LMFDB - Embedded newform 552.2.u.a.17.9

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			17.9
Character	$\chi$	$=$	552.17
Dual form			552.2.u.a.65.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.781802 - 1.54557i) q^{3} +(2.99625 - 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(-1.77757 + 2.41666i) q^{9} +O(q^{10})$	\(q+(-0.781802 - 1.54557i) q^{3} +(2.99625 - 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(-1.77757 + 2.41666i) q^{9} +(-1.81960 - 3.98437i) q^{11} +(-0.199177 - 1.38531i) q^{13} +(-5.31859 - 3.12550i) q^{15} +(-3.64235 + 4.20350i) q^{17} +(2.85032 - 2.46981i) q^{19} +(2.08302 + 6.17172i) q^{21} +(3.44262 + 3.33892i) q^{23} +(3.19262 - 6.99086i) q^{25} +(5.12482 + 0.858008i) q^{27} +(-2.98733 - 2.58853i) q^{29} +(-8.53689 + 2.50666i) q^{31} +(-4.73556 + 5.92731i) q^{33} +(-12.1840 + 5.56423i) q^{35} +(3.86016 - 6.00652i) q^{37} +(-1.98537 + 1.39088i) q^{39} +(-2.23146 - 3.47222i) q^{41} +(0.999481 - 3.40392i) q^{43} +(-0.672591 + 10.6638i) q^{45} +1.34072i q^{47} +(6.85369 + 2.01242i) q^{49} +(9.34439 + 2.34320i) q^{51} +(-0.302667 + 2.10509i) q^{53} +(-13.1242 - 8.43441i) q^{55} +(-6.04566 - 2.47446i) q^{57} +(4.94467 - 0.710937i) q^{59} +(-3.53114 - 12.0260i) q^{61} +(7.91032 - 8.04451i) q^{63} +(-3.26430 - 3.76720i) q^{65} +(-8.31771 - 3.79857i) q^{67} +(2.46908 - 7.93118i) q^{69} +(2.30225 + 1.05140i) q^{71} +(-0.0909771 - 0.104993i) q^{73} +(-13.3009 + 0.531057i) q^{75} +(4.64090 + 15.8055i) q^{77} +(14.9218 - 2.14543i) q^{79} +(-2.68049 - 8.59156i) q^{81} +(3.47436 + 2.23284i) q^{83} +(-2.81926 + 19.6084i) q^{85} +(-1.66526 + 6.64084i) q^{87} +(11.2243 + 3.29576i) q^{89} +5.26333i q^{91} +(10.5484 + 11.2346i) q^{93} +(3.78446 - 12.8887i) q^{95} +(-2.42501 - 3.77339i) q^{97} +(12.8633 + 2.68514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.781802	−	1.54557i	−0.451374	−	0.892335i
$3$	−0.781802	−	1.54557i	−0.451374	−	0.892335i
$4$		0			0
$5$	2.99625	−	1.92558i	1.33997	−	0.861143i	0.343026	−	0.939326i	$-0.388548\pi$
$5$	2.99625	−	1.92558i	1.33997	−	0.861143i	0.996939	+	0.0781824i	$0.0249116\pi$
$6$		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
$9$	−1.77757	+	2.41666i	−0.592523	+	0.805553i
$10$		0			0
$11$	−1.81960	−	3.98437i	−0.548631	−	1.20133i	−0.957418	−	0.288704i	$-0.906776\pi$
$11$	−1.81960	−	3.98437i	−0.548631	−	1.20133i	0.408788	−	0.912630i	$-0.365952\pi$
$12$		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
$15$	−5.31859	−	3.12550i	−1.37325	−	0.807000i
$16$		0			0
$17$	−3.64235	+	4.20350i	−0.883400	+	1.01950i	0.116255	+	0.993219i	$0.462911\pi$
$17$	−3.64235	+	4.20350i	−0.883400	+	1.01950i	−0.999655	+	0.0262782i	$0.991634\pi$
$18$		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
$21$	2.08302	+	6.17172i	0.454551	+	1.34678i
$22$		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
$27$	5.12482	+	0.858008i	0.986273	+	0.165124i
$28$		0			0
$29$	−2.98733	−	2.58853i	−0.554733	−	0.480679i	0.331797	−	0.943351i	$-0.392345\pi$
$29$	−2.98733	−	2.58853i	−0.554733	−	0.480679i	−0.886529	+	0.462672i	$0.846891\pi$
$30$		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
$33$	−4.73556	+	5.92731i	−0.824354	+	1.03181i
$34$		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
$39$	−1.98537	+	1.39088i	−0.317914	+	0.222719i
$40$		0			0
$41$	−2.23146	−	3.47222i	−0.348496	−	0.542270i	0.622115	−	0.782926i	$-0.286274\pi$
$41$	−2.23146	−	3.47222i	−0.348496	−	0.542270i	−0.970610	+	0.240656i	$0.922637\pi$
$42$		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	$0.0311748\pi$
$47$			1.34072i			0.195564i	−0.995208	+	0.0977820i	$0.968825\pi$
$48$		0			0
$49$	6.85369	+	2.01242i	0.979098	+	0.287489i
$50$		0			0
$51$	9.34439	+	2.34320i	1.30848	+	0.328114i
$52$		0			0
$53$	−0.302667	+	2.10509i	−0.0415745	+	0.289157i	0.958418	+	0.285367i	$0.0921155\pi$
$53$	−0.302667	+	2.10509i	−0.0415745	+	0.289157i	−0.999993	+	0.00378988i	$0.998794\pi$
$54$		0			0
$55$	−13.1242	−	8.43441i	−1.76967	−	1.13730i
$56$		0			0
$57$	−6.04566	−	2.47446i	−0.800767	−	0.327750i
$58$		0			0
$59$	4.94467	−	0.710937i	0.643742	−	0.0925561i	0.187290	−	0.982305i	$-0.440029\pi$
$59$	4.94467	−	0.710937i	0.643742	−	0.0925561i	0.456451	+	0.889749i	$0.349120\pi$
$60$		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
$63$	7.91032	−	8.04451i	0.996606	−	1.01351i
$64$		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
$69$	2.46908	−	7.93118i	0.297243	−	0.954802i
$70$		0			0
$71$	2.30225	+	1.05140i	0.273226	+	0.124778i	0.547317	−	0.836926i	$-0.315649\pi$
$71$	2.30225	+	1.05140i	0.273226	+	0.124778i	−0.274090	+	0.961704i	$0.588377\pi$
$72$		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
$75$	−13.3009	+	0.531057i	−1.53585	+	0.0613211i
$76$		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
$81$	−2.68049	−	8.59156i	−0.297832	−	0.954618i
$82$		0			0
$83$	3.47436	+	2.23284i	0.381361	+	0.245086i	0.717250	−	0.696816i	$-0.245400\pi$
$83$	3.47436	+	2.23284i	0.381361	+	0.245086i	−0.335889	+	0.941901i	$0.609037\pi$
$84$		0			0
$85$	−2.81926	+	19.6084i	−0.305791	+	2.12683i
$86$		0			0
$87$	−1.66526	+	6.64084i	−0.178535	+	0.711973i
$88$		0			0
$89$	11.2243	+	3.29576i	1.18978	+	0.349350i	0.815936	−	0.578142i	$-0.196222\pi$
$89$	11.2243	+	3.29576i	1.18978	+	0.349350i	0.373842	+	0.927493i	$0.378040\pi$
$90$		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
$99$	12.8633	+	2.68514i	1.29281	+	0.269867i
$100$		0			0
$101$	7.45594	−	11.6017i	0.741894	−	1.15441i	−0.241052	−	0.970512i	$-0.577492\pi$
$101$	7.45594	−	11.6017i	0.741894	−	1.15441i	0.982946	−	0.183897i	$-0.0588712\pi$
$102$		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
$105$	18.1254	+	14.4810i	1.76885	+	1.41320i
$106$		0			0
$107$	−10.0640	+	2.95506i	−0.972923	+	0.285676i	−0.729300	−	0.684194i	$-0.760154\pi$
$107$	−10.0640	+	2.95506i	−0.972923	+	0.285676i	−0.243623	+	0.969870i	$0.578336\pi$
$108$		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
$111$	−12.3014	−	1.27023i	−1.16760	−	0.120565i
$112$		0			0
$113$	−5.30480	+	11.6159i	−0.499033	+	1.09273i	0.477749	+	0.878496i	$0.341453\pi$
$113$	−5.30480	+	11.6159i	−0.499033	+	1.09273i	−0.976782	+	0.214234i	$0.931274\pi$
$114$		0			0
$115$	16.7443	+	3.37523i	1.56141	+	0.314742i
$116$		0			0
$117$	3.70187	+	1.98114i	0.342238	+	0.183156i
$118$		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
$123$	−3.62200	+	6.16347i	−0.326585	+	0.555741i
$124$		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
$129$	−6.04239	+	1.11642i	−0.532003	+	0.0982957i
$130$		0			0
$131$	1.65453	+	0.237885i	0.144557	+	0.0207842i	0.214213	−	0.976787i	$-0.431281\pi$
$131$	1.65453	+	0.237885i	0.144557	+	0.0207842i	−0.0696564	+	0.997571i	$0.522190\pi$
$132$		0			0
$133$	−11.9320	+	7.66824i	−1.03464	+	0.664920i
$134$		0			0
$135$	17.0074	−	7.29742i	1.46377	−	0.628062i
$136$		0			0
$137$	22.2736			1.90297			0.951483	−	0.307701i	$-0.0995597\pi$
$137$	22.2736			1.90297			0.951483	+	0.307701i	$0.0995597\pi$
$138$		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
$141$	2.07218	−	1.04818i	0.174509	−	0.0882725i
$142$		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
$147$	−2.24789	−	12.1662i	−0.185403	−	1.00345i
$148$		0			0
$149$	−6.67101	−	14.6075i	−0.546511	−	1.19669i	−0.958392	−	0.285454i	$-0.907856\pi$
$149$	−6.67101	−	14.6075i	−0.546511	−	1.19669i	0.411882	−	0.911237i	$-0.364872\pi$
$150$		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
$153$	−3.68389	−	16.2743i	−0.297825	−	1.31570i
$154$		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
$159$	3.49019	−	1.17797i	0.276790	−	0.0934194i
$160$		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
$165$	−2.77544	+	26.8784i	−0.216068	+	2.09248i
$166$		0			0
$167$	2.41664	+	2.09403i	0.187005	+	0.162041i	0.743332	−	0.668923i	$-0.233244\pi$
$167$	2.41664	+	2.09403i	0.187005	+	0.162041i	−0.556327	+	0.830964i	$0.687790\pi$
$168$		0			0
$169$	10.5940	−	3.11068i	0.814923	−	0.239283i
$170$		0			0
$171$	0.902061	+	11.2785i	0.0689823	+	0.862490i
$172$		0			0
$173$	14.0251	−	6.40504i	1.06631	−	0.486966i	0.196574	−	0.980489i	$-0.437018\pi$
$173$	14.0251	−	6.40504i	1.06631	−	0.486966i	0.869733	+	0.493523i	$0.164291\pi$
$174$		0			0
$175$	−15.6259	+	24.3144i	−1.18121	+	1.83799i
$176$		0			0
$177$	−4.96456	−	7.08652i	−0.373159	−	0.532656i
$178$		0			0
$179$	5.39773	+	8.39902i	0.403445	+	0.627773i	0.982224	−	0.187712i	$-0.0601071\pi$
$179$	5.39773	+	8.39902i	0.403445	+	0.627773i	−0.578779	+	0.815484i	$0.696471\pi$
$180$		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
$189$	−18.6177	−	5.93673i	−1.35424	−	0.431833i
$190$		0			0
$191$	−1.15453	+	8.02992i	−0.0835387	+	0.581024i	0.904460	+	0.426559i	$0.140274\pi$
$191$	−1.15453	+	8.02992i	−0.0835387	+	0.581024i	−0.987998	+	0.154465i	$0.950635\pi$
$192$		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
$195$	−3.27044	+	7.99041i	−0.234201	+	0.572205i
$196$		0			0
$197$	−9.48320	+	1.36348i	−0.675650	+	0.0971438i	−0.471595	−	0.881815i	$-0.656321\pi$
$197$	−9.48320	+	1.36348i	−0.675650	+	0.0971438i	−0.204056	+	0.978959i	$0.565412\pi$
$198$		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
$201$	0.631850	+	15.8253i	0.0445673	+	1.11623i
$202$		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
$207$	−14.1885	+	2.38447i	−0.986171	+	0.165732i
$208$		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
$213$	−0.174889	−	4.38027i	−0.0119832	−	0.300131i
$214$		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
$219$	−0.0911481	+	0.222695i	−0.00615922	+	0.0150484i
$220$		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
$225$	11.2194	+	20.1422i	0.747962	+	1.34282i
$226$		0			0
$227$	7.60809	+	2.23394i	0.504967	+	0.148272i	0.524287	−	0.851542i	$-0.324332\pi$
$227$	7.60809	+	2.23394i	0.504967	+	0.148272i	−0.0193202	+	0.999813i	$0.506150\pi$
$228$		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	$0.286090\pi$
$233$	−4.94957	+	16.8567i	−0.324257	+	1.10432i	−0.946824	+	0.321751i	$0.895729\pi$
$234$		0			0
$235$	2.58166	+	4.01714i	0.168409	+	0.262049i
$236$		0			0
$237$	−14.9818	−	21.3854i	−0.973173	−	1.38913i
$238$		0			0
$239$	2.94622	−	4.58441i	0.190575	−	0.296541i	−0.732797	−	0.680448i	$-0.761785\pi$
$239$	2.94622	−	4.58441i	0.190575	−	0.296541i	0.923372	+	0.383907i	$0.125422\pi$
$240$		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
$243$	−11.1832	+	10.8598i	−0.717406	+	0.696656i
$244$		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
$249$	0.734741	−	7.11551i	0.0465623	−	0.450927i
$250$		0			0
$251$	−3.62547	+	7.93867i	−0.228838	+	0.501084i	−0.988867	−	0.148805i	$-0.952457\pi$
$251$	−3.62547	+	7.93867i	−0.228838	+	0.501084i	0.760029	+	0.649889i	$0.225185\pi$
$252$		0			0
$253$	7.03930	−	19.7922i	0.442557	−	1.24432i
$254$		0			0
$255$	32.5102	−	10.9725i	2.03587	−	0.687125i
$256$		0			0
$257$	−3.86009	+	3.34479i	−0.240786	+	0.208642i	−0.766891	−	0.641777i	$-0.778197\pi$
$257$	−3.86009	+	3.34479i	−0.240786	+	0.208642i	0.526105	+	0.850420i	$0.323652\pi$
$258$		0			0
$259$	−17.5840	+	20.2930i	−1.09261	+	1.26094i
$260$		0			0
$261$	11.5658	−	2.61805i	0.715904	−	0.162053i
$262$		0			0
$263$	3.45520	+	24.0314i	0.213057	+	1.48184i	0.762869	+	0.646553i	$0.223790\pi$
$263$	3.45520	+	24.0314i	0.213057	+	1.48184i	−0.549812	+	0.835288i	$0.685301\pi$
$264$		0			0
$265$	3.14665	+	6.89020i	0.193297	+	0.423262i
$266$		0			0
$267$	−3.68138	−	19.9246i	−0.225297	−	1.21937i
$268$		0			0
$269$	4.05071	+	0.582404i	0.246976	+	0.0355098i	0.264691	−	0.964333i	$-0.414730\pi$
$269$	4.05071	+	0.582404i	0.246976	+	0.0355098i	−0.0177149	+	0.999843i	$0.505639\pi$
$270$		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
$273$	8.13484	−	4.11488i	0.492343	−	0.249044i
$274$		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
$279$	9.11718	−	25.0865i	0.545832	−	1.50189i
$280$		0			0
$281$	−8.92171	+	5.73363i	−0.532224	+	0.342040i	−0.778991	−	0.627035i	$-0.784268\pi$
$281$	−8.92171	+	5.73363i	−0.532224	+	0.342040i	0.246767	+	0.969075i	$0.420632\pi$
$282$		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
$285$	−22.8791	+	4.22726i	−1.35524	+	0.250401i
$286$		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
$291$	−3.93616	+	6.69807i	−0.230742	+	0.392648i
$292$		0			0
$293$	−3.60005	+	4.15468i	−0.210317	+	0.242719i	−0.851101	−	0.525003i	$-0.824064\pi$
$293$	−3.60005	+	4.15468i	−0.210317	+	0.242719i	0.640783	+	0.767722i	$0.278610\pi$
$294$		0			0
$295$	13.4465	−	11.6515i	0.782887	−	0.678376i
$296$		0			0
$297$	−5.90652	−	21.9804i	−0.342731	−	1.27543i
$298$		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
$303$	−23.7603	−	2.45346i	−1.36499	−	0.140948i
$304$		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
$309$	−21.1869	−	16.9270i	−1.20528	−	0.962943i
$310$		0			0
$311$	−5.65005	+	2.58029i	−0.320385	+	0.146315i	−0.569115	−	0.822258i	$-0.692714\pi$
$311$	−5.65005	+	2.58029i	−0.320385	+	0.146315i	0.248730	+	0.968573i	$0.419987\pi$
$312$		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
$315$	8.21100	−	39.3353i	0.462637	−	2.21629i
$316$		0			0
$317$	−12.9278	−	20.1160i	−0.726096	−	1.12983i	−0.986410	−	0.164303i	$-0.947462\pi$
$317$	−12.9278	−	20.1160i	−0.726096	−	1.12983i	0.260314	−	0.965524i	$-0.416174\pi$
$318$		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
$327$	3.07349	−	12.2567i	0.169965	−	0.677797i
$328$		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
$333$	7.65402	+	20.0057i	0.419438	+	1.09631i
$334$		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
$339$	22.1005	−	0.882394i	1.20033	−	0.0479251i
$340$		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
$345$	−7.87408	−	28.5182i	−0.423926	−	1.53537i
$346$		0			0
$347$	−26.0960	−	11.9176i	−1.40090	−	0.639772i	−0.435419	−	0.900228i	$-0.643400\pi$
$347$	−26.0960	−	11.9176i	−1.40090	−	0.639772i	−0.965486	+	0.260456i	$0.916127\pi$
$348$		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
$351$	0.167857	−	7.27035i	0.00895955	−	0.388063i
$352$		0			0
$353$	5.49908	+	18.7281i	0.292686	+	0.996798i	0.966237	+	0.257657i	$0.0829504\pi$
$353$	5.49908	+	18.7281i	0.292686	+	0.996798i	−0.673550	+	0.739142i	$0.735231\pi$
$354$		0			0
$355$	8.92267	−	1.28289i	0.473566	−	0.0680885i
$356$		0			0
$357$	−33.5299	−	13.7236i	−1.77459	−	0.726331i
$358$		0			0
$359$	−0.983323	−	0.631944i	−0.0518978	−	0.0333527i	0.514435	−	0.857530i	$-0.328002\pi$
$359$	−0.983323	−	0.631944i	−0.0518978	−	0.0333527i	−0.566332	+	0.824177i	$0.691638\pi$
$360$		0			0
$361$	−0.679653	+	4.72709i	−0.0357712	+	0.248794i
$362$		0			0
$363$	13.7531	+	3.44872i	0.721849	+	0.181011i
$364$		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
$375$	−13.5678	+	9.50510i	−0.700638	+	0.490841i
$376$		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
$381$	12.1690	−	15.2314i	0.623435	−	0.780329i
$382$		0			0
$383$	22.8489	−	6.70905i	1.16753	−	0.342817i	0.360173	−	0.932885i	$-0.382718\pi$
$383$	22.8489	−	6.70905i	1.16753	−	0.342817i	0.807353	+	0.590069i	$0.200899\pi$
$384$		0			0
$385$	44.3399	+	38.4208i	2.25977	+	1.95810i
$386$		0			0
$387$	6.44947	+	8.46611i	0.327845	+	0.430357i
$388$		0			0
$389$	8.48983	−	18.5901i	0.430451	−	0.942557i	−0.562802	−	0.826592i	$-0.690277\pi$
$389$	8.48983	−	18.5901i	0.430451	−	0.942557i	0.993253	−	0.115965i	$-0.0369961\pi$
$390$		0			0
$391$	−26.5744	+	2.30952i	−1.34392	+	0.116797i
$392$		0			0
$393$	−0.925847	−	2.74317i	−0.0467028	−	0.138375i
$394$		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
$399$	21.1803	+	12.4467i	1.06034	+	0.623115i
$400$		0			0
$401$	2.75960	+	19.1935i	0.137808	+	0.958476i	0.934974	+	0.354716i	$0.115422\pi$
$401$	2.75960	+	19.1935i	0.137808	+	0.958476i	−0.797166	+	0.603760i	$0.793669\pi$
$402$		0			0
$403$	5.17284	+	11.3269i	0.257678	+	0.564236i
$404$		0			0
$405$	−24.5751	−	20.5810i	−1.22115	−	1.02268i
$406$		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
$411$	−17.4136	−	34.4255i	−0.858949	−	1.69808i
$412$		0			0
$413$	−18.7868			−0.924436
$414$		0			0
$415$	14.7096			0.722065
$416$		0			0
$417$	4.40168	+	8.70182i	0.215551	+	0.426130i
$418$		0			0
$419$	−2.43323	+	1.56374i	−0.118871	+	0.0763939i	−0.598725	−	0.800954i	$-0.704326\pi$
$419$	−2.43323	+	1.56374i	−0.118871	+	0.0763939i	0.479854	+	0.877348i	$0.340690\pi$
$420$		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
$423$	−3.24006	−	2.38322i	−0.157537	−	0.115876i
$424$		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
$429$	9.15437	+	5.37962i	0.441977	+	0.259730i
$430$		0			0
$431$	6.01699	−	6.94398i	0.289828	−	0.334480i	−0.592099	−	0.805865i	$-0.701701\pi$
$431$	6.01699	−	6.94398i	0.289828	−	0.334480i	0.881927	+	0.471386i	$0.156246\pi$
$432$		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
$435$	7.79791	+	23.1042i	0.373881	+	1.10776i
$436$		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
$441$	−17.0463	+	12.9858i	−0.811726	+	0.618372i
$442$		0			0
$443$	20.8244	+	18.0445i	0.989398	+	0.857318i	0.989769	−	0.142682i	$-0.0455726\pi$
$443$	20.8244	+	18.0445i	0.989398	+	0.857318i	−0.000370744		1.00000i	$0.500118\pi$
$444$		0			0
$445$	39.9772	−	11.7384i	1.89510	−	0.556452i
$446$		0			0
$447$	−17.3615	+	21.7307i	−0.821169	+	1.02783i
$448$		0			0
$449$	−17.0253	+	7.77519i	−0.803473	+	0.366934i	−0.774442	−	0.632645i	$-0.781969\pi$
$449$	−17.0253	+	7.77519i	−0.803473	+	0.366934i	−0.0290309	+	0.999579i	$0.509242\pi$
$450$		0			0
$451$	−9.77425	+	15.2090i	−0.460252	+	0.716166i
$452$		0			0
$453$	−34.3557	+	24.0684i	−1.61417	+	1.13083i
$454$		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	$0.0766967\pi$
$461$			10.2470i			0.477250i	−0.971112	+	0.238625i	$0.923303\pi$
$462$		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
$465$	53.2388	+	13.3502i	2.46889	+	0.619099i
$466$		0			0
$467$	4.56505	−	31.7506i	0.211245	−	1.46924i	−0.557762	−	0.830001i	$-0.688340\pi$
$467$	4.56505	−	31.7506i	0.211245	−	1.46924i	0.769007	−	0.639241i	$-0.220751\pi$
$468$		0			0
$469$	28.9292	+	18.5917i	1.33583	+	0.858483i
$470$		0			0
$471$	−11.2634	−	4.61006i	−0.518991	−	0.212421i
$472$		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
$477$	−4.54928	−	4.47339i	−0.208297	−	0.204823i
$478$		0			0
$479$	−0.0757814	−	0.0874564i	−0.00346254	−	0.00399599i	0.754016	−	0.656856i	$-0.228114\pi$
$479$	−0.0757814	−	0.0874564i	−0.00346254	−	0.00399599i	−0.757478	+	0.652860i	$0.773569\pi$
$480$		0			0
$481$	−9.08974	−	4.15114i	−0.414456	−	0.189276i
$482$		0			0
$483$	−13.4358	+	28.2019i	−0.611352	+	1.28323i
$484$		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
$489$	23.6145	−	0.942846i	1.06789	−	0.0426369i
$490$		0			0
$491$	−0.360932	−	1.22922i	−0.0162886	−	0.0554740i	0.950948	−	0.309352i	$-0.100112\pi$
$491$	−0.360932	−	1.22922i	−0.0162886	−	0.0554740i	−0.967236	+	0.253878i	$0.918294\pi$
$492$		0			0
$493$	21.7618	−	3.12887i	0.980102	−	0.140917i
$494$		0			0
$495$	43.7123	−	16.7240i	1.96472	−	0.751686i
$496$		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
$501$	1.34713	−	5.37220i	0.0601855	−	0.240012i
$502$		0			0
$503$	23.1919	+	6.80974i	1.03407	+	0.303631i	0.754366	−	0.656454i	$-0.227944\pi$
$503$	23.1919	+	6.80974i	1.03407	+	0.303631i	0.279708	+	0.960085i	$0.409762\pi$
$504$		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	−0.883821	−	0.467824i	$-0.845038\pi$
$509$	2.54085	−	8.65336i	0.112621	−	0.383553i	0.996443	+	0.0842710i	$0.0268562\pi$
$510$		0			0
$511$	0.282464	+	0.439523i	0.0124955	+	0.0194433i
$512$		0			0
$513$	16.7265	−	10.2118i	0.738493	−	0.450861i
$514$		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
$519$	−20.8643	−	16.6693i	−0.915840	−	0.731700i
$520$		0			0
$521$	34.3952	−	10.0994i	1.50688	−	0.442461i	0.578999	−	0.815329i	$-0.303444\pi$
$521$	34.3952	−	10.0994i	1.50688	−	0.442461i	0.927885	+	0.372868i	$0.121625\pi$
$522$		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
$525$	49.7959	+	5.14188i	2.17327	+	0.224410i
$526$		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
$531$	−7.07141	+	13.2133i	−0.306873	+	0.573410i
$532$		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
$537$	8.76132	−	14.9089i	0.378079	−	0.643368i
$538$		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
$543$	−8.80873	+	1.62755i	−0.378019	+	0.0698448i
$544$		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
$549$	35.3395	+	12.8434i	1.50825	+	0.548144i
$550$		0			0
$551$	−14.9080			−0.635104
$552$		0			0
$553$	−56.6938			−2.41087
$554$		0			0
$555$	−39.3040	+	19.8813i	−1.66836	+	0.843915i
$556$		0			0
$557$	37.7464	−	24.2581i	1.59937	−	1.02785i	0.631834	−	0.775103i	$-0.282302\pi$
$557$	37.7464	−	24.2581i	1.59937	−	1.02785i	0.967532	−	0.252747i	$-0.0813341\pi$
$558$		0			0
$559$	−4.91455	−	0.706605i	−0.207863	−	0.0298862i
$560$		0			0
$561$	−7.66689	−	41.4952i	−0.323696	−	1.75193i
$562$		0			0
$563$	0.445445	+	0.975388i	0.0187733	+	0.0411077i	0.918786	−	0.394755i	$-0.129171\pi$
$563$	0.445445	+	0.975388i	0.0187733	+	0.0411077i	−0.900013	+	0.435863i	$0.856443\pi$
$564$		0			0
$565$	6.47275	+	45.0189i	0.272310	+	1.89396i
$566$		0			0
$567$	5.37970	+	33.4162i	0.225926	+	1.40335i
$568$		0			0
$569$	−6.71551	+	7.75011i	−0.281529	+	0.324902i	−0.878848	−	0.477102i	$-0.841687\pi$
$569$	−6.71551	+	7.75011i	−0.281529	+	0.324902i	0.597319	+	0.802004i	$0.296233\pi$
$570$		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
$573$	13.3134	−	4.49340i	0.556175	−	0.187715i
$574$		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
$579$	−1.49145	+	14.4437i	−0.0619823	+	0.600261i
$580$		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
$585$	14.9066	−	1.19223i	0.616311	−	0.0492928i
$586$		0			0
$587$	0.293330	−	0.133959i	0.0121070	−	0.00552910i	−0.409352	−	0.912376i	$-0.634245\pi$
$587$	0.293330	−	0.133959i	0.0121070	−	0.00552910i	0.421459	+	0.906847i	$0.361518\pi$
$588$		0			0
$589$	−18.1419	+	28.2293i	−0.747523	+	1.16317i
$590$		0			0
$591$	9.52134	+	13.5910i	0.391656	+	0.559058i
$592$		0			0
$593$	−15.2828	−	23.7805i	−0.627588	−	0.976547i	−0.998847	−	0.0480169i	$-0.984710\pi$
$593$	−15.2828	−	23.7805i	−0.627588	−	0.976547i	0.371258	−	0.928530i	$-0.378926\pi$
$594$		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	$0.00880940\pi$
$599$			1.35452i			0.0553440i	−0.999617	+	0.0276720i	$0.991191\pi$
$600$		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
$603$	23.9652	−	13.3488i	0.975937	−	0.543607i
$604$		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
$609$	9.75306	−	23.8289i	0.395214	−	0.965596i
$610$		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
$615$	1.01580	+	25.4417i	0.0409610	+	1.02591i
$616$		0			0
$617$	8.49179	+	9.80004i	0.341866	+	0.394535i	0.900483	−	0.434891i	$-0.143213\pi$
$617$	8.49179	+	9.80004i	0.341866	+	0.394535i	−0.558617	+	0.829426i	$0.688668\pi$
$618$		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
$621$	14.7780	+	20.0652i	0.593020	+	0.805187i
$622$		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
$627$	1.14153	+	28.5907i	0.0455881	+	1.14180i
$628$		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
$633$	0.168857	−	0.412556i	0.00671148	−	0.0163976i
$634$		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
$639$	−6.63328	+	3.69481i	−0.262409	+	0.146164i
$640$		0			0
$641$	−40.3625	−	11.8515i	−1.59422	−	0.468106i	−0.640291	−	0.768132i	$-0.721186\pi$
$641$	−40.3625	−	11.8515i	−1.59422	−	0.468106i	−0.953931	+	0.300026i	$0.903005\pi$
$642$		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	−0.975687	−	0.219168i	$-0.929666\pi$
$647$	−0.925764	+	3.15286i	−0.0363955	+	0.123952i	0.939292	+	0.343120i	$0.111484\pi$
$648$		0			0
$649$	−11.8300	−	18.4078i	−0.464367	−	0.722569i
$650$		0			0
$651$	−33.2529	−	47.4659i	−1.30328	−	1.86034i
$652$		0			0
$653$	10.0112	−	15.5777i	0.391768	−	0.609603i	−0.588210	−	0.808708i	$-0.700167\pi$
$653$	10.0112	−	15.5777i	0.391768	−	0.609603i	0.979978	+	0.199105i	$0.0638036\pi$
$654$		0			0
$655$	5.41546	−	2.47316i	0.211599	−	0.0966342i
$656$		0			0
$657$	0.415451	−	0.0332280i	0.0162083	−	0.00129635i
$658$		0			0
$659$	−24.2171	+	7.11079i	−0.943365	+	0.276997i	−0.717022	−	0.697051i	$-0.754495\pi$
$659$	−24.2171	+	7.11079i	−0.943365	+	0.276997i	−0.226343	+	0.974048i	$0.572677\pi$
$660$		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
$663$	1.38487	−	13.4116i	0.0537837	−	0.520862i
$664$		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
$669$	−19.5153	+	6.58660i	−0.754504	+	0.254652i
$670$		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
$675$	22.3598	−	33.0877i	0.860630	−	1.27354i
$676$		0			0
$677$	3.58335	+	24.9227i	0.137719	+	0.957859i	0.935100	+	0.354383i	$0.115309\pi$
$677$	3.58335	+	24.9227i	0.137719	+	0.957859i	−0.797381	+	0.603476i	$0.793782\pi$
$678$		0			0
$679$	7.00742	+	15.3441i	0.268920	+	0.588853i
$680$		0			0
$681$	−2.49532	−	13.5053i	−0.0956208	−	0.517525i
$682$		0			0
$683$	20.9492	+	3.01204i	0.801600	+	0.115253i	0.530926	−	0.847418i	$-0.321844\pi$
$683$	20.9492	+	3.01204i	0.801600	+	0.115253i	0.270674	+	0.962671i	$0.412753\pi$
$684$		0			0
$685$	66.7375	−	42.8896i	2.54991	−	1.63873i
$686$		0			0
$687$	16.7113	−	8.45314i	0.637575	−	0.322507i
$688$		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
$693$	−46.4460	−	16.8798i	−1.76434	−	0.641212i
$694$		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
$699$	29.9227	−	5.52869i	1.13178	−	0.209114i
$700$		0			0
$701$	17.7901	+	38.9549i	0.671924	+	1.47131i	0.870979	+	0.491320i	$0.163485\pi$
$701$	17.7901	+	38.9549i	0.671924	+	1.47131i	−0.199055	+	0.979988i	$0.563787\pi$
$702$		0			0
$703$	−3.83232	−	26.6544i	−0.144539	−	1.00529i
$704$		0			0
$705$	4.19042	−	7.13074i	0.157820	−	0.268559i
$706$		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
$711$	−21.3398	+	39.8746i	−0.800304	+	1.49541i
$712$		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
$717$	−9.38888	−	0.969487i	−0.350634	−	0.0362062i
$718$		0			0
$719$	−7.58627	−	6.57354i	−0.282920	−	0.245152i	0.501827	−	0.864968i	$-0.332662\pi$
$719$	−7.58627	−	6.57354i	−0.282920	−	0.245152i	−0.784747	+	0.619817i	$0.787207\pi$
$720$		0			0
$721$	−56.4958	+	16.5887i	−2.10401	+	0.617794i
$722$		0			0
$723$	24.9160	+	19.9063i	0.926636	+	0.740325i
$724$		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
$729$	25.5276	+	8.79428i	0.945468	+	0.325714i
$730$		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
$741$	−2.22373	+	8.86795i	−0.0816907	+	0.325772i
$742$		0			0
$743$	−0.664955	+	4.62486i	−0.0243948	+	0.169670i	−0.998377	−	0.0569563i	$-0.981860\pi$
$743$	−0.664955	+	4.62486i	−0.0243948	+	0.169670i	0.973982	+	0.226626i	$0.0727695\pi$
$744$		0			0
$745$	−48.1158	−	30.9222i	−1.76283	−	1.13290i
$746$		0			0
$747$	−11.5719	+	4.42733i	−0.423395	+	0.161988i
$748$		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
$753$	15.1042	−	0.603056i	0.550426	−	0.0219766i
$754$		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
$759$	−36.0935	+	4.59384i	−1.31011	+	0.166746i
$760$		0			0
$761$	13.0329	+	5.95192i	0.472442	+	0.215757i	0.637384	−	0.770546i	$-0.280016\pi$
$761$	13.0329	+	5.95192i	0.472442	+	0.215757i	−0.164942	+	0.986303i	$0.552744\pi$
$762$		0			0
$763$	−17.9670	−	20.7350i	−0.650449	−	0.750658i
$764$		0			0
$765$	−42.3753	−	41.6684i	−1.53208	−	1.50652i
$766$		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
$771$	8.18744	+	3.35108i	0.294863	+	0.120686i
$772$		0			0
$773$	−8.60214	−	5.52826i	−0.309398	−	0.198838i	0.376722	−	0.926326i	$-0.377051\pi$
$773$	−8.60214	−	5.52826i	−0.309398	−	0.198838i	−0.686120	+	0.727488i	$0.740687\pi$
$774$		0			0
$775$	−9.73135	+	67.6830i	−0.349560	+	2.43125i
$776$		0			0
$777$	45.1114	+	11.3121i	1.61836	+	0.405821i
$778$		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
$789$	34.4410	−	24.1281i	1.22613	−	0.858982i
$790$		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
$795$	8.18923	−	10.2501i	0.290442	−	0.363535i
$796$		0			0
$797$	−5.17788	+	1.52036i	−0.183410	+	0.0538540i	−0.372148	−	0.928173i	$-0.621379\pi$
$797$	−5.17788	+	1.52036i	−0.183410	+	0.0538540i	0.188738	+	0.982028i	$0.439560\pi$
$798$		0			0
$799$	−5.63571	−	4.88337i	−0.199377	−	0.172761i
$800$		0			0
$801$	−27.9168	+	21.2670i	−0.986391	+	0.751431i
$802$		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
$807$	−2.26671	−	6.71598i	−0.0797919	−	0.236414i
$808$		0			0
$809$	−22.4795	+	19.4786i	−0.790339	+	0.684832i	−0.953375	−	0.301788i	$-0.902417\pi$
$809$	−22.4795	+	19.4786i	−0.790339	+	0.684832i	0.163037	+	0.986620i	$0.447871\pi$
$810$		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
$813$	−22.1284	−	13.0039i	−0.776076	−	0.456065i
$814$		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
$819$	−12.7197	−	9.35594i	−0.444461	−	0.326923i
$820$		0			0
$821$	−15.4121	−	2.21593i	−0.537887	−	0.0773365i	−0.131983	−	0.991252i	$-0.542134\pi$
$821$	−15.4121	−	2.21593i	−0.537887	−	0.0773365i	−0.405904	+	0.913916i	$0.633043\pi$
$822$		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
$825$	26.3182	+	52.0293i	0.916282	+	1.81143i
$826$		0			0
$827$	51.2667			1.78272			0.891359	−	0.453299i	$-0.149753\pi$
$827$	51.2667			1.78272			0.891359	+	0.453299i	$0.149753\pi$
$828$		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
$831$	10.2390	+	20.2417i	0.355186	+	0.702178i
$832$		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
$837$	−45.9008	+	5.52146i	−1.58656	+	0.190849i
$838$		0			0
$839$	−5.54213	−	12.1356i	−0.191336	−	0.418967i	0.789514	−	0.613732i	$-0.210333\pi$
$839$	−5.54213	−	12.1356i	−0.191336	−	0.418967i	−0.980850	+	0.194766i	$0.937605\pi$
$840$		0			0
$841$	−1.90351	−	13.2392i	−0.0656384	−	0.456525i
$842$		0			0
$843$	15.8367	+	9.30655i	0.545446	+	0.320535i
$844$		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
$849$	2.92598	+	8.66932i	0.100419	+	0.297530i
$850$		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
$855$	24.4204	+	32.0563i	0.835161	+	1.09630i
$856$		0			0
$857$	−18.7706	−	16.2649i	−0.641193	−	0.555597i	0.272422	−	0.962178i	$-0.412175\pi$
$857$	−18.7706	−	16.2649i	−0.641193	−	0.555597i	−0.913615	+	0.406581i	$0.866721\pi$
$858$		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
$861$	16.7814	−	21.0046i	0.571909	−	0.715837i
$862$		0			0
$863$	9.63614	−	4.40068i	0.328018	−	0.149801i	−0.244598	−	0.969625i	$-0.578656\pi$
$863$	9.63614	−	4.40068i	0.328018	−	0.149801i	0.572616	+	0.819824i	$0.305929\pi$
$864$		0			0
$865$	29.6893	−	46.1975i	1.00947	−	1.57076i
$866$		0			0
$867$	−19.7694	+	13.8497i	−0.671404	+	0.470361i
$868$		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
$879$	9.23589	+	2.31599i	0.311519	+	0.0781165i
$880$		0			0
$881$	−5.08231	+	35.3483i	−0.171227	+	1.19091i	0.705068	+	0.709139i	$0.250916\pi$
$881$	−5.08231	+	35.3483i	−0.171227	+	1.19091i	−0.876296	+	0.481774i	$0.839993\pi$
$882$		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
$885$	−28.5207	−	11.6734i	−0.958713	−	0.392397i
$886$		0			0
$887$	−7.21836	+	1.03784i	−0.242369	+	0.0348474i	−0.262429	−	0.964951i	$-0.584523\pi$
$887$	−7.21836	+	1.03784i	−0.242369	+	0.0348474i	0.0200599	+	0.999799i	$0.493614\pi$
$888$		0			0
$889$	−11.9257	−	40.6153i	−0.399976	−	1.36219i
$890$		0			0
$891$	−29.3546	+	26.3133i	−0.983415	+	0.881529i
$892$		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
$897$	−11.4789	−	1.84073i	−0.383270	−	0.0614602i
$898$		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
$903$	23.0900	−	0.921902i	0.768386	−	0.0306790i
$904$		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
$909$	14.7838	+	38.6412i	0.490349	+	1.28165i
$910$		0			0
$911$	−17.8076	−	11.4443i	−0.589994	−	0.379166i	0.211314	−	0.977418i	$-0.432226\pi$
$911$	−17.8076	−	11.4443i	−0.589994	−	0.379166i	−0.801308	+	0.598252i	$0.795862\pi$
$912$		0			0
$913$	2.57450	−	17.9060i	0.0852035	−	0.592604i
$914$		0			0
$915$	−18.8064	+	74.9977i	−0.621722	+	2.47935i
$916$		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
$927$	−9.59790	+	45.9793i	−0.315236	+	1.51016i
$928$		0			0
$929$	30.6763	−	47.7333i	1.00646	−	1.56608i	0.195726	−	0.980659i	$-0.437294\pi$
$929$	30.6763	−	47.7333i	1.00646	−	1.56608i	0.810731	−	0.585419i	$-0.199070\pi$
$930$		0			0
$931$	24.5055	−	11.1913i	0.803135	−	0.366780i
$932$		0			0
$933$	8.40525	+	6.71527i	0.275175	+	0.219848i
$934$		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
$939$	43.7787	+	4.52054i	1.42866	+	0.147522i
$940$		0			0
$941$	−5.61221	+	12.2890i	−0.182953	+	0.400611i	−0.978780	−	0.204913i	$-0.934309\pi$
$941$	−5.61221	+	12.2890i	−0.182953	+	0.400611i	0.795827	+	0.605524i	$0.207036\pi$
$942$		0			0
$943$	3.91140	−	19.4042i	0.127373	−	0.631888i
$944$		0			0
$945$	−67.2148	+	18.0618i	−2.18650	+	0.587549i
$946$		0			0
$947$	16.1567	−	13.9999i	0.525023	−	0.454935i	−0.351574	−	0.936160i	$-0.614353\pi$
$947$	16.1567	−	13.9999i	0.525023	−	0.454935i	0.876597	+	0.481225i	$0.159808\pi$
$948$		0			0
$949$	−0.127327	+	0.146944i	−0.00413322	+	0.00476999i
$950$		0			0
$951$	−20.9837	+	35.7075i	−0.680444	+	1.15790i
$952$		0			0
$953$	−4.56726	−	31.7660i	−0.147948	−	1.02900i	−0.919572	−	0.392922i	$-0.871464\pi$
$953$	−4.56726	−	31.7660i	−0.147948	−	1.02900i	0.771624	−	0.636079i	$-0.219445\pi$
$954$		0			0
$955$	12.0029	+	26.2828i	0.388406	+	0.850491i
$956$		0			0
$957$	29.4897	−	5.44868i	0.953267	−	0.176131i
$958$		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
$963$	10.7481	−	29.5741i	0.346352	−	0.953011i
$964$		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
$969$	32.4218	−	16.4000i	1.04154	−	0.526845i
$970$		0			0
$971$	−24.9458	+	16.0317i	−0.800548	+	0.514481i	−0.875795	−	0.482684i	$-0.839662\pi$
$971$	−24.9458	+	16.0317i	−0.800548	+	0.514481i	0.0752468	+	0.997165i	$0.476026\pi$
$972$		0			0
$973$	20.9580	+	3.01330i	0.671882	+	0.0966021i
$974$		0			0
$975$	3.38490	+	18.3200i	0.108404	+	0.586710i
$976$		0			0
$977$	18.9985	+	41.6008i	0.607815	+	1.33093i	0.924059	+	0.382251i	$0.124851\pi$
$977$	18.9985	+	41.6008i	0.607815	+	1.33093i	−0.316244	+	0.948678i	$0.602422\pi$
$978$		0			0
$979$	−7.29228	−	50.7189i	−0.233062	−	1.62098i
$980$		0			0
$981$	−21.3465	+	4.83202i	−0.681540	+	0.154275i
$982$		0			0
$983$	−19.7737	+	22.8201i	−0.630684	+	0.727848i	−0.977699	−	0.210012i	$-0.932650\pi$
$983$	−19.7737	+	22.8201i	−0.630684	+	0.727848i	0.347015	+	0.937859i	$0.387195\pi$
$984$		0			0
$985$	−25.7886	+	22.3459i	−0.821693	+	0.712001i
$986$		0			0
$987$	−8.27455	+	2.79274i	−0.263382	+	0.0888939i
$988$		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
$993$	−1.17733	+	11.4017i	−0.0373613	+	0.361821i
$994$		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
$999$	24.9363	−	27.4703i	0.788949	−	0.869123i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.781802 - 1.54557i) q^{3} +(2.99625 - 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(-1.77757 + 2.41666i) q^{9} +O(q^{10})\)	\(q+(-0.781802 - 1.54557i) q^{3} +(2.99625 - 1.92558i) q^{5} +(-3.72244 - 0.535207i) q^{7} +(-1.77757 + 2.41666i) q^{9} +(-1.81960 - 3.98437i) q^{11} +(-0.199177 - 1.38531i) q^{13} +(-5.31859 - 3.12550i) q^{15} +(-3.64235 + 4.20350i) q^{17} +(2.85032 - 2.46981i) q^{19} +(2.08302 + 6.17172i) q^{21} +(3.44262 + 3.33892i) q^{23} +(3.19262 - 6.99086i) q^{25} +(5.12482 + 0.858008i) q^{27} +(-2.98733 - 2.58853i) q^{29} +(-8.53689 + 2.50666i) q^{31} +(-4.73556 + 5.92731i) q^{33} +(-12.1840 + 5.56423i) q^{35} +(3.86016 - 6.00652i) q^{37} +(-1.98537 + 1.39088i) q^{39} +(-2.23146 - 3.47222i) q^{41} +(0.999481 - 3.40392i) q^{43} +(-0.672591 + 10.6638i) q^{45} +1.34072i q^{47} +(6.85369 + 2.01242i) q^{49} +(9.34439 + 2.34320i) q^{51} +(-0.302667 + 2.10509i) q^{53} +(-13.1242 - 8.43441i) q^{55} +(-6.04566 - 2.47446i) q^{57} +(4.94467 - 0.710937i) q^{59} +(-3.53114 - 12.0260i) q^{61} +(7.91032 - 8.04451i) q^{63} +(-3.26430 - 3.76720i) q^{65} +(-8.31771 - 3.79857i) q^{67} +(2.46908 - 7.93118i) q^{69} +(2.30225 + 1.05140i) q^{71} +(-0.0909771 - 0.104993i) q^{73} +(-13.3009 + 0.531057i) q^{75} +(4.64090 + 15.8055i) q^{77} +(14.9218 - 2.14543i) q^{79} +(-2.68049 - 8.59156i) q^{81} +(3.47436 + 2.23284i) q^{83} +(-2.81926 + 19.6084i) q^{85} +(-1.66526 + 6.64084i) q^{87} +(11.2243 + 3.29576i) q^{89} +5.26333i q^{91} +(10.5484 + 11.2346i) q^{93} +(3.78446 - 12.8887i) q^{95} +(-2.42501 - 3.77339i) q^{97} +(12.8633 + 2.68514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{9}+O(q^{10}) \) 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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