275i	−0.137237	−	0.954501i	0.798549	−	0.601930i	$-0.205602\pi$
$888$		0			0
$889$	−17.4863	+	5.13445i	−0.586473	+	0.172204i
$890$		0			0
$891$	3.51082	−	4.05170i	0.117617	−	0.135737i
$892$		0			0
$893$	4.28989	+	4.95080i	0.143556	+	0.165672i
$894$		0			0
$895$	6.47106	−	14.1696i	0.216304	−	0.473639i
$896$		0			0
$897$	13.9967	−	0.826800i	0.467335	−	0.0276060i
$898$		0			0
$899$	8.03006	−	17.5834i	0.267818	−	0.586439i
$900$		0			0
$901$	9.14374	+	10.5524i	0.304622	+	0.351553i
$902$		0			0
$903$	−16.8624	+	19.4602i	−0.561144	+	0.647595i
$904$		0			0
$905$	25.4926	−	7.48530i	0.847402	−	0.248820i
$906$		0			0
$907$	−5.04101	−	35.0610i	−0.167384	−	1.16418i	−0.884265	−	0.466985i	$-0.845340\pi$
$907$	−5.04101	−	35.0610i	−0.167384	−	1.16418i	0.716881	−	0.697195i	$-0.245569\pi$
$908$		0			0
$909$	−6.82053	−	14.9349i	−0.226223	−	0.495359i
$910$		0			0
$911$	42.6905	+	27.4355i	1.41440	+	0.908979i	0.999999	−	0.00111665i	$-0.000355442\pi$
$911$	42.6905	+	27.4355i	1.41440	+	0.908979i	0.414399	+	0.910095i	$0.363992\pi$
$912$		0			0
$913$	−2.47346	+	17.2033i	−0.0818597	+	0.569347i
$914$		0			0
$915$	12.7469	−	8.19194i	0.421400	−	0.270817i
$916$		0			0
$917$	2.63590	+	0.773969i	0.0870450	+	0.0255587i
$918$		0			0
$919$	31.3352			1.03365			0.516827	−	0.856090i	$-0.327113\pi$
$919$	31.3352			1.03365			0.516827	+	0.856090i	$0.327113\pi$
$920$		0			0
$921$	8.09526			0.266748
$922$		0			0
$923$	−11.0061	−	3.23169i	−0.362271	−	0.106372i
$924$		0			0
$925$	−5.11718	+	3.28861i	−0.168252	+	0.108129i
$926$		0			0
$927$	2.05825	−	14.3154i	0.0676016	−	0.470180i
$928$		0			0
$929$	26.2755	+	16.8863i	0.862073	+	0.554020i	0.895318	−	0.445427i	$-0.146948\pi$
$929$	26.2755	+	16.8863i	0.862073	+	0.554020i	−0.0332457	+	0.999447i	$0.510584\pi$
$930$		0			0
$931$	1.63686	+	3.58422i	0.0536459	+	0.117468i
$932$		0			0
$933$	2.58906	+	18.0073i	0.0847619	+	0.589532i
$934$		0			0
$935$	104.029	−	30.5456i	3.40211	−	0.998949i
$936$		0			0
$937$	−1.30100	+	1.50143i	−0.0425017	+	0.0490496i	−0.776602	−	0.629991i	$-0.783059\pi$
$937$	−1.30100	+	1.50143i	−0.0425017	+	0.0490496i	0.734101	+	0.679041i	$0.237604\pi$
$938$		0			0
$939$	9.96263	+	11.4975i	0.325118	+	0.375206i
$940$		0			0
$941$	−7.24599	+	15.8665i	−0.236212	+	0.517233i	−0.990200	−	0.139655i	$-0.955400\pi$
$941$	−7.24599	+	15.8665i	−0.236212	+	0.517233i	0.753988	+	0.656888i	$0.228128\pi$
$942$		0			0
$943$	−41.5300	−	42.5727i	−1.35240	−	1.38636i
$944$		0			0
$945$	−3.93516	+	8.61679i	−0.128011	+	0.280304i
$946$		0			0
$947$	18.3481	+	21.1748i	0.596232	+	0.688089i	0.971014	−	0.239024i	$-0.0768276\pi$
$947$	18.3481	+	21.1748i	0.596232	+	0.688089i	−0.374781	+	0.927113i	$0.622282\pi$
$948$		0			0
$949$	12.5614	−	14.4967i	0.407761	−	0.470582i
$950$		0			0
$951$	−0.702148	+	0.206169i	−0.0227687	+	0.00668550i
$952$		0			0
$953$	−5.15045	−	35.8222i	−0.166839	−	1.16039i	−0.885366	−	0.464894i	$-0.846092\pi$
$953$	−5.15045	−	35.8222i	−0.166839	−	1.16039i	0.718527	−	0.695499i	$-0.244817\pi$
$954$		0			0
$955$	18.3010	+	40.0737i	0.592207	+	1.29675i
$956$		0			0
$957$	−16.5552	−	10.6394i	−0.535152	−	0.343921i
$958$		0			0
$959$	7.71263	−	53.6425i	0.249054	−	1.73221i
$960$		0			0
$961$	−2.74925	+	1.76683i	−0.0886853	+	0.0569946i
$962$		0			0
$963$	−6.89690	−	2.02511i	−0.222249	−	0.0652583i
$964$		0			0
$965$	4.78544			0.154049
$966$		0			0
$967$	−58.8579			−1.89274			−0.946371	−	0.323083i	$-0.895281\pi$
$967$	−58.8579			−1.89274			−0.946371	+	0.323083i	$0.895281\pi$
$968$		0			0
$969$	4.79307	+	1.40737i	0.153976	+	0.0452113i
$970$		0			0
$971$	−1.00667	+	0.646945i	−0.0323054	+	0.0207614i	−0.556694	−	0.830718i	$-0.687930\pi$
$971$	−1.00667	+	0.646945i	−0.0323054	+	0.0207614i	0.524388	+	0.851479i	$0.324294\pi$
$972$		0			0
$973$	−3.87416	+	26.9454i	−0.124200	+	0.863830i
$974$		0			0
$975$	4.55856	+	2.92961i	0.145991	+	0.0938227i
$976$		0			0
$977$	−20.3622	−	44.5869i	−0.651443	−	1.42646i	−0.890285	−	0.455403i	$-0.849495\pi$
$977$	−20.3622	−	44.5869i	−0.651443	−	1.42646i	0.238842	−	0.971058i	$-0.423232\pi$
$978$		0			0
$979$	9.83708	+	68.4184i	0.314394	+	2.18666i
$980$		0			0
$981$	10.4129	−	3.05751i	0.332459	−	0.0976189i
$982$		0			0
$983$	10.0861	−	11.6400i	0.321698	−	0.371259i	−0.571748	−	0.820429i	$-0.693735\pi$
$983$	10.0861	−	11.6400i	0.321698	−	0.371259i	0.893447	+	0.449170i	$0.148280\pi$
$984$		0			0
$985$	−26.4334	−	30.5058i	−0.842238	−	0.971995i
$986$		0			0
$987$	−15.2275	+	33.3437i	−0.484698	+	1.06134i
$988$		0			0
$989$	−2.85646	+	34.0081i	−0.0908303	+	1.08139i
$990$		0			0
$991$	4.45789	−	9.76142i	0.141610	−	0.310082i	−0.825517	−	0.564377i	$-0.809116\pi$
$991$	4.45789	−	9.76142i	0.141610	−	0.310082i	0.967127	+	0.254296i	$0.0818436\pi$
$992$		0			0
$993$	−6.43377	−	7.42496i	−0.204169	−	0.235624i
$994$		0			0
$995$	−33.5244	+	38.6892i	−1.06279	+	1.22653i
$996$		0			0
$997$	1.48859	−	0.437090i	0.0471442	−	0.0138428i	−0.258075	−	0.966125i	$-0.583088\pi$
$997$	1.48859	−	0.437090i	0.0471442	−	0.0138428i	0.305220	+	0.952282i	$0.401270\pi$
$998$		0			0
$999$	0.467057	+	3.24845i	0.0147770	+	0.102776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.q.b.121.2	yes	30
23.4	even	11	inner	552.2.q.b.73.2	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.q.b.73.2	✓	30	23.4	even	11	inner
552.2.q.b.121.2	yes	30	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.959493 - 0.281733i) q^{3} +(-2.20233 + 1.41535i) q^{5} +(-0.514962 + 3.58164i) q^{7} +(0.841254 + 0.540641i) q^{9} +O(q^{10})\)	\(q+(-0.959493 - 0.281733i) q^{3} +(-2.20233 + 1.41535i) q^{5} +(-0.514962 + 3.58164i) q^{7} +(0.841254 + 0.540641i) q^{9} +(-2.22711 - 4.87669i) q^{11} +(-0.416071 - 2.89384i) q^{13} +(2.51187 - 0.737551i) q^{15} +(5.05879 - 5.83815i) q^{17} +(-0.423471 - 0.488712i) q^{19} +(1.50317 - 3.29148i) q^{21} +(-0.961254 - 4.69851i) q^{23} +(0.769957 - 1.68597i) q^{25} +(-0.654861 - 0.755750i) q^{27} +(-2.40378 + 2.77411i) q^{29} +(-5.05280 + 1.48364i) q^{31} +(0.762975 + 5.30660i) q^{33} +(-3.93516 - 8.61679i) q^{35} +(-2.76087 - 1.77431i) q^{37} +(-0.416071 + 2.89384i) q^{39} +(10.4326 - 6.70460i) q^{41} +(-6.82789 - 2.00485i) q^{43} -2.61791 q^{45} -10.1303 q^{47} +(-5.84650 - 1.71669i) q^{49} +(-6.49867 + 4.17644i) q^{51} +(-0.257234 + 1.78910i) q^{53} +(11.8071 + 7.58794i) q^{55} +(0.268632 + 0.588221i) q^{57} +(0.444147 + 3.08911i) q^{59} +(5.55347 - 1.63065i) q^{61} +(-2.36959 + 2.73466i) q^{63} +(5.01212 + 5.78429i) q^{65} +(5.49914 - 12.0414i) q^{67} +(-0.401406 + 4.77900i) q^{69} +(1.62989 - 3.56895i) q^{71} +(4.29657 + 4.95851i) q^{73} +(-1.21376 + 1.40075i) q^{75} +(18.6134 - 5.46540i) q^{77} +(1.44201 + 10.0294i) q^{79} +(0.415415 + 0.909632i) q^{81} +(-2.72723 - 1.75269i) q^{83} +(-2.87808 + 20.0175i) q^{85} +(3.08797 - 1.98452i) q^{87} +(-12.3708 - 3.63240i) q^{89} +10.5789 q^{91} +5.26611 q^{93} +(1.62432 + 0.476944i) q^{95} +(-7.03916 + 4.52380i) q^{97} +(0.762975 - 5.30660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{3} - 3 q^{9}+O(q^{10}) \) 30 * q - 3 * q^3 - 3 * q^9	\( 30 q - 3 q^{3} - 3 q^{9} + 9 q^{11} + 13 q^{13} + 17 q^{17} - 9 q^{19} - 11 q^{21} - 12 q^{23} - 23 q^{25} - 3 q^{27} - q^{29} - 37 q^{31} + 9 q^{33} + 10 q^{35} + 7 q^{37} + 13 q^{39} + 16 q^{41} + 20 q^{43} - 22 q^{45} + 22 q^{47} + 19 q^{49} + 17 q^{51} + 25 q^{53} + 10 q^{55} + 24 q^{57} + 7 q^{59} + 8 q^{61} - 28 q^{65} - 23 q^{67} - q^{69} + 5 q^{71} + 34 q^{73} - 23 q^{75} + 62 q^{77} + 20 q^{79} - 3 q^{81} + 29 q^{83} - 46 q^{85} + 10 q^{87} - 67 q^{89} - 118 q^{91} - 26 q^{93} - 99 q^{95} - 41 q^{97} + 9 q^{99}+O(q^{100}) \) 30 * q - 3 * q^3 - 3 * q^9 + 9 * q^11 + 13 * q^13 + 17 * q^17 - 9 * q^19 - 11 * q^21 - 12 * q^23 - 23 * q^25 - 3 * q^27 - q^29 - 37 * q^31 + 9 * q^33 + 10 * q^35 + 7 * q^37 + 13 * q^39 + 16 * q^41 + 20 * q^43 - 22 * q^45 + 22 * q^47 + 19 * q^49 + 17 * q^51 + 25 * q^53 + 10 * q^55 + 24 * q^57 + 7 * q^59 + 8 * q^61 - 28 * q^65 - 23 * q^67 - q^69 + 5 * q^71 + 34 * q^73 - 23 * q^75 + 62 * q^77 + 20 * q^79 - 3 * q^81 + 29 * q^83 - 46 * q^85 + 10 * q^87 - 67 * q^89 - 118 * q^91 - 26 * q^93 - 99 * q^95 - 41 * q^97 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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