LMFDB - Embedded newform 552.2.u.a.17.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(17,552)]

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, 11, 7]))

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

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

chi := DirichletCharacter("552.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.u (of order $22$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.5
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.49329 + 0.877542i) q^{3} +(-2.99625 + 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(1.45984 - 2.62085i) q^{9} +O(q^{10})$	\(q+(-1.49329 + 0.877542i) q^{3} +(-2.99625 + 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(1.45984 - 2.62085i) q^{9} +(1.81960 + 3.98437i) q^{11} +(-0.199177 - 1.38531i) q^{13} +(2.78451 - 5.50478i) q^{15} +(3.64235 - 4.20350i) q^{17} +(2.85032 - 2.46981i) q^{19} +(6.02836 - 2.46738i) q^{21} +(-3.44262 - 3.33892i) q^{23} +(3.19262 - 6.99086i) q^{25} +(0.119936 + 5.19477i) q^{27} +(2.98733 + 2.58853i) q^{29} +(-8.53689 + 2.50666i) q^{31} +(-6.21365 - 4.35306i) q^{33} +(12.1840 - 5.56423i) q^{35} +(3.86016 - 6.00652i) q^{37} +(1.51309 + 1.89388i) q^{39} +(2.23146 + 3.47222i) q^{41} +(0.999481 - 3.40392i) q^{43} +(0.672591 + 10.6638i) q^{45} -1.34072i q^{47} +(6.85369 + 2.01242i) q^{49} +(-1.75035 + 9.47336i) q^{51} +(0.302667 - 2.10509i) q^{53} +(-13.1242 - 8.43441i) q^{55} +(-2.08899 + 6.18943i) q^{57} +(-4.94467 + 0.710937i) q^{59} +(-3.53114 - 12.0260i) q^{61} +(-6.83687 + 8.97465i) q^{63} +(3.26430 + 3.76720i) q^{65} +(-8.31771 - 3.79857i) q^{67} +(8.07087 + 1.96494i) q^{69} +(-2.30225 - 1.05140i) q^{71} +(-0.0909771 - 0.104993i) q^{73} +(1.36726 + 13.2411i) q^{75} +(-4.64090 - 15.8055i) q^{77} +(14.9218 - 2.14543i) q^{79} +(-4.73772 - 7.65206i) q^{81} +(-3.47436 - 2.23284i) q^{83} +(-2.81926 + 19.6084i) q^{85} +(-6.73250 - 1.24393i) q^{87} +(-11.2243 - 3.29576i) q^{89} +5.26333i q^{91} +(10.5484 - 11.2346i) q^{93} +(-3.78446 + 12.8887i) q^{95} +(-2.42501 - 3.77339i) q^{97} +(13.0988 + 1.04765i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^9	$ 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) $ 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$-1$	$1$	$1$

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
$3$	−1.49329	+	0.877542i	−0.862153	+	0.506649i
$3$	−1.49329	+	0.877542i	−0.862153	+	0.506649i
$4$		0			0
$5$	−2.99625	+	1.92558i	−1.33997	+	0.861143i	−0.996939	−	0.0781824i	$-0.975088\pi$
$5$	−2.99625	+	1.92558i	−1.33997	+	0.861143i	−0.343026	+	0.939326i	$0.611452\pi$
$6$		0			0
$7$	−3.72244	−	0.535207i	−1.40695	−	0.202289i	−0.603359	−	0.797470i	$-0.706171\pi$
$7$	−3.72244	−	0.535207i	−1.40695	−	0.202289i	−0.803592	+	0.595180i	$0.797081\pi$
$8$		0			0
$9$	1.45984	−	2.62085i	0.486614	−	0.873617i
$10$		0			0
$11$	1.81960	+	3.98437i	0.548631	+	1.20133i	0.957418	+	0.288704i	$0.0932244\pi$
$11$	1.81960	+	3.98437i	0.548631	+	1.20133i	−0.408788	+	0.912630i	$0.634048\pi$
$12$		0			0
$13$	−0.199177	−	1.38531i	−0.0552418	−	0.384215i	−0.998621	−	0.0524988i	$-0.983281\pi$
$13$	−0.199177	−	1.38531i	−0.0552418	−	0.384215i	0.943379	−	0.331716i	$-0.107628\pi$
$14$		0			0
$15$	2.78451	−	5.50478i	0.718957	−	1.42133i
$16$		0			0
$17$	3.64235	−	4.20350i	0.883400	−	1.01950i	−0.116255	−	0.993219i	$-0.537089\pi$
$17$	3.64235	−	4.20350i	0.883400	−	1.01950i	0.999655	−	0.0262782i	$-0.00836558\pi$
$18$		0			0
$19$	2.85032	−	2.46981i	0.653908	−	0.566614i	−0.263452	−	0.964672i	$-0.584861\pi$
$19$	2.85032	−	2.46981i	0.653908	−	0.566614i	0.917360	+	0.398058i	$0.130316\pi$
$20$		0			0
$21$	6.02836	−	2.46738i	1.31550	−	0.538426i
$22$		0			0
$23$	−3.44262	−	3.33892i	−0.717836	−	0.696213i
$23$	−3.44262	−	3.33892i	−0.717836	−	0.696213i
$24$		0			0
$25$	3.19262	−	6.99086i	0.638524	−	1.39817i
$26$		0			0
$27$	0.119936	+	5.19477i	0.0230817	+	0.999734i
$28$		0			0
$29$	2.98733	+	2.58853i	0.554733	+	0.480679i	0.886529	−	0.462672i	$-0.153109\pi$
$29$	2.98733	+	2.58853i	0.554733	+	0.480679i	−0.331797	+	0.943351i	$0.607655\pi$
$30$		0			0
$31$	−8.53689	+	2.50666i	−1.53327	+	0.450209i	−0.936050	−	0.351868i	$-0.885547\pi$
$31$	−8.53689	+	2.50666i	−1.53327	+	0.450209i	−0.597221	+	0.802077i	$0.703729\pi$
$32$		0			0
$33$	−6.21365	−	4.35306i	−1.08166	−	0.757770i
$34$		0			0
$35$	12.1840	−	5.56423i	2.05947	−	0.940527i
$36$		0			0
$37$	3.86016	−	6.00652i	0.634606	−	0.987467i	−0.363825	−	0.931467i	$-0.618529\pi$
$37$	3.86016	−	6.00652i	0.634606	−	0.987467i	0.998431	−	0.0559991i	$-0.0178344\pi$
$38$		0			0
$39$	1.51309	+	1.89388i	0.242289	+	0.303264i
$40$		0			0
$41$	2.23146	+	3.47222i	0.348496	+	0.542270i	0.970610	−	0.240656i	$-0.0773626\pi$
$41$	2.23146	+	3.47222i	0.348496	+	0.542270i	−0.622115	+	0.782926i	$0.713726\pi$
$42$		0			0
$43$	0.999481	−	3.40392i	0.152419	−	0.519093i	−0.847512	−	0.530776i	$-0.821901\pi$
$43$	0.999481	−	3.40392i	0.152419	−	0.519093i	0.999932	+	0.0116828i	$0.00371884\pi$
$44$		0			0
$45$	0.672591	+	10.6638i	0.100264	+	1.58966i
$46$		0			0
$47$		−	1.34072i		−	0.195564i	−0.995208	−	0.0977820i	$-0.968825\pi$
$47$		−	1.34072i		−	0.195564i	0.995208	−	0.0977820i	$-0.0311748\pi$
$48$		0			0
$49$	6.85369	+	2.01242i	0.979098	+	0.287489i
$50$		0			0
$51$	−1.75035	+	9.47336i	−0.245098	+	1.32654i
$52$		0			0
$53$	0.302667	−	2.10509i	0.0415745	−	0.289157i	−0.958418	−	0.285367i	$-0.907885\pi$
$53$	0.302667	−	2.10509i	0.0415745	−	0.289157i	0.999993	−	0.00378988i	$-0.00120636\pi$
$54$		0			0
$55$	−13.1242	−	8.43441i	−1.76967	−	1.13730i
$56$		0			0
$57$	−2.08899	+	6.18943i	−0.276694	+	0.819810i
$58$		0			0
$59$	−4.94467	+	0.710937i	−0.643742	+	0.0925561i	−0.456451	−	0.889749i	$-0.650880\pi$
$59$	−4.94467	+	0.710937i	−0.643742	+	0.0925561i	−0.187290	+	0.982305i	$0.559971\pi$
$60$		0			0
$61$	−3.53114	−	12.0260i	−0.452116	−	1.53977i	−0.798689	−	0.601744i	$-0.794473\pi$
$61$	−3.53114	−	12.0260i	−0.452116	−	1.53977i	0.346573	−	0.938023i	$-0.387345\pi$
$62$		0			0
$63$	−6.83687	+	8.97465i	−0.861365	+	1.13070i
$64$		0			0
$65$	3.26430	+	3.76720i	0.404886	+	0.467264i
$66$		0			0
$67$	−8.31771	−	3.79857i	−1.01617	−	0.464069i	−0.163513	−	0.986541i	$-0.552283\pi$
$67$	−8.31771	−	3.79857i	−1.01617	−	0.464069i	−0.852657	+	0.522472i	$0.825010\pi$
$68$		0			0
$69$	8.07087	+	1.96494i	0.971619	+	0.236551i
$70$		0			0
$71$	−2.30225	−	1.05140i	−0.273226	−	0.124778i	0.274090	−	0.961704i	$-0.411623\pi$
$71$	−2.30225	−	1.05140i	−0.273226	−	0.124778i	−0.547317	+	0.836926i	$0.684351\pi$
$72$		0			0
$73$	−0.0909771	−	0.104993i	−0.0106481	−	0.0122885i	0.750401	−	0.660983i	$-0.229861\pi$
$73$	−0.0909771	−	0.104993i	−0.0106481	−	0.0122885i	−0.761049	+	0.648695i	$0.775315\pi$
$74$		0			0
$75$	1.36726	+	13.2411i	0.157877	+	1.52895i
$76$		0			0
$77$	−4.64090	−	15.8055i	−0.528880	−	1.80120i
$78$		0			0
$79$	14.9218	−	2.14543i	1.67883	−	0.241380i	0.764001	−	0.645215i	$-0.223232\pi$
$79$	14.9218	−	2.14543i	1.67883	−	0.241380i	0.914832	+	0.403835i	$0.132323\pi$
$80$		0			0
$81$	−4.73772	−	7.65206i	−0.526414	−	0.850228i
$82$		0			0
$83$	−3.47436	−	2.23284i	−0.381361	−	0.245086i	0.335889	−	0.941901i	$-0.390963\pi$
$83$	−3.47436	−	2.23284i	−0.381361	−	0.245086i	−0.717250	+	0.696816i	$0.754600\pi$
$84$		0			0
$85$	−2.81926	+	19.6084i	−0.305791	+	2.12683i
$86$		0			0
$87$	−6.73250	−	1.24393i	−0.721800	−	0.133364i
$88$		0			0
$89$	−11.2243	−	3.29576i	−1.18978	−	0.349350i	−0.373842	−	0.927493i	$-0.621960\pi$
$89$	−11.2243	−	3.29576i	−1.18978	−	0.349350i	−0.815936	+	0.578142i	$0.803778\pi$
$90$		0			0
$91$			5.26333i			0.551747i
$92$		0			0
$93$	10.5484	−	11.2346i	1.09382	−	1.16498i
$94$		0			0
$95$	−3.78446	+	12.8887i	−0.388278	+	1.32235i
$96$		0			0
$97$	−2.42501	−	3.77339i	−0.246222	−	0.383130i	0.696041	−	0.718002i	$-0.254943\pi$
$97$	−2.42501	−	3.77339i	−0.246222	−	0.383130i	−0.942263	+	0.334872i	$0.891307\pi$
$98$		0			0
$99$	13.0988	+	1.04765i	1.31648	+	0.105292i
$100$		0			0
$101$	−7.45594	+	11.6017i	−0.741894	+	1.15441i	0.241052	+	0.970512i	$0.422508\pi$
$101$	−7.45594	+	11.6017i	−0.741894	+	1.15441i	−0.982946	+	0.183897i	$0.941129\pi$
$102$		0			0
$103$	14.2419	−	6.50407i	1.40330	−	0.640865i	0.437277	−	0.899327i	$-0.355943\pi$
$103$	14.2419	−	6.50407i	1.40330	−	0.640865i	0.966021	+	0.258462i	$0.0832156\pi$
$104$		0			0
$105$	−13.3114	+	19.0010i	−1.29906	+	1.85430i
$106$		0			0
$107$	10.0640	−	2.95506i	0.972923	−	0.285676i	0.243623	−	0.969870i	$-0.421664\pi$
$107$	10.0640	−	2.95506i	0.972923	−	0.285676i	0.729300	+	0.684194i	$0.239846\pi$
$108$		0			0
$109$	5.51358	+	4.77754i	0.528105	+	0.457605i	0.877642	−	0.479317i	$-0.159116\pi$
$109$	5.51358	+	4.77754i	0.528105	+	0.457605i	−0.349537	+	0.936923i	$0.613661\pi$
$110$		0			0
$111$	−0.493369	+	12.3569i	−0.0468285	+	1.17287i
$112$		0			0
$113$	5.30480	−	11.6159i	0.499033	−	1.09273i	−0.477749	−	0.878496i	$-0.658547\pi$
$113$	5.30480	−	11.6159i	0.499033	−	1.09273i	0.976782	−	0.214234i	$-0.0687256\pi$
$114$		0			0
$115$	16.7443	+	3.37523i	1.56141	+	0.314742i
$116$		0			0
$117$	−3.92145	−	1.50032i	−0.362538	−	0.138704i
$118$		0			0
$119$	−15.8082	+	13.6979i	−1.44913	+	1.25568i
$120$		0			0
$121$	−5.36081	+	6.18670i	−0.487346	+	0.562427i
$122$		0			0
$123$	−6.37924	−	3.22684i	−0.575197	−	0.290954i
$124$		0			0
$125$	1.36115	+	9.46703i	0.121745	+	0.846756i
$126$		0			0
$127$	4.67583	+	10.2386i	0.414913	+	0.908533i	0.995538	+	0.0943615i	$0.0300809\pi$
$127$	4.67583	+	10.2386i	0.414913	+	0.908533i	−0.580625	+	0.814171i	$0.697192\pi$
$128$		0			0
$129$	1.49456	+	5.96013i	0.131589	+	0.524760i
$130$		0			0
$131$	−1.65453	−	0.237885i	−0.144557	−	0.0207842i	0.0696564	−	0.997571i	$-0.477810\pi$
$131$	−1.65453	−	0.237885i	−0.144557	−	0.0207842i	−0.214213	+	0.976787i	$0.568719\pi$
$132$		0			0
$133$	−11.9320	+	7.66824i	−1.03464	+	0.664920i
$134$		0			0
$135$	−10.3623	−	15.3339i	−0.891843	−	1.31973i
$136$		0			0
$137$	−22.2736			−1.90297			−0.951483	−	0.307701i	$-0.900440\pi$
$137$	−22.2736			−1.90297			−0.951483	+	0.307701i	$0.900440\pi$
$138$		0			0
$139$	−5.63017			−0.477545			−0.238772	−	0.971076i	$-0.576745\pi$
$139$	−5.63017			−0.477545			−0.238772	+	0.971076i	$0.576745\pi$
$140$		0			0
$141$	1.17654	+	2.00209i	0.0990823	+	0.168606i
$142$		0			0
$143$	5.15716	−	3.31430i	0.431263	−	0.277156i
$144$		0			0
$145$	−13.9352	−	2.00358i	−1.15726	−	0.166388i
$146$		0			0
$147$	−12.0005	+	3.00926i	−0.989788	+	0.248199i
$148$		0			0
$149$	6.67101	+	14.6075i	0.546511	+	1.19669i	0.958392	+	0.285454i	$0.0921444\pi$
$149$	6.67101	+	14.6075i	0.546511	+	1.19669i	−0.411882	+	0.911237i	$0.635128\pi$
$150$		0			0
$151$	−3.44665	−	23.9720i	−0.280484	−	1.95081i	−0.308559	−	0.951205i	$-0.599847\pi$
$151$	−3.44665	−	23.9720i	−0.280484	−	1.95081i	0.0280743	−	0.999606i	$-0.491062\pi$
$152$		0			0
$153$	−5.69948	−	15.6825i	−0.460776	−	1.26785i
$154$		0			0
$155$	20.7519	−	23.9490i	1.66684	−	1.92363i
$156$		0			0
$157$	5.31032	−	4.60141i	0.423809	−	0.367233i	−0.416687	−	0.909050i	$-0.636809\pi$
$157$	5.31032	−	4.60141i	0.423809	−	0.367233i	0.840496	+	0.541817i	$0.182263\pi$
$158$		0			0
$159$	1.39534	+	3.40912i	0.110657	+	0.270361i
$160$		0			0
$161$	11.0279	+	14.2714i	0.869123	+	1.12475i
$162$		0			0
$163$	−5.66822	+	12.4117i	−0.443969	+	0.972158i	0.546883	+	0.837209i	$0.315814\pi$
$163$	−5.66822	+	12.4117i	−0.443969	+	0.972158i	−0.990853	+	0.134949i	$0.956913\pi$
$164$		0			0
$165$	26.9998	+	1.07801i	2.10193	+	0.0839228i
$166$		0			0
$167$	−2.41664	−	2.09403i	−0.187005	−	0.162041i	0.556327	−	0.830964i	$-0.312210\pi$
$167$	−2.41664	−	2.09403i	−0.187005	−	0.162041i	−0.743332	+	0.668923i	$0.766756\pi$
$168$		0			0
$169$	10.5940	−	3.11068i	0.814923	−	0.239283i
$170$		0			0
$171$	−2.31200	−	11.0758i	−0.176803	−	0.846987i
$172$		0			0
$173$	−14.0251	+	6.40504i	−1.06631	+	0.486966i	−0.869733	−	0.493523i	$-0.835709\pi$
$173$	−14.0251	+	6.40504i	−1.06631	+	0.486966i	−0.196574	+	0.980489i	$0.562982\pi$
$174$		0			0
$175$	−15.6259	+	24.3144i	−1.18121	+	1.83799i
$176$		0			0
$177$	6.75996	−	5.40079i	0.508110	−	0.405948i
$178$		0			0
$179$	−5.39773	−	8.39902i	−0.403445	−	0.627773i	0.578779	−	0.815484i	$-0.303529\pi$
$179$	−5.39773	−	8.39902i	−0.403445	−	0.627773i	−0.982224	+	0.187712i	$0.939893\pi$
$180$		0			0
$181$	1.45706	−	4.96231i	0.108303	−	0.368845i	−0.887451	−	0.460902i	$-0.847526\pi$
$181$	1.45706	−	4.96231i	0.108303	−	0.368845i	0.995754	+	0.0920567i	$0.0293441\pi$
$182$		0			0
$183$	15.8263	+	14.8595i	1.16991	+	1.09845i
$184$		0			0
$185$			25.4301i			1.86966i
$186$		0			0
$187$	23.3759	+	6.86379i	1.70942	+	0.501930i
$188$		0			0
$189$	2.33382	−	19.4014i	0.169760	−	1.41125i
$190$		0			0
$191$	1.15453	−	8.02992i	0.0835387	−	0.581024i	−0.904460	−	0.426559i	$-0.859726\pi$
$191$	1.15453	−	8.02992i	0.0835387	−	0.581024i	0.987998	−	0.154465i	$-0.0493654\pi$
$192$		0			0
$193$	−7.05259	−	4.53242i	−0.507656	−	0.326251i	0.261616	−	0.965172i	$-0.415745\pi$
$193$	−7.05259	−	4.53242i	−0.507656	−	0.326251i	−0.769272	+	0.638921i	$0.779381\pi$
$194$		0			0
$195$	−8.18043	−	2.76097i	−0.585813	−	0.197717i
$196$		0			0
$197$	9.48320	−	1.36348i	0.675650	−	0.0971438i	0.204056	−	0.978959i	$-0.434588\pi$
$197$	9.48320	−	1.36348i	0.675650	−	0.0971438i	0.471595	+	0.881815i	$0.343679\pi$
$198$		0			0
$199$	−5.84186	−	19.8956i	−0.414119	−	1.41036i	−0.857712	−	0.514131i	$-0.828115\pi$
$199$	−5.84186	−	19.8956i	−0.414119	−	1.41036i	0.443593	−	0.896228i	$-0.353704\pi$
$200$		0			0
$201$	15.7542	−	1.62676i	1.11121	−	0.114743i
$202$		0			0
$203$	−9.73476	−	11.2345i	−0.683246	−	0.788508i
$204$		0			0
$205$	−13.3720	−	6.10681i	−0.933944	−	0.426518i
$206$		0			0
$207$	−13.7765	+	4.14830i	−0.957532	+	0.288327i
$208$		0			0
$209$	15.0271	+	6.86265i	1.03945	+	0.474699i
$210$		0			0
$211$	0.168541	+	0.194506i	0.0116028	+	0.0133904i	0.761521	−	0.648140i	$-0.224453\pi$
$211$	0.168541	+	0.194506i	0.0116028	+	0.0133904i	−0.749919	+	0.661530i	$0.769907\pi$
$212$		0			0
$213$	4.36058	−	0.450269i	0.298782	−	0.0308519i
$214$		0			0
$215$	3.55980	+	12.1236i	0.242777	+	0.826821i
$216$		0			0
$217$	33.1197	−	4.76189i	2.24831	−	0.323258i
$218$		0			0
$219$	0.227991	+	0.0769493i	0.0154062	+	0.00519975i
$220$		0			0
$221$	−6.54861	−	4.20853i	−0.440507	−	0.283097i
$222$		0			0
$223$	1.69235	−	11.7705i	0.113328	−	0.788214i	−0.851315	−	0.524655i	$-0.824194\pi$
$223$	1.69235	−	11.7705i	0.113328	−	0.788214i	0.964643	−	0.263559i	$-0.0848964\pi$
$224$		0			0
$225$	−13.6613	−	18.5729i	−0.910753	−	1.23820i
$226$		0			0
$227$	−7.60809	−	2.23394i	−0.504967	−	0.148272i	0.0193202	−	0.999813i	$-0.493850\pi$
$227$	−7.60809	−	2.23394i	−0.504967	−	0.148272i	−0.524287	+	0.851542i	$0.675668\pi$
$228$		0			0
$229$			10.8124i			0.714502i	0.934008	+	0.357251i	$0.116286\pi$
$229$			10.8124i			0.714502i	−0.934008	+	0.357251i	$0.883714\pi$
$230$		0			0
$231$	20.8002	+	19.5296i	1.36855	+	1.28495i
$232$		0			0
$233$	4.94957	−	16.8567i	0.324257	−	1.10432i	−0.622567	−	0.782566i	$-0.713910\pi$
$233$	4.94957	−	16.8567i	0.324257	−	1.10432i	0.946824	−	0.321751i	$-0.104271\pi$
$234$		0			0
$235$	2.58166	+	4.01714i	0.168409	+	0.262049i
$236$		0			0
$237$	−20.3999	+	16.2983i	−1.32512	+	1.05869i
$238$		0			0
$239$	−2.94622	+	4.58441i	−0.190575	+	0.296541i	−0.923372	−	0.383907i	$-0.874578\pi$
$239$	−2.94622	+	4.58441i	−0.190575	+	0.296541i	0.732797	+	0.680448i	$0.238215\pi$
$240$		0			0
$241$	−16.7487	+	7.64886i	−1.07888	+	0.492707i	−0.873923	−	0.486065i	$-0.838432\pi$
$241$	−16.7487	+	7.64886i	−1.07888	+	0.492707i	−0.204954	+	0.978772i	$0.565705\pi$
$242$		0			0
$243$	13.7898	+	7.26920i	0.884616	+	0.466320i
$244$		0			0
$245$	−24.4105	+	7.16756i	−1.55953	+	0.457918i
$246$		0			0
$247$	−3.98917	−	3.45664i	−0.253825	−	0.219940i
$248$		0			0
$249$	7.14765	+	0.285381i	0.452964	+	0.0180853i
$250$		0			0
$251$	3.62547	−	7.93867i	0.228838	−	0.501084i	−0.760029	−	0.649889i	$-0.774815\pi$
$251$	3.62547	−	7.93867i	0.228838	−	0.501084i	0.988867	+	0.148805i	$0.0475426\pi$
$252$		0			0
$253$	7.03930	−	19.7922i	0.442557	−	1.24432i
$254$		0			0
$255$	−12.9972	−	31.7550i	−0.813915	−	1.98858i
$256$		0			0
$257$	3.86009	−	3.34479i	0.240786	−	0.208642i	−0.526105	−	0.850420i	$-0.676348\pi$
$257$	3.86009	−	3.34479i	0.240786	−	0.208642i	0.766891	+	0.641777i	$0.221803\pi$
$258$		0			0
$259$	−17.5840	+	20.2930i	−1.09261	+	1.26094i
$260$		0			0
$261$	11.1452	−	4.05049i	0.689870	−	0.250719i
$262$		0			0
$263$	−3.45520	−	24.0314i	−0.213057	−	1.48184i	−0.762869	−	0.646553i	$-0.776210\pi$
$263$	−3.45520	−	24.0314i	−0.213057	−	1.48184i	0.549812	−	0.835288i	$-0.314699\pi$
$264$		0			0
$265$	3.14665	+	6.89020i	0.193297	+	0.423262i
$266$		0			0
$267$	19.6534	−	4.92829i	1.20277	−	0.301606i
$268$		0			0
$269$	−4.05071	−	0.582404i	−0.246976	−	0.0355098i	0.0177149	−	0.999843i	$-0.494361\pi$
$269$	−4.05071	−	0.582404i	−0.246976	−	0.0355098i	−0.264691	+	0.964333i	$0.585270\pi$
$270$		0			0
$271$	12.4661	−	8.01149i	0.757263	−	0.486664i	−0.104154	−	0.994561i	$-0.533214\pi$
$271$	12.4661	−	8.01149i	0.757263	−	0.486664i	0.861417	+	0.507898i	$0.169577\pi$
$272$		0			0
$273$	−4.61879	−	7.85969i	−0.279542	−	0.475690i
$274$		0			0
$275$	33.6635			2.02999
$276$		0			0
$277$	−13.0966			−0.786899			−0.393450	−	0.919346i	$-0.628718\pi$
$277$	−13.0966			−0.786899			−0.393450	+	0.919346i	$0.628718\pi$
$278$		0			0
$279$	−5.89293	+	26.0332i	−0.352801	+	1.55857i
$280$		0			0
$281$	8.92171	−	5.73363i	0.532224	−	0.342040i	−0.246767	−	0.969075i	$-0.579368\pi$
$281$	8.92171	−	5.73363i	0.532224	−	0.342040i	0.778991	+	0.627035i	$0.215732\pi$
$282$		0			0
$283$	−5.22886	−	0.751797i	−0.310823	−	0.0446897i	−0.0148620	−	0.999890i	$-0.504731\pi$
$283$	−5.22886	−	0.751797i	−0.310823	−	0.0446897i	−0.295961	+	0.955200i	$0.595640\pi$
$284$		0			0
$285$	−5.65906	−	22.5676i	−0.335214	−	1.33679i
$286$		0			0
$287$	−6.44813	−	14.1194i	−0.380621	−	0.833444i
$288$		0			0
$289$	−1.98331	−	13.7942i	−0.116666	−	0.811426i
$290$		0			0
$291$	6.93255	+	3.50672i	0.406393	+	0.205568i
$292$		0			0
$293$	3.60005	−	4.15468i	0.210317	−	0.242719i	−0.640783	−	0.767722i	$-0.721390\pi$
$293$	3.60005	−	4.15468i	0.210317	−	0.242719i	0.851101	+	0.525003i	$0.175936\pi$
$294$		0			0
$295$	13.4465	−	11.6515i	0.782887	−	0.678376i
$296$		0			0
$297$	−20.4797	+	9.93028i	−1.18835	+	0.576213i
$298$		0			0
$299$	−3.93974	+	5.43412i	−0.227841	+	0.314263i
$300$		0			0
$301$	−5.54231	+	12.1360i	−0.319454	+	0.699506i
$302$		0			0
$303$	0.952948	−	23.8676i	0.0547454	−	1.37116i
$304$		0			0
$305$	33.7371	+	29.2334i	1.93178	+	1.67390i
$306$		0			0
$307$	12.0203	−	3.52949i	0.686036	−	0.201438i	0.0799043	−	0.996803i	$-0.474539\pi$
$307$	12.0203	−	3.52949i	0.686036	−	0.201438i	0.606132	+	0.795364i	$0.292720\pi$
$308$		0			0
$309$	−15.5598	+	22.2104i	−0.885164	+	1.26350i
$310$		0			0
$311$	5.65005	−	2.58029i	0.320385	−	0.146315i	−0.248730	−	0.968573i	$-0.580013\pi$
$311$	5.65005	−	2.58029i	0.320385	−	0.146315i	0.569115	+	0.822258i	$0.307286\pi$
$312$		0			0
$313$	−13.7377	+	21.3763i	−0.776500	+	1.20826i	0.197186	+	0.980366i	$0.436820\pi$
$313$	−13.7377	+	21.3763i	−0.776500	+	1.20826i	−0.973686	+	0.227892i	$0.926817\pi$
$314$		0			0
$315$	3.20364	−	40.0553i	0.180505	−	2.25686i
$316$		0			0
$317$	12.9278	+	20.1160i	0.726096	+	1.12983i	0.986410	+	0.164303i	$0.0525376\pi$
$317$	12.9278	+	20.1160i	0.726096	+	1.12983i	−0.260314	+	0.965524i	$0.583826\pi$
$318$		0			0
$319$	−4.87794	+	16.6127i	−0.273112	+	0.930134i
$320$		0			0
$321$	−12.4353	+	13.2443i	−0.694071	+	0.739227i
$322$		0			0
$323$		−	20.9772i		−	1.16720i
$324$		0			0
$325$	−10.3204	−	3.03034i	−0.572472	−	0.168093i
$326$		0			0
$327$	−12.4259	−	2.29587i	−0.687152	−	0.126962i
$328$		0			0
$329$	−0.717562	+	4.99075i	−0.0395605	+	0.275149i
$330$		0			0
$331$	−5.56722	−	3.57783i	−0.306002	−	0.196656i	0.378623	−	0.925551i	$-0.376398\pi$
$331$	−5.56722	−	3.57783i	−0.306002	−	0.196656i	−0.684625	+	0.728895i	$0.740034\pi$
$332$		0			0
$333$	−10.1070	−	18.8855i	−0.553860	−	1.03492i
$334$		0			0
$335$	32.2364	−	4.63489i	1.76126	−	0.253231i
$336$		0			0
$337$	6.10766	+	20.8008i	0.332705	+	1.13309i	0.940726	+	0.339169i	$0.110146\pi$
$337$	6.10766	+	20.8008i	0.332705	+	1.13309i	−0.608020	+	0.793921i	$0.708036\pi$
$338$		0			0
$339$	2.27181	+	22.0011i	0.123388	+	1.19494i
$340$		0			0
$341$	−25.5212	−	29.4530i	−1.38205	−	1.59497i
$342$		0			0
$343$	−0.489284	−	0.223448i	−0.0264188	−	0.0120651i
$344$		0			0
$345$	−27.9660	+	9.65362i	−1.50564	+	0.519733i
$346$		0			0
$347$	26.0960	+	11.9176i	1.40090	+	0.639772i	0.965486	−	0.260456i	$-0.0838730\pi$
$347$	26.0960	+	11.9176i	1.40090	+	0.639772i	0.435419	+	0.900228i	$0.356600\pi$
$348$		0			0
$349$	−21.4862	−	24.7964i	−1.15013	−	1.32732i	−0.936606	−	0.350384i	$-0.886051\pi$
$349$	−21.4862	−	24.7964i	−1.15013	−	1.32732i	−0.213524	−	0.976938i	$-0.568494\pi$
$350$		0			0
$351$	7.17246	−	1.20083i	0.382838	−	0.0640954i
$352$		0			0
$353$	−5.49908	−	18.7281i	−0.292686	−	0.996798i	−0.966237	−	0.257657i	$-0.917050\pi$
$353$	−5.49908	−	18.7281i	−0.292686	−	0.996798i	0.673550	−	0.739142i	$-0.264769\pi$
$354$		0			0
$355$	8.92267	−	1.28289i	0.473566	−	0.0680885i
$356$		0			0
$357$	11.5858	−	34.3272i	0.613185	−	1.81679i
$358$		0			0
$359$	0.983323	+	0.631944i	0.0518978	+	0.0333527i	0.566332	−	0.824177i	$-0.308362\pi$
$359$	0.983323	+	0.631944i	0.0518978	+	0.0333527i	−0.514435	+	0.857530i	$0.671998\pi$
$360$		0			0
$361$	−0.679653	+	4.72709i	−0.0357712	+	0.248794i
$362$		0			0
$363$	2.57616	−	13.9429i	0.135213	−	0.731812i
$364$		0			0
$365$	0.474763	+	0.139403i	0.0248502	+	0.00729668i
$366$		0			0
$367$			29.6259i			1.54646i	0.634126	+	0.773230i	$0.281360\pi$
$367$			29.6259i			1.54646i	−0.634126	+	0.773230i	$0.718640\pi$
$368$		0			0
$369$	12.3578	−	0.779435i	0.643319	−	0.0405758i
$370$		0			0
$371$	−2.25332	+	7.67410i	−0.116987	+	0.398419i
$372$		0			0
$373$	−6.09104	−	9.47785i	−0.315382	−	0.490744i	0.646983	−	0.762505i	$-0.276031\pi$
$373$	−6.09104	−	9.47785i	−0.315382	−	0.490744i	−0.962365	+	0.271760i	$0.912394\pi$
$374$		0			0
$375$	−10.3403	−	12.9426i	−0.533971	−	0.668351i
$376$		0			0
$377$	2.99091	−	4.65394i	0.154040	−	0.239690i
$378$		0			0
$379$	18.5575	−	8.47491i	0.953233	−	0.435327i	0.122791	−	0.992433i	$-0.460815\pi$
$379$	18.5575	−	8.47491i	0.953233	−	0.435327i	0.830442	+	0.557106i	$0.188088\pi$
$380$		0			0
$381$	−15.9672	−	11.1860i	−0.818025	−	0.573078i
$382$		0			0
$383$	−22.8489	+	6.70905i	−1.16753	+	0.342817i	−0.807353	−	0.590069i	$-0.799101\pi$
$383$	−22.8489	+	6.70905i	−1.16753	+	0.342817i	−0.360173	+	0.932885i	$0.617282\pi$
$384$		0			0
$385$	44.3399	+	38.4208i	2.25977	+	1.95810i
$386$		0			0
$387$	−7.46208	−	7.58867i	−0.379319	−	0.385754i
$388$		0			0
$389$	−8.48983	+	18.5901i	−0.430451	+	0.942557i	0.562802	+	0.826592i	$0.309723\pi$
$389$	−8.48983	+	18.5901i	−0.430451	+	0.942557i	−0.993253	+	0.115965i	$0.963004\pi$
$390$		0			0
$391$	−26.5744	+	2.30952i	−1.34392	+	0.116797i
$392$		0			0
$393$	2.67945	−	1.09669i	0.135160	−	0.0553205i
$394$		0			0
$395$	−40.5783	+	35.1613i	−2.04172	+	1.76916i
$396$		0			0
$397$	−12.5371	+	14.4686i	−0.629218	+	0.726156i	−0.977430	−	0.211259i	$-0.932244\pi$
$397$	−12.5371	+	14.4686i	−0.629218	+	0.726156i	0.348212	+	0.937416i	$0.386789\pi$
$398$		0			0
$399$	11.0888	−	21.9217i	0.555133	−	1.09746i
$400$		0			0
$401$	−2.75960	−	19.1935i	−0.137808	−	0.958476i	−0.934974	−	0.354716i	$-0.884578\pi$
$401$	−2.75960	−	19.1935i	−0.137808	−	0.958476i	0.797166	−	0.603760i	$-0.206331\pi$
$402$		0			0
$403$	5.17284	+	11.3269i	0.257678	+	0.564236i
$404$		0			0
$405$	28.9300	+	13.8047i	1.43754	+	0.685959i
$406$		0			0
$407$	30.9562	+	4.45083i	1.53444	+	0.220619i
$408$		0			0
$409$	15.4148	−	9.90651i	0.762214	−	0.489845i	−0.100874	−	0.994899i	$-0.532164\pi$
$409$	15.4148	−	9.90651i	0.762214	−	0.489845i	0.863088	+	0.505054i	$0.168527\pi$
$410$		0			0
$411$	33.2611	−	19.5461i	1.64065	−	0.964136i
$412$		0			0
$413$	18.7868			0.924436
$414$		0			0
$415$	14.7096			0.722065
$416$		0			0
$417$	8.40749	−	4.94071i	0.411717	−	0.241948i
$418$		0			0
$419$	2.43323	−	1.56374i	0.118871	−	0.0763939i	−0.479854	−	0.877348i	$-0.659310\pi$
$419$	2.43323	−	1.56374i	0.118871	−	0.0763939i	0.598725	+	0.800954i	$0.295674\pi$
$420$		0			0
$421$	3.28389	+	0.472152i	0.160047	+	0.0230113i	0.221872	−	0.975076i	$-0.428783\pi$
$421$	3.28389	+	0.472152i	0.160047	+	0.0230113i	−0.0618256	+	0.998087i	$0.519692\pi$
$422$		0			0
$423$	−3.51383	−	1.95724i	−0.170848	−	0.0951642i
$424$		0			0
$425$	−17.7574	−	38.8833i	−0.861362	−	1.88612i
$426$		0			0
$427$	6.70810	+	46.6559i	0.324628	+	2.25783i
$428$		0			0
$429$	−4.79270	+	9.47484i	−0.231394	+	0.457450i
$430$		0			0
$431$	−6.01699	+	6.94398i	−0.289828	+	0.334480i	−0.881927	−	0.471386i	$-0.843754\pi$
$431$	−6.01699	+	6.94398i	−0.289828	+	0.334480i	0.592099	+	0.805865i	$0.298299\pi$
$432$		0			0
$433$	−24.5070	+	21.2354i	−1.17773	+	1.02051i	−0.178398	+	0.983958i	$0.557091\pi$
$433$	−24.5070	+	21.2354i	−1.17773	+	1.02051i	−0.999332	+	0.0365500i	$0.988363\pi$
$434$		0			0
$435$	22.5676	−	9.23679i	1.08203	−	0.442870i
$436$		0			0
$437$	−18.0591	−	1.01435i	−0.863882	−	0.0485230i
$438$		0			0
$439$	−2.75781	+	6.03876i	−0.131623	+	0.288214i	−0.963956	−	0.266062i	$-0.914277\pi$
$439$	−2.75781	+	6.03876i	−0.131623	+	0.288214i	0.832333	+	0.554276i	$0.187005\pi$
$440$		0			0
$441$	15.2796	−	15.0247i	0.727598	−	0.715461i
$442$		0			0
$443$	−20.8244	−	18.0445i	−0.989398	−	0.857318i	0.000370744	−	1.00000i	$-0.499882\pi$
$443$	−20.8244	−	18.0445i	−0.989398	−	0.857318i	−0.989769	+	0.142682i	$0.954427\pi$
$444$		0			0
$445$	39.9772	−	11.7384i	1.89510	−	0.556452i
$446$		0			0
$447$	−22.7804	−	15.9591i	−1.07748	−	0.754842i
$448$		0			0
$449$	17.0253	−	7.77519i	0.803473	−	0.366934i	0.0290309	−	0.999579i	$-0.490758\pi$
$449$	17.0253	−	7.77519i	0.803473	−	0.366934i	0.774442	+	0.632645i	$0.218031\pi$
$450$		0			0
$451$	−9.77425	+	15.2090i	−0.460252	+	0.716166i
$452$		0			0
$453$	26.1833	+	32.7726i	1.23020	+	1.53979i
$454$		0			0
$455$	−10.1349	−	15.7703i	−0.475133	−	0.739322i
$456$		0			0
$457$	9.12587	−	31.0799i	0.426890	−	1.45386i	−0.412816	−	0.910814i	$-0.635455\pi$
$457$	9.12587	−	31.0799i	0.426890	−	1.45386i	0.839706	−	0.543041i	$-0.182727\pi$
$458$		0			0
$459$	22.2730	+	18.4170i	1.03962	+	0.859633i
$460$		0			0
$461$		−	10.2470i		−	0.477250i	−0.971112	−	0.238625i	$-0.923303\pi$
$461$		−	10.2470i		−	0.477250i	0.971112	−	0.238625i	$-0.0766967\pi$
$462$		0			0
$463$	−28.7089	−	8.42968i	−1.33421	−	0.391760i	−0.464612	−	0.885514i	$-0.653806\pi$
$463$	−28.7089	−	8.42968i	−1.33421	−	0.391760i	−0.869602	+	0.493754i	$0.835624\pi$
$464$		0			0
$465$	−9.97244	+	53.9735i	−0.462461	+	2.50296i
$466$		0			0
$467$	−4.56505	+	31.7506i	−0.211245	+	1.46924i	0.557762	+	0.830001i	$0.311660\pi$
$467$	−4.56505	+	31.7506i	−0.211245	+	1.46924i	−0.769007	+	0.639241i	$0.779249\pi$
$468$		0			0
$469$	28.9292	+	18.5917i	1.33583	+	0.858483i
$470$		0			0
$471$	−3.89192	+	11.5313i	−0.179330	+	0.531333i
$472$		0			0
$473$	15.3811	−	2.21147i	0.707226	−	0.101684i
$474$		0			0
$475$	−8.16615	−	27.8114i	−0.374689	−	1.27607i
$476$		0			0
$477$	−5.07529	−	3.86635i	−0.232382	−	0.177028i
$478$		0			0
$479$	0.0757814	+	0.0874564i	0.00346254	+	0.00399599i	0.757478	−	0.652860i	$-0.226431\pi$
$479$	0.0757814	+	0.0874564i	0.00346254	+	0.00399599i	−0.754016	+	0.656856i	$0.771886\pi$
$480$		0			0
$481$	−9.08974	−	4.15114i	−0.414456	−	0.189276i
$482$		0			0
$483$	−28.9917	−	11.6340i	−1.31917	−	0.529364i
$484$		0			0
$485$	14.5319	+	6.63649i	0.659859	+	0.301348i
$486$		0			0
$487$	−0.540010	−	0.623204i	−0.0244702	−	0.0282401i	0.743383	−	0.668866i	$-0.233220\pi$
$487$	−0.540010	−	0.623204i	−0.0244702	−	0.0282401i	−0.767853	+	0.640626i	$0.778675\pi$
$488$		0			0
$489$	−2.42745	−	23.5084i	−0.109773	−	1.06308i
$490$		0			0
$491$	0.360932	+	1.22922i	0.0162886	+	0.0554740i	0.967236	−	0.253878i	$-0.0817061\pi$
$491$	0.360932	+	1.22922i	0.0162886	+	0.0554740i	−0.950948	+	0.309352i	$0.899888\pi$
$492$		0			0
$493$	21.7618	−	3.12887i	0.980102	−	0.140917i
$494$		0			0
$495$	−41.2646	+	22.0837i	−1.85471	+	0.992587i
$496$		0			0
$497$	8.00727	+	5.14596i	0.359175	+	0.230828i
$498$		0			0
$499$	−0.381552	+	2.65375i	−0.0170806	+	0.118798i	−0.996578	−	0.0826593i	$-0.973659\pi$
$499$	−0.381552	+	2.65375i	−0.0170806	+	0.118798i	0.979497	+	0.201457i	$0.0645678\pi$
$500$		0			0
$501$	5.44634	+	1.00630i	0.243325	+	0.0449580i
$502$		0			0
$503$	−23.1919	−	6.80974i	−1.03407	−	0.303631i	−0.279708	−	0.960085i	$-0.590238\pi$
$503$	−23.1919	−	6.80974i	−1.03407	−	0.303631i	−0.754366	+	0.656454i	$0.772056\pi$
$504$		0			0
$505$		−	49.1185i		−	2.18574i
$506$		0			0
$507$	−13.0902	+	13.9418i	−0.581356	+	0.619178i
$508$		0			0
$509$	−2.54085	+	8.65336i	−0.112621	+	0.383553i	−0.996443	−	0.0842710i	$-0.973144\pi$
$509$	−2.54085	+	8.65336i	−0.112621	+	0.383553i	0.883821	+	0.467824i	$0.154962\pi$
$510$		0			0
$511$	0.282464	+	0.439523i	0.0124955	+	0.0194433i
$512$		0			0
$513$	13.1720	+	14.5105i	0.581557	+	0.640655i
$514$		0			0
$515$	−30.1483	+	46.9117i	−1.32849	+	2.06718i
$516$		0			0
$517$	5.34193	−	2.43958i	0.234938	−	0.107292i
$518$		0			0
$519$	15.3229	−	21.8722i	0.672599	−	0.960083i
$520$		0			0
$521$	−34.3952	+	10.0994i	−1.50688	+	0.442461i	−0.927885	−	0.372868i	$-0.878375\pi$
$521$	−34.3952	+	10.0994i	−1.50688	+	0.442461i	−0.578999	+	0.815329i	$0.696556\pi$
$522$		0			0
$523$	−15.0555	−	13.0457i	−0.658331	−	0.570447i	0.260317	−	0.965523i	$-0.416173\pi$
$523$	−15.0555	−	13.0457i	−0.658331	−	0.570447i	−0.918648	+	0.395076i	$0.870718\pi$
$524$		0			0
$525$	1.99716	−	50.0208i	0.0871631	−	2.18309i
$526$		0			0
$527$	−20.5576	+	45.0149i	−0.895504	+	1.96088i
$528$		0			0
$529$	0.703240	+	22.9892i	0.0305756	+	0.999532i
$530$		0			0
$531$	−5.35518	+	13.9971i	−0.232395	+	0.607423i
$532$		0			0
$533$	4.36564	−	3.78285i	0.189097	−	0.163853i
$534$		0			0
$535$	−24.4641	+	28.2331i	−1.05768	+	1.22062i
$536$		0			0
$537$	15.4309	+	7.80547i	0.665891	+	0.336831i
$538$		0			0
$539$	4.45273	+	30.9695i	0.191793	+	1.33395i
$540$		0			0
$541$	8.44967	+	18.5022i	0.363280	+	0.795472i	0.999709	+	0.0241363i	$0.00768358\pi$
$541$	8.44967	+	18.5022i	0.363280	+	0.795472i	−0.636429	+	0.771335i	$0.719589\pi$
$542$		0			0
$543$	2.17881	+	8.68881i	0.0935016	+	0.372872i
$544$		0			0
$545$	−25.7196	−	3.69792i	−1.10171	−	0.158401i
$546$		0			0
$547$	−17.7817	+	11.4276i	−0.760293	+	0.488610i	−0.862440	−	0.506159i	$-0.831065\pi$
$547$	−17.7817	+	11.4276i	−0.760293	+	0.488610i	0.102148	+	0.994769i	$0.467429\pi$
$548$		0			0
$549$	−36.6732	−	8.30140i	−1.56517	−	0.354295i
$550$		0			0
$551$	14.9080			0.635104
$552$		0			0
$553$	−56.6938			−2.41087
$554$		0			0
$555$	−22.3160	−	37.9746i	−0.947260	−	1.61193i
$556$		0			0
$557$	−37.7464	+	24.2581i	−1.59937	+	1.02785i	−0.631834	+	0.775103i	$0.717698\pi$
$557$	−37.7464	+	24.2581i	−1.59937	+	1.02785i	−0.967532	+	0.252747i	$0.918666\pi$
$558$		0			0
$559$	−4.91455	−	0.706605i	−0.207863	−	0.0298862i
$560$		0			0
$561$	−40.9303	+	10.2637i	−1.72808	+	0.433334i
$562$		0			0
$563$	−0.445445	−	0.975388i	−0.0187733	−	0.0411077i	0.900013	−	0.435863i	$-0.143557\pi$
$563$	−0.445445	−	0.975388i	−0.0187733	−	0.0411077i	−0.918786	+	0.394755i	$0.870829\pi$
$564$		0			0
$565$	6.47275	+	45.0189i	0.272310	+	1.89396i
$566$		0			0
$567$	13.5405	+	31.0200i	0.568647	+	1.30272i
$568$		0			0
$569$	6.71551	−	7.75011i	0.281529	−	0.324902i	−0.597319	−	0.802004i	$-0.703767\pi$
$569$	6.71551	−	7.75011i	0.281529	−	0.324902i	0.878848	+	0.477102i	$0.158313\pi$
$570$		0			0
$571$	−4.52808	+	3.92361i	−0.189494	+	0.164198i	−0.744441	−	0.667688i	$-0.767284\pi$
$571$	−4.52808	+	3.92361i	−0.189494	+	0.164198i	0.554947	+	0.831886i	$0.312739\pi$
$572$		0			0
$573$	5.32254	+	13.0042i	0.222352	+	0.543256i
$574$		0			0
$575$	−34.3329	+	13.4070i	−1.43178	+	0.559109i
$576$		0			0
$577$	10.0579	−	22.0237i	0.418715	−	0.916857i	−0.576310	−	0.817231i	$-0.695508\pi$
$577$	10.0579	−	22.0237i	0.418715	−	0.916857i	0.995025	−	0.0996260i	$-0.0317646\pi$
$578$		0			0
$579$	14.5090	+	0.579292i	0.602972	+	0.0240745i
$580$		0			0
$581$	11.7381	+	10.1711i	0.486978	+	0.421969i
$582$		0			0
$583$	8.93821	−	2.62449i	0.370183	−	0.108695i
$584$		0			0
$585$	14.6386	−	3.05572i	0.605233	−	0.126339i
$586$		0			0
$587$	−0.293330	+	0.133959i	−0.0121070	+	0.00552910i	−0.421459	−	0.906847i	$-0.638482\pi$
$587$	−0.293330	+	0.133959i	−0.0121070	+	0.00552910i	0.409352	+	0.912376i	$0.365755\pi$
$588$		0			0
$589$	−18.1419	+	28.2293i	−0.747523	+	1.16317i
$590$		0			0
$591$	−12.9647	+	10.3580i	−0.533296	+	0.426070i
$592$		0			0
$593$	15.2828	+	23.7805i	0.627588	+	0.976547i	0.998847	+	0.0480169i	$0.0152901\pi$
$593$	15.2828	+	23.7805i	0.627588	+	0.976547i	−0.371258	+	0.928530i	$0.621074\pi$
$594$		0			0
$595$	20.9890	−	71.4821i	0.860467	−	2.93048i
$596$		0			0
$597$	26.1828	+	24.5834i	1.07159	+	1.00613i
$598$		0			0
$599$		−	1.35452i		−	0.0553440i	−0.999617	−	0.0276720i	$-0.991191\pi$
$599$		−	1.35452i		−	0.0553440i	0.999617	−	0.0276720i	$-0.00880940\pi$
$600$		0			0
$601$	4.31712	+	1.26762i	0.176099	+	0.0517073i	0.368593	−	0.929591i	$-0.379840\pi$
$601$	4.31712	+	1.26762i	0.176099	+	0.0517073i	−0.192494	+	0.981298i	$0.561658\pi$
$602$		0			0
$603$	−22.0980	+	16.2542i	−0.899901	+	0.661921i
$604$		0			0
$605$	4.14938	−	28.8596i	0.168696	−	1.17331i
$606$		0			0
$607$	23.5972	+	15.1650i	0.957780	+	0.615528i	0.923383	−	0.383880i	$-0.125412\pi$
$607$	23.5972	+	15.1650i	0.957780	+	0.615528i	0.0343975	+	0.999408i	$0.489049\pi$
$608$		0			0
$609$	24.3956	+	8.23375i	0.988559	+	0.333648i
$610$		0			0
$611$	−1.85731	+	0.267041i	−0.0751387	+	0.0108033i
$612$		0			0
$613$	6.83176	+	23.2668i	0.275932	+	0.939739i	0.974536	+	0.224230i	$0.0719868\pi$
$613$	6.83176	+	23.2668i	0.275932	+	0.939739i	−0.698604	+	0.715509i	$0.746195\pi$
$614$		0			0
$615$	25.3274	−	2.61528i	1.02130	−	0.105458i
$616$		0			0
$617$	−8.49179	−	9.80004i	−0.341866	−	0.394535i	0.558617	−	0.829426i	$-0.311332\pi$
$617$	−8.49179	−	9.80004i	−0.341866	−	0.394535i	−0.900483	+	0.434891i	$0.856787\pi$
$618$		0			0
$619$	29.8559	+	13.6347i	1.20001	+	0.548027i	0.912233	−	0.409671i	$-0.134356\pi$
$619$	29.8559	+	13.6347i	1.20001	+	0.548027i	0.287777	+	0.957697i	$0.407084\pi$
$620$		0			0
$621$	16.9320	−	18.2841i	0.679458	−	0.733714i
$622$		0			0
$623$	40.0180	+	18.2756i	1.60329	+	0.732198i
$624$		0			0
$625$	2.85642	+	3.29649i	0.114257	+	0.131860i
$626$		0			0
$627$	−28.4621	+	2.93897i	−1.13667	+	0.117371i
$628$		0			0
$629$	−11.1884	−	38.1040i	−0.446109	−	1.51931i
$630$		0			0
$631$	9.48051	−	1.36309i	0.377413	−	0.0542638i	0.0490020	−	0.998799i	$-0.484396\pi$
$631$	9.48051	−	1.36309i	0.377413	−	0.0542638i	0.328411	+	0.944535i	$0.393487\pi$
$632$		0			0
$633$	−0.422367	−	0.142553i	−0.0167876	−	0.00566598i
$634$		0			0
$635$	−33.7252	−	21.6739i	−1.33835	−	0.860103i
$636$		0			0
$637$	1.42273	−	9.89529i	0.0563705	−	0.392066i
$638$		0			0
$639$	−6.11648	+	4.49897i	−0.241964	+	0.177976i
$640$		0			0
$641$	40.3625	+	11.8515i	1.59422	+	0.468106i	0.953931	−	0.300026i	$-0.0969955\pi$
$641$	40.3625	+	11.8515i	1.59422	+	0.468106i	0.640291	+	0.768132i	$0.278814\pi$
$642$		0			0
$643$		−	18.8143i		−	0.741965i	−0.928640	−	0.370983i	$-0.879021\pi$
$643$		−	18.8143i		−	0.741965i	0.928640	−	0.370983i	$-0.120979\pi$
$644$		0			0
$645$	−15.9548	−	14.9802i	−0.628219	−	0.589844i
$646$		0			0
$647$	0.925764	−	3.15286i	0.0363955	−	0.123952i	−0.939292	−	0.343120i	$-0.888516\pi$
$647$	0.925764	−	3.15286i	0.0363955	−	0.123952i	0.975687	+	0.219168i	$0.0703344\pi$
$648$		0			0
$649$	−11.8300	−	18.4078i	−0.464367	−	0.722569i
$650$		0			0
$651$	−45.2786	+	36.1748i	−1.77461	+	1.41780i
$652$		0			0
$653$	−10.0112	+	15.5777i	−0.391768	+	0.609603i	−0.979978	−	0.199105i	$-0.936196\pi$
$653$	−10.0112	+	15.5777i	−0.391768	+	0.609603i	0.588210	+	0.808708i	$0.299833\pi$
$654$		0			0
$655$	5.41546	−	2.47316i	0.211599	−	0.0966342i
$656$		0			0
$657$	−0.407984	+	0.0851641i	−0.0159170	+	0.00332257i
$658$		0			0
$659$	24.2171	−	7.11079i	0.943365	−	0.276997i	0.226343	−	0.974048i	$-0.427323\pi$
$659$	24.2171	−	7.11079i	0.943365	−	0.276997i	0.717022	+	0.697051i	$0.245505\pi$
$660$		0			0
$661$	9.45697	+	8.19451i	0.367834	+	0.318730i	0.819090	−	0.573665i	$-0.194479\pi$
$661$	9.45697	+	8.19451i	0.367834	+	0.318730i	−0.451257	+	0.892394i	$0.649024\pi$
$662$		0			0
$663$	13.4721	+	0.537895i	0.523215	+	0.0208901i
$664$		0			0
$665$	20.9856	−	45.9520i	0.813785	−	1.78194i
$666$		0			0
$667$	−1.64132	−	18.8858i	−0.0635523	−	0.731260i
$668$		0			0
$669$	7.80197	+	19.0620i	0.301642	+	0.736978i
$670$		0			0
$671$	41.4906	−	35.9518i	1.60173	−	1.38791i
$672$		0			0
$673$	−21.0685	+	24.3144i	−0.812133	+	0.937251i	−0.998981	−	0.0451379i	$-0.985627\pi$
$673$	−21.0685	+	24.3144i	−0.812133	+	0.937251i	0.186848	+	0.982389i	$0.440173\pi$
$674$		0			0
$675$	36.6988	+	15.7465i	1.41254	+	0.606082i
$676$		0			0
$677$	−3.58335	−	24.9227i	−0.137719	−	0.957859i	−0.935100	−	0.354383i	$-0.884691\pi$
$677$	−3.58335	−	24.9227i	−0.137719	−	0.957859i	0.797381	−	0.603476i	$-0.206218\pi$
$678$		0			0
$679$	7.00742	+	15.3441i	0.268920	+	0.588853i
$680$		0			0
$681$	13.3215	−	3.34049i	0.510480	−	0.128008i
$682$		0			0
$683$	−20.9492	−	3.01204i	−0.801600	−	0.115253i	−0.270674	−	0.962671i	$-0.587247\pi$
$683$	−20.9492	−	3.01204i	−0.801600	−	0.115253i	−0.530926	+	0.847418i	$0.678156\pi$
$684$		0			0
$685$	66.7375	−	42.8896i	2.54991	−	1.63873i
$686$		0			0
$687$	−9.48831	−	16.1460i	−0.362001	−	0.616009i
$688$		0			0
$689$	−2.97649			−0.113395
$690$		0			0
$691$	−18.6701			−0.710243			−0.355122	−	0.934820i	$-0.615561\pi$
$691$	−18.6701			−0.710243			−0.355122	+	0.934820i	$0.615561\pi$
$692$		0			0
$693$	−48.1988	−	10.9104i	−1.83092	−	0.414450i
$694$		0			0
$695$	16.8694	−	10.8413i	0.639894	−	0.411235i
$696$		0			0
$697$	22.7232	+	3.26711i	0.860704	+	0.123751i
$698$		0			0
$699$	7.40129	+	29.5154i	0.279942	+	1.11637i
$700$		0			0
$701$	−17.7901	−	38.9549i	−0.671924	−	1.47131i	−0.870979	−	0.491320i	$-0.836515\pi$
$701$	−17.7901	−	38.9549i	−0.671924	−	1.47131i	0.199055	−	0.979988i	$-0.436213\pi$
$702$		0			0
$703$	−3.83232	−	26.6544i	−0.144539	−	1.00529i
$704$		0			0
$705$	−7.38037	−	3.73325i	−0.277961	−	0.140602i
$706$		0			0
$707$	33.9636	−	39.1961i	1.27733	−	1.47412i
$708$		0			0
$709$	30.4079	−	26.3486i	1.14199	−	0.989541i	0.141992	−	0.989868i	$-0.454649\pi$
$709$	30.4079	−	26.3486i	1.14199	−	0.989541i	1.00000		0.000326516i	$0.000103933\pi$
$710$		0			0
$711$	16.1606	−	42.2398i	0.606070	−	1.58412i
$712$		0			0
$713$	37.7588	+	19.8745i	1.41408	+	0.744307i
$714$		0			0
$715$	−9.07021	+	19.8610i	−0.339207	+	0.742759i
$716$		0			0
$717$	0.376558	−	9.43129i	0.0140628	−	0.352218i
$718$		0			0
$719$	7.58627	+	6.57354i	0.282920	+	0.245152i	0.784747	−	0.619817i	$-0.212793\pi$
$719$	7.58627	+	6.57354i	0.282920	+	0.245152i	−0.501827	+	0.864968i	$0.667338\pi$
$720$		0			0
$721$	−56.4958	+	16.5887i	−2.10401	+	0.617794i
$722$		0			0
$723$	18.2985	−	26.1196i	0.680527	−	0.971400i
$724$		0			0
$725$	27.6335	−	12.6198i	1.02628	−	0.468687i
$726$		0			0
$727$	25.8800	−	40.2700i	0.959835	−	1.49353i	0.0925585	−	0.995707i	$-0.470495\pi$
$727$	25.8800	−	40.2700i	0.959835	−	1.49353i	0.867277	−	0.497826i	$-0.165868\pi$
$728$		0			0
$729$	−26.9712	+	1.24608i	−0.998934	+	0.0461512i
$730$		0			0
$731$	−10.6679	−	16.5996i	−0.394567	−	0.613958i
$732$		0			0
$733$	−7.84509	+	26.7179i	−0.289765	+	0.986849i	0.678014	+	0.735049i	$0.262841\pi$
$733$	−7.84509	+	26.7179i	−0.289765	+	0.986849i	−0.967779	+	0.251800i	$0.918977\pi$
$734$		0			0
$735$	30.1621	−	32.1244i	1.11255	−	1.18493i
$736$		0			0
$737$		−	40.0527i		−	1.47536i
$738$		0			0
$739$	−44.1075	−	12.9511i	−1.62252	−	0.476416i	−0.660828	−	0.750538i	$-0.729795\pi$
$739$	−44.1075	−	12.9511i	−1.62252	−	0.476416i	−0.961695	+	0.274122i	$0.911613\pi$
$740$		0			0
$741$	8.99034	+	1.66110i	0.330268	+	0.0610222i
$742$		0			0
$743$	0.664955	−	4.62486i	0.0243948	−	0.169670i	−0.973982	−	0.226626i	$-0.927230\pi$
$743$	0.664955	−	4.62486i	0.0243948	−	0.169670i	0.998377	+	0.0569563i	$0.0181396\pi$
$744$		0			0
$745$	−48.1158	−	30.9222i	−1.76283	−	1.13290i
$746$		0			0
$747$	−10.9240	+	5.84620i	−0.399687	+	0.213901i
$748$		0			0
$749$	−39.0442	+	5.61371i	−1.42664	+	0.205121i
$750$		0			0
$751$	−4.87023	−	16.5865i	−0.177717	−	0.605249i	−0.999378	−	0.0352720i	$-0.988770\pi$
$751$	−4.87023	−	16.5865i	−0.177717	−	0.605249i	0.821661	−	0.569977i	$-0.193048\pi$
$752$		0			0
$753$	1.55263	+	15.0362i	0.0565809	+	0.547951i
$754$		0			0
$755$	56.4869	+	65.1893i	2.05577	+	2.37248i
$756$		0			0
$757$	16.1388	+	7.37032i	0.586573	+	0.267879i	0.686516	−	0.727114i	$-0.259139\pi$
$757$	16.1388	+	7.37032i	0.586573	+	0.267879i	−0.0999436	+	0.994993i	$0.531866\pi$
$758$		0			0
$759$	6.85672	+	35.7328i	0.248883	+	1.29702i
$760$		0			0
$761$	−13.0329	−	5.95192i	−0.472442	−	0.215757i	0.164942	−	0.986303i	$-0.447256\pi$
$761$	−13.0329	−	5.95192i	−0.472442	−	0.215757i	−0.637384	+	0.770546i	$0.719984\pi$
$762$		0			0
$763$	−17.9670	−	20.7350i	−0.650449	−	0.750658i
$764$		0			0
$765$	47.2749	+	36.0140i	1.70923	+	1.30209i
$766$		0			0
$767$	1.96973	+	6.70829i	0.0711229	+	0.242222i
$768$		0			0
$769$	15.7291	−	2.26150i	0.567205	−	0.0815518i	0.147254	−	0.989099i	$-0.452956\pi$
$769$	15.7291	−	2.26150i	0.567205	−	0.0815518i	0.419951	+	0.907547i	$0.362047\pi$
$770$		0			0
$771$	−2.82905	+	8.38214i	−0.101886	+	0.301875i
$772$		0			0
$773$	8.60214	+	5.52826i	0.309398	+	0.198838i	0.686120	−	0.727488i	$-0.259313\pi$
$773$	8.60214	+	5.52826i	0.309398	+	0.198838i	−0.376722	+	0.926326i	$0.622949\pi$
$774$		0			0
$775$	−9.73135	+	67.6830i	−0.349560	+	2.43125i
$776$		0			0
$777$	8.45006	−	45.7340i	0.303144	−	1.64070i
$778$		0			0
$779$	14.9361	+	4.38564i	0.535142	+	0.157132i
$780$		0			0
$781$		−	11.0861i		−	0.396693i
$782$		0			0
$783$	−13.0885	+	15.8289i	−0.467746	+	0.565680i
$784$		0			0
$785$	−7.05068	+	24.0124i	−0.251650	+	0.857040i
$786$		0			0
$787$	−7.14042	−	11.1107i	−0.254528	−	0.396054i	0.690350	−	0.723476i	$-0.257457\pi$
$787$	−7.14042	−	11.1107i	−0.254528	−	0.396054i	−0.944878	+	0.327422i	$0.893820\pi$
$788$		0			0
$789$	26.2482	+	32.8539i	0.934461	+	1.16963i
$790$		0			0
$791$	−25.9637	+	40.4003i	−0.923163	+	1.43647i
$792$		0			0
$793$	−15.9563	+	7.28701i	−0.566626	+	0.258769i
$794$		0			0
$795$	−10.7453	−	7.52777i	−0.381097	−	0.266982i
$796$		0			0
$797$	5.17788	−	1.52036i	0.183410	−	0.0538540i	−0.188738	−	0.982028i	$-0.560440\pi$
$797$	5.17788	−	1.52036i	0.183410	−	0.0538540i	0.372148	+	0.928173i	$0.378621\pi$
$798$		0			0
$799$	−5.63571	−	4.88337i	−0.199377	−	0.172761i
$800$		0			0
$801$	−25.0235	+	24.6060i	−0.884161	+	0.869411i
$802$		0			0
$803$	0.252790	−	0.553533i	0.00892076	−	0.0195337i
$804$		0			0
$805$	−60.5232	−	21.5257i	−2.13316	−	0.758683i
$806$		0			0
$807$	6.55998	−	2.68497i	0.230922	−	0.0945153i
$808$		0			0
$809$	22.4795	−	19.4786i	0.790339	−	0.684832i	−0.163037	−	0.986620i	$-0.552129\pi$
$809$	22.4795	−	19.4786i	0.790339	−	0.684832i	0.953375	+	0.301788i	$0.0975834\pi$
$810$		0			0
$811$	18.2406	−	21.0507i	0.640513	−	0.739192i	−0.338952	−	0.940804i	$-0.610073\pi$
$811$	18.2406	−	21.0507i	0.640513	−	0.739192i	0.979465	+	0.201612i	$0.0646180\pi$
$812$		0			0
$813$	−11.5851	+	22.9030i	−0.406309	+	0.803245i
$814$		0			0
$815$	−6.91618	−	48.1031i	−0.242263	−	1.68498i
$816$		0			0
$817$	−5.55821	−	12.1708i	−0.194457	−	0.425802i
$818$		0			0
$819$	13.7944	+	7.68363i	0.482015	+	0.268488i
$820$		0			0
$821$	15.4121	+	2.21593i	0.537887	+	0.0773365i	0.405904	−	0.913916i	$-0.366957\pi$
$821$	15.4121	+	2.21593i	0.537887	+	0.0773365i	0.131983	+	0.991252i	$0.457866\pi$
$822$		0			0
$823$	7.36015	−	4.73008i	0.256559	−	0.164880i	−0.406039	−	0.913856i	$-0.633090\pi$
$823$	7.36015	−	4.73008i	0.256559	−	0.164880i	0.662598	+	0.748975i	$0.269454\pi$
$824$		0			0
$825$	−50.2694	+	29.5411i	−1.75016	+	1.02849i
$826$		0			0
$827$	−51.2667			−1.78272			−0.891359	−	0.453299i	$-0.850247\pi$
$827$	−51.2667			−1.78272			−0.891359	+	0.453299i	$0.850247\pi$
$828$		0			0
$829$	23.3643			0.811475			0.405738	−	0.913990i	$-0.367015\pi$
$829$	23.3643			0.811475			0.405738	+	0.913990i	$0.367015\pi$
$830$		0			0
$831$	19.5571	−	11.4928i	0.678427	−	0.398682i
$832$		0			0
$833$	33.4227	−	21.4795i	1.15803	−	0.744220i
$834$		0			0
$835$	11.2731	+	1.62082i	0.390121	+	0.0560909i
$836$		0			0
$837$	−14.0454	−	44.0465i	−0.485480	−	1.52247i
$838$		0			0
$839$	5.54213	+	12.1356i	0.191336	+	0.418967i	0.980850	−	0.194766i	$-0.0623947\pi$
$839$	5.54213	+	12.1356i	0.191336	+	0.418967i	−0.789514	+	0.613732i	$0.789667\pi$
$840$		0			0
$841$	−1.90351	−	13.2392i	−0.0656384	−	0.456525i
$842$		0			0
$843$	−8.29121	+	16.3912i	−0.285564	+	0.564541i
$844$		0			0
$845$	−25.7525	+	29.7199i	−0.885912	+	1.02240i
$846$		0			0
$847$	23.2665	−	20.1605i	0.799445	−	0.692723i
$848$		0			0
$849$	8.46795	−	3.46589i	0.290619	−	0.118949i
$850$		0			0
$851$	−33.3444	+	7.78941i	−1.14303	+	0.267018i
$852$		0			0
$853$	4.81504	−	10.5435i	0.164864	−	0.361002i	−0.809111	−	0.587655i	$-0.800051\pi$
$853$	4.81504	−	10.5435i	0.164864	−	0.361002i	0.973975	+	0.226653i	$0.0727785\pi$
$854$		0			0
$855$	28.2546	+	28.7340i	0.966288	+	0.982681i
$856$		0			0
$857$	18.7706	+	16.2649i	0.641193	+	0.555597i	0.913615	−	0.406581i	$-0.133279\pi$
$857$	18.7706	+	16.2649i	0.641193	+	0.555597i	−0.272422	+	0.962178i	$0.587825\pi$
$858$		0			0
$859$	30.4932	−	8.95363i	1.04042	−	0.305494i	0.283477	−	0.958979i	$-0.408512\pi$
$859$	30.4932	−	8.95363i	1.04042	−	0.305494i	0.756939	+	0.653485i	$0.226694\pi$
$860$		0			0
$861$	22.0193	+	15.4259i	0.750417	+	0.525715i
$862$		0			0
$863$	−9.63614	+	4.40068i	−0.328018	+	0.149801i	−0.572616	−	0.819824i	$-0.694071\pi$
$863$	−9.63614	+	4.40068i	−0.328018	+	0.149801i	0.244598	+	0.969625i	$0.421344\pi$
$864$		0			0
$865$	29.6893	−	46.1975i	1.00947	−	1.57076i
$866$		0			0
$867$	15.0667	+	18.8584i	0.511692	+	0.640465i
$868$		0			0
$869$	35.6999	+	55.5502i	1.21104	+	1.88441i
$870$		0			0
$871$	−3.60549	+	12.2792i	−0.122167	+	0.416064i
$872$		0			0
$873$	−13.4296	+	0.847040i	−0.454524	+	0.0286680i
$874$		0			0
$875$		−	35.9690i		−	1.21597i
$876$		0			0
$877$	−43.0611	−	12.6439i	−1.45407	−	0.426953i	−0.543184	−	0.839613i	$-0.682782\pi$
$877$	−43.0611	−	12.6439i	−1.45407	−	0.426953i	−0.910885	+	0.412660i	$0.864600\pi$
$878$		0			0
$879$	−1.73002	+	9.36336i	−0.0583523	+	0.315818i
$880$		0			0
$881$	5.08231	−	35.3483i	0.171227	−	1.19091i	−0.705068	−	0.709139i	$-0.749084\pi$
$881$	5.08231	−	35.3483i	0.171227	−	1.19091i	0.876296	−	0.481774i	$-0.160007\pi$
$882$		0			0
$883$	−30.3021	−	19.4740i	−1.01975	−	0.655351i	−0.0798482	−	0.996807i	$-0.525444\pi$
$883$	−30.3021	−	19.4740i	−1.01975	−	0.655351i	−0.939898	+	0.341456i	$0.889080\pi$
$884$		0			0
$885$	−9.85493	+	29.1990i	−0.331270	+	0.981512i
$886$		0			0
$887$	7.21836	−	1.03784i	0.242369	−	0.0348474i	−0.0200599	−	0.999799i	$-0.506386\pi$
$887$	7.21836	−	1.03784i	0.242369	−	0.0348474i	0.262429	+	0.964951i	$0.415477\pi$
$888$		0			0
$889$	−11.9257	−	40.6153i	−0.399976	−	1.36219i
$890$		0			0
$891$	21.8679	−	32.8006i	0.732601	−	1.09886i
$892$		0			0
$893$	−3.31133	−	3.82148i	−0.110809	−	0.127881i
$894$		0			0
$895$	32.3459	+	14.7719i	1.08120	+	0.493770i
$896$		0			0
$897$	1.11451	−	11.5720i	0.0372125	−	0.386378i
$898$		0			0
$899$	−31.9911	−	14.6098i	−1.06696	−	0.487265i
$900$		0			0
$901$	−7.74633	−	8.93975i	−0.258068	−	0.297826i
$902$		0			0
$903$	−2.37353	−	22.9862i	−0.0789861	−	0.764931i
$904$		0			0
$905$	5.18956	+	17.6740i	0.172507	+	0.587504i
$906$		0			0
$907$	−57.0557	+	8.20337i	−1.89450	+	0.272388i	−0.988539	−	0.150968i	$-0.951761\pi$
$907$	−57.0557	+	8.20337i	−1.89450	+	0.272388i	−0.905963	+	0.423356i	$0.860852\pi$
$908$		0			0
$909$	19.5218	+	36.4775i	0.647496	+	1.20988i
$910$		0			0
$911$	17.8076	+	11.4443i	0.589994	+	0.379166i	0.801308	−	0.598252i	$-0.204138\pi$
$911$	17.8076	+	11.4443i	0.589994	+	0.379166i	−0.211314	+	0.977418i	$0.567774\pi$
$912$		0			0
$913$	2.57450	−	17.9060i	0.0852035	−	0.592604i
$914$		0			0
$915$	−76.0328	−	14.0482i	−2.51357	−	0.464420i
$916$		0			0
$917$	6.03158	+	1.77103i	0.199180	+	0.0584846i
$918$		0			0
$919$		−	16.0940i		−	0.530892i	−0.964126	−	0.265446i	$-0.914481\pi$
$919$		−	16.0940i		−	0.530892i	0.964126	−	0.265446i	$-0.0855192\pi$
$920$		0			0
$921$	−14.8526	+	15.8189i	−0.489409	+	0.521250i
$922$		0			0
$923$	−0.997959	+	3.39874i	−0.0328482	+	0.111871i
$924$		0			0
$925$	−29.6668	−	46.1624i	−0.975437	−	1.51781i
$926$		0			0
$927$	3.74476	−	46.8209i	0.122994	−	1.53780i
$928$		0			0
$929$	−30.6763	+	47.7333i	−1.00646	+	1.56608i	−0.195726	+	0.980659i	$0.562706\pi$
$929$	−30.6763	+	47.7333i	−1.00646	+	1.56608i	−0.810731	+	0.585419i	$0.800930\pi$
$930$		0			0
$931$	24.5055	−	11.1913i	0.803135	−	0.366780i
$932$		0			0
$933$	−6.17287	+	8.81129i	−0.202091	+	0.288469i
$934$		0			0
$935$	−83.2569	+	24.4464i	−2.72279	+	0.799484i
$936$		0			0
$937$	5.41497	+	4.69210i	0.176899	+	0.153284i	0.738810	−	0.673914i	$-0.235388\pi$
$937$	5.41497	+	4.69210i	0.176899	+	0.153284i	−0.561911	+	0.827198i	$0.689934\pi$
$938$		0			0
$939$	1.75582	−	43.9764i	0.0572991	−	1.43512i
$940$		0			0
$941$	5.61221	−	12.2890i	0.182953	−	0.400611i	−0.795827	−	0.605524i	$-0.792964\pi$
$941$	5.61221	−	12.2890i	0.182953	−	0.400611i	0.978780	+	0.204913i	$0.0656910\pi$
$942$		0			0
$943$	3.91140	−	19.4042i	0.127373	−	0.631888i
$944$		0			0
$945$	30.3662	+	62.6255i	0.987812	+	2.03721i
$946$		0			0
$947$	−16.1567	+	13.9999i	−0.525023	+	0.454935i	−0.876597	−	0.481225i	$-0.840192\pi$
$947$	−16.1567	+	13.9999i	−0.525023	+	0.454935i	0.351574	+	0.936160i	$0.385647\pi$
$948$		0			0
$949$	−0.127327	+	0.146944i	−0.00413322	+	0.00476999i
$950$		0			0
$951$	−36.9576	−	18.6944i	−1.19843	−	0.606208i
$952$		0			0
$953$	4.56726	+	31.7660i	0.147948	+	1.02900i	0.919572	+	0.392922i	$0.128536\pi$
$953$	4.56726	+	31.7660i	0.147948	+	1.02900i	−0.771624	+	0.636079i	$0.780555\pi$
$954$		0			0
$955$	12.0029	+	26.2828i	0.388406	+	0.850491i
$956$		0			0
$957$	−7.29418	−	29.0882i	−0.235787	−	0.940289i
$958$		0			0
$959$	82.9124	+	11.9210i	2.67738	+	0.384949i
$960$		0			0
$961$	40.5163	−	26.0383i	1.30698	−	0.839944i
$962$		0			0
$963$	6.94708	−	30.6901i	0.223866	−	0.988976i
$964$		0			0
$965$	29.8589			0.961191
$966$		0			0
$967$	12.8845			0.414339			0.207170	−	0.978305i	$-0.433575\pi$
$967$	12.8845			0.414339			0.207170	+	0.978305i	$0.433575\pi$
$968$		0			0
$969$	18.4084	+	31.3251i	0.591363	+	1.00631i
$970$		0			0
$971$	24.9458	−	16.0317i	0.800548	−	0.514481i	−0.0752468	−	0.997165i	$-0.523974\pi$
$971$	24.9458	−	16.0317i	0.800548	−	0.514481i	0.875795	+	0.482684i	$0.160338\pi$
$972$		0			0
$973$	20.9580	+	3.01330i	0.671882	+	0.0966021i
$974$		0			0
$975$	18.0706	−	4.53139i	0.578723	−	0.145121i
$976$		0			0
$977$	−18.9985	−	41.6008i	−0.607815	−	1.33093i	−0.924059	−	0.382251i	$-0.875149\pi$
$977$	−18.9985	−	41.6008i	−0.607815	−	1.33093i	0.316244	−	0.948678i	$-0.397578\pi$
$978$		0			0
$979$	−7.29228	−	50.7189i	−0.233062	−	1.62098i
$980$		0			0
$981$	20.5702	−	7.47581i	0.656755	−	0.238684i
$982$		0			0
$983$	19.7737	−	22.8201i	0.630684	−	0.727848i	−0.347015	−	0.937859i	$-0.612805\pi$
$983$	19.7737	−	22.8201i	0.630684	−	0.727848i	0.977699	+	0.210012i	$0.0673503\pi$
$984$		0			0
$985$	−25.7886	+	22.3459i	−0.821693	+	0.712001i
$986$		0			0
$987$	−3.30806	−	8.08234i	−0.105297	−	0.257264i
$988$		0			0
$989$	−14.8062	+	8.38121i	−0.470811	+	0.266507i
$990$		0			0
$991$	−10.7485	+	23.5359i	−0.341436	+	0.747641i	−0.999988	−	0.00489411i	$-0.998442\pi$
$991$	−10.7485	+	23.5359i	−0.341436	+	0.747641i	0.658552	+	0.752536i	$0.271169\pi$
$992$		0			0
$993$	11.4532	+	0.457285i	0.363456	+	0.0145115i
$994$		0			0
$995$	55.8141	+	48.3632i	1.76943	+	1.53322i
$996$		0			0
$997$	5.51225	−	1.61854i	0.174575	−	0.0512597i	−0.193277	−	0.981144i	$-0.561912\pi$
$997$	5.51225	−	1.61854i	0.174575	−	0.0512597i	0.367852	+	0.929884i	$0.380093\pi$
$998$		0			0
$999$	31.6655	+	19.3322i	1.00185	+	0.611645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.u.a.17.5	✓	240
3.2	odd	2	inner	552.2.u.a.17.9	yes	240
23.19	odd	22	inner	552.2.u.a.65.9	yes	240
69.65	even	22	inner	552.2.u.a.65.5	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.u.a.17.5	✓	240	1.1	even	1	trivial
552.2.u.a.17.9	yes	240	3.2	odd	2	inner
552.2.u.a.65.5	yes	240	69.65	even	22	inner
552.2.u.a.65.9	yes	240	23.19	odd	22	inner

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.u (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.49329 + 0.877542i) q^{3} +(-2.99625 + 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(1.45984 - 2.62085i) q^{9} +O(q^{10})\)	\(q+(-1.49329 + 0.877542i) q^{3} +(-2.99625 + 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(1.45984 - 2.62085i) q^{9} +(1.81960 + 3.98437i) q^{11} +(-0.199177 - 1.38531i) q^{13} +(2.78451 - 5.50478i) q^{15} +(3.64235 - 4.20350i) q^{17} +(2.85032 - 2.46981i) q^{19} +(6.02836 - 2.46738i) q^{21} +(-3.44262 - 3.33892i) q^{23} +(3.19262 - 6.99086i) q^{25} +(0.119936 + 5.19477i) q^{27} +(2.98733 + 2.58853i) q^{29} +(-8.53689 + 2.50666i) q^{31} +(-6.21365 - 4.35306i) q^{33} +(12.1840 - 5.56423i) q^{35} +(3.86016 - 6.00652i) q^{37} +(1.51309 + 1.89388i) q^{39} +(2.23146 + 3.47222i) q^{41} +(0.999481 - 3.40392i) q^{43} +(0.672591 + 10.6638i) q^{45} -1.34072i q^{47} +(6.85369 + 2.01242i) q^{49} +(-1.75035 + 9.47336i) q^{51} +(0.302667 - 2.10509i) q^{53} +(-13.1242 - 8.43441i) q^{55} +(-2.08899 + 6.18943i) q^{57} +(-4.94467 + 0.710937i) q^{59} +(-3.53114 - 12.0260i) q^{61} +(-6.83687 + 8.97465i) q^{63} +(3.26430 + 3.76720i) q^{65} +(-8.31771 - 3.79857i) q^{67} +(8.07087 + 1.96494i) q^{69} +(-2.30225 - 1.05140i) q^{71} +(-0.0909771 - 0.104993i) q^{73} +(1.36726 + 13.2411i) q^{75} +(-4.64090 - 15.8055i) q^{77} +(14.9218 - 2.14543i) q^{79} +(-4.73772 - 7.65206i) q^{81} +(-3.47436 - 2.23284i) q^{83} +(-2.81926 + 19.6084i) q^{85} +(-6.73250 - 1.24393i) q^{87} +(-11.2243 - 3.29576i) q^{89} +5.26333i q^{91} +(10.5484 - 11.2346i) q^{93} +(-3.78446 + 12.8887i) q^{95} +(-2.42501 - 3.77339i) q^{97} +(13.0988 + 1.04765i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^9	\( 240 q - 4 q^{9} - 16 q^{25} + 12 q^{27} - 8 q^{31} + 44 q^{37} + 20 q^{39} + 44 q^{43} + 124 q^{49} + 12 q^{55} + 16 q^{69} - 74 q^{75} - 144 q^{81} + 24 q^{85} - 170 q^{87} + 12 q^{93} - 198 q^{99}+O(q^{100}) \) 240 * q - 4 * q^9 - 16 * q^25 + 12 * q^27 - 8 * q^31 + 44 * q^37 + 20 * q^39 + 44 * q^43 + 124 * q^49 + 12 * q^55 + 16 * q^69 - 74 * q^75 - 144 * q^81 + 24 * q^85 - 170 * q^87 + 12 * q^93 - 198 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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