LMFDB - Embedded newform 820.2.bi.a.189.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(189,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.189"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.bi (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$20$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			189.10
Character	$\chi$	$=$	820.189
Dual form			820.2.bi.a.269.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.323438 q^{3} +(-0.368890 + 2.20543i) q^{5} +(-1.10691 - 3.40672i) q^{7} -2.89539 q^{9} +(2.23783 + 3.08011i) q^{11} +(1.70933 - 5.26078i) q^{13} +(0.119313 - 0.713321i) q^{15} +(4.40830 - 3.20282i) q^{17} +(-3.22215 + 1.04694i) q^{19} +(0.358017 + 1.10186i) q^{21} +(-0.505667 - 0.164301i) q^{23} +(-4.72784 - 1.62712i) q^{25} +1.90679 q^{27} +(5.43089 - 7.47498i) q^{29} +(5.47917 - 3.98085i) q^{31} +(-0.723801 - 0.996227i) q^{33} +(7.92160 - 1.18451i) q^{35} +(4.64893 - 6.39870i) q^{37} +(-0.552863 + 1.70154i) q^{39} +(1.89538 + 6.11617i) q^{41} +(0.902310 + 0.293178i) q^{43} +(1.06808 - 6.38557i) q^{45} +(-2.79826 + 8.61215i) q^{47} +(-4.71735 + 3.42736i) q^{49} +(-1.42581 + 1.03591i) q^{51} +(-3.81986 - 2.77529i) q^{53} +(-7.61849 + 3.79916i) q^{55} +(1.04217 - 0.338621i) q^{57} +(3.05698 - 9.40843i) q^{59} +(-2.05425 - 6.32232i) q^{61} +(3.20493 + 9.86376i) q^{63} +(10.9717 + 5.71045i) q^{65} +(-5.32921 - 3.87190i) q^{67} +(0.163552 + 0.0531412i) q^{69} +(0.637848 + 0.877922i) q^{71} -1.26023i q^{73} +(1.52916 + 0.526274i) q^{75} +(8.01599 - 11.0331i) q^{77} -1.60115i q^{79} +8.06943 q^{81} -2.18693i q^{83} +(5.43741 + 10.9037i) q^{85} +(-1.75656 + 2.41770i) q^{87} +(2.46675 - 0.801496i) q^{89} -19.8140 q^{91} +(-1.77217 + 1.28756i) q^{93} +(-1.12033 - 7.49244i) q^{95} +(-5.97081 - 4.33805i) q^{97} +(-6.47940 - 8.91812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) $ 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$-1$

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
$3$	−0.323438			−0.186737			−0.0933686	−	0.995632i	$-0.529764\pi$
$3$	−0.323438			−0.186737			−0.0933686	+	0.995632i	$0.529764\pi$
$4$		0			0
$5$	−0.368890	+	2.20543i	−0.164973	+	0.986298i
$5$	−0.368890	+	2.20543i	−0.164973	+	0.986298i
$6$		0			0
$7$	−1.10691	−	3.40672i	−0.418372	−	1.28762i	−0.909199	−	0.416361i	$-0.863305\pi$
$7$	−1.10691	−	3.40672i	−0.418372	−	1.28762i	0.490827	−	0.871257i	$-0.336695\pi$
$8$		0			0
$9$	−2.89539			−0.965129
$10$		0			0
$11$	2.23783	+	3.08011i	0.674732	+	0.928689i	0.999856	−	0.0169823i	$-0.00540591\pi$
$11$	2.23783	+	3.08011i	0.674732	+	0.928689i	−0.325124	+	0.945672i	$0.605406\pi$
$12$		0			0
$13$	1.70933	−	5.26078i	0.474083	−	1.45908i	−0.373108	−	0.927788i	$-0.621708\pi$
$13$	1.70933	−	5.26078i	0.474083	−	1.45908i	0.847191	−	0.531289i	$-0.178292\pi$
$14$		0			0
$15$	0.119313	−	0.713321i	0.0308065	−	0.184179i
$16$		0			0
$17$	4.40830	−	3.20282i	1.06917	−	0.776797i	0.0934068	−	0.995628i	$-0.470224\pi$
$17$	4.40830	−	3.20282i	1.06917	−	0.776797i	0.975763	+	0.218831i	$0.0702243\pi$
$18$		0			0
$19$	−3.22215	+	1.04694i	−0.739213	+	0.240185i	−0.654333	−	0.756207i	$-0.727051\pi$
$19$	−3.22215	+	1.04694i	−0.739213	+	0.240185i	−0.0848795	+	0.996391i	$0.527051\pi$
$20$		0			0
$21$	0.358017	+	1.10186i	0.0781257	+	0.240446i
$22$		0			0
$23$	−0.505667	−	0.164301i	−0.105439	−	0.0342591i	0.255822	−	0.966724i	$-0.417654\pi$
$23$	−0.505667	−	0.164301i	−0.105439	−	0.0342591i	−0.361261	+	0.932465i	$0.617654\pi$
$24$		0			0
$25$	−4.72784	−	1.62712i	−0.945568	−	0.325425i
$26$		0			0
$27$	1.90679			0.366963
$28$		0			0
$29$	5.43089	−	7.47498i	1.00849	−	1.38807i	0.0885246	−	0.996074i	$-0.471785\pi$
$29$	5.43089	−	7.47498i	1.00849	−	1.38807i	0.919967	−	0.391996i	$-0.128215\pi$
$30$		0			0
$31$	5.47917	−	3.98085i	0.984088	−	0.714982i	0.0254696	−	0.999676i	$-0.491892\pi$
$31$	5.47917	−	3.98085i	0.984088	−	0.714982i	0.958619	+	0.284694i	$0.0918919\pi$
$32$		0			0
$33$	−0.723801	−	0.996227i	−0.125998	−	0.173421i
$34$		0			0
$35$	7.92160	−	1.18451i	1.33900	−	0.200218i
$36$		0			0
$37$	4.64893	−	6.39870i	0.764279	−	1.05194i	−0.232567	−	0.972580i	$-0.574712\pi$
$37$	4.64893	−	6.39870i	0.764279	−	1.05194i	0.996846	−	0.0793599i	$-0.0252876\pi$
$38$		0			0
$39$	−0.552863	+	1.70154i	−0.0885289	+	0.272464i
$40$		0			0
$41$	1.89538	+	6.11617i	0.296009	+	0.955185i
$41$	1.89538	+	6.11617i	0.296009	+	0.955185i
$42$		0			0
$43$	0.902310	+	0.293178i	0.137601	+	0.0447092i	0.377008	−	0.926210i	$-0.376953\pi$
$43$	0.902310	+	0.293178i	0.137601	+	0.0447092i	−0.239407	+	0.970919i	$0.576953\pi$
$44$		0			0
$45$	1.06808	−	6.38557i	0.159220	−	0.951905i
$46$		0			0
$47$	−2.79826	+	8.61215i	−0.408168	+	1.25621i	0.510053	+	0.860143i	$0.329626\pi$
$47$	−2.79826	+	8.61215i	−0.408168	+	1.25621i	−0.918221	+	0.396068i	$0.870374\pi$
$48$		0			0
$49$	−4.71735	+	3.42736i	−0.673907	+	0.489622i
$50$		0			0
$51$	−1.42581	+	1.03591i	−0.199654	+	0.145057i
$52$		0			0
$53$	−3.81986	−	2.77529i	−0.524698	−	0.381216i	0.293673	−	0.955906i	$-0.405122\pi$
$53$	−3.81986	−	2.77529i	−0.524698	−	0.381216i	−0.818371	+	0.574690i	$0.805122\pi$
$54$		0			0
$55$	−7.61849	+	3.79916i	−1.02728	+	0.512279i
$56$		0			0
$57$	1.04217	−	0.338621i	0.138038	−	0.0448514i
$58$		0			0
$59$	3.05698	−	9.40843i	0.397985	−	1.22487i	−0.528627	−	0.848854i	$-0.677293\pi$
$59$	3.05698	−	9.40843i	0.397985	−	1.22487i	0.926612	−	0.376018i	$-0.122707\pi$
$60$		0			0
$61$	−2.05425	−	6.32232i	−0.263019	−	0.809490i	−0.992143	−	0.125108i	$-0.960072\pi$
$61$	−2.05425	−	6.32232i	−0.263019	−	0.809490i	0.729124	−	0.684382i	$-0.239928\pi$
$62$		0			0
$63$	3.20493	+	9.86376i	0.403783	+	1.24272i
$64$		0			0
$65$	10.9717	+	5.71045i	1.36087	+	0.708295i
$66$		0			0
$67$	−5.32921	−	3.87190i	−0.651067	−	0.473028i	0.212568	−	0.977146i	$-0.431817\pi$
$67$	−5.32921	−	3.87190i	−0.651067	−	0.473028i	−0.863634	+	0.504119i	$0.831817\pi$
$68$		0			0
$69$	0.163552	+	0.0531412i	0.0196893	+	0.00639745i
$70$		0			0
$71$	0.637848	+	0.877922i	0.0756986	+	0.104190i	0.845187	−	0.534470i	$-0.179489\pi$
$71$	0.637848	+	0.877922i	0.0756986	+	0.104190i	−0.769489	+	0.638660i	$0.779489\pi$
$72$		0			0
$73$		−	1.26023i		−	0.147498i	−0.997277	−	0.0737492i	$-0.976504\pi$
$73$		−	1.26023i		−	0.147498i	0.997277	−	0.0737492i	$-0.0234964\pi$
$74$		0			0
$75$	1.52916	+	0.526274i	0.176573	+	0.0607689i
$76$		0			0
$77$	8.01599	−	11.0331i	0.913507	−	1.25734i
$78$		0			0
$79$		−	1.60115i		−	0.180143i	−0.995935	−	0.0900715i	$-0.971290\pi$
$79$		−	1.60115i		−	0.180143i	0.995935	−	0.0900715i	$-0.0287096\pi$
$80$		0			0
$81$	8.06943			0.896604
$82$		0			0
$83$		−	2.18693i		−	0.240047i	−0.992771	−	0.120023i	$-0.961703\pi$
$83$		−	2.18693i		−	0.240047i	0.992771	−	0.120023i	$-0.0382969\pi$
$84$		0			0
$85$	5.43741	+	10.9037i	0.589770	+	1.18267i
$86$		0			0
$87$	−1.75656	+	2.41770i	−0.188323	+	0.259204i
$88$		0			0
$89$	2.46675	−	0.801496i	0.261475	−	0.0849584i	−0.175346	−	0.984507i	$-0.556104\pi$
$89$	2.46675	−	0.801496i	0.261475	−	0.0849584i	0.436821	+	0.899548i	$0.356104\pi$
$90$		0			0
$91$	−19.8140			−2.07708
$92$		0			0
$93$	−1.77217	+	1.28756i	−0.183766	+	0.133514i
$94$		0			0
$95$	−1.12033	−	7.49244i	−0.114944	−	0.768708i
$96$		0			0
$97$	−5.97081	−	4.33805i	−0.606244	−	0.440462i	0.241846	−	0.970315i	$-0.422247\pi$
$97$	−5.97081	−	4.33805i	−0.606244	−	0.440462i	−0.848090	+	0.529853i	$0.822247\pi$
$98$		0			0
$99$	−6.47940	−	8.91812i	−0.651204	−	0.896305i
$100$		0			0
$101$	11.0083	−	3.57682i	1.09537	−	0.355907i	0.295050	−	0.955482i	$-0.404664\pi$
$101$	11.0083	−	3.57682i	1.09537	−	0.355907i	0.800318	+	0.599575i	$0.204664\pi$
$102$		0			0
$103$	1.62343	−	0.527485i	0.159962	−	0.0519747i	−0.227942	−	0.973675i	$-0.573200\pi$
$103$	1.62343	−	0.527485i	0.159962	−	0.0519747i	0.387903	+	0.921700i	$0.373200\pi$
$104$		0			0
$105$	−2.56215	+	0.383115i	−0.250040	+	0.0373882i
$106$		0			0
$107$	−11.9301	+	3.87632i	−1.15332	+	0.374738i	−0.822394	−	0.568918i	$-0.807362\pi$
$107$	−11.9301	+	3.87632i	−1.15332	+	0.374738i	−0.330930	+	0.943655i	$0.607362\pi$
$108$		0			0
$109$			7.87682i			0.754462i	0.926119	+	0.377231i	$0.123124\pi$
$109$			7.87682i			0.754462i	−0.926119	+	0.377231i	$0.876876\pi$
$110$		0			0
$111$	−1.50364	+	2.06959i	−0.142719	+	0.196436i
$112$		0			0
$113$	−1.80397	−	2.48296i	−0.169704	−	0.233577i	0.715691	−	0.698417i	$-0.246112\pi$
$113$	−1.80397	−	2.48296i	−0.169704	−	0.233577i	−0.885395	+	0.464840i	$0.846112\pi$
$114$		0			0
$115$	0.548890	−	1.05460i	0.0511842	−	0.0983422i
$116$		0			0
$117$	−4.94917	+	15.2320i	−0.457551	+	1.40820i
$118$		0			0
$119$	−15.7907	−	11.4726i	−1.44753	−	1.05169i
$120$		0			0
$121$	−1.08001	+	3.32394i	−0.0981831	+	0.302176i
$122$		0			0
$123$	−0.613039	−	1.97820i	−0.0552759	−	0.178369i
$124$		0			0
$125$	5.33256	−	9.82669i	0.476959	−	0.878926i
$126$		0			0
$127$	−4.52109	+	6.22275i	−0.401182	+	0.552180i	−0.961040	−	0.276409i	$-0.910856\pi$
$127$	−4.52109	+	6.22275i	−0.401182	+	0.552180i	0.559858	+	0.828588i	$0.310856\pi$
$128$		0			0
$129$	−0.291842	−	0.0948251i	−0.0256952	−	0.00834888i
$130$		0			0
$131$	−15.3480	+	11.1509i	−1.34096	+	0.974263i	−0.341549	+	0.939864i	$0.610952\pi$
$131$	−15.3480	+	11.1509i	−1.34096	+	0.974263i	−0.999408	+	0.0343989i	$0.989048\pi$
$132$		0			0
$133$	7.13326	+	9.81809i	0.618532	+	0.851337i
$134$		0			0
$135$	−0.703398	+	4.20530i	−0.0605388	+	0.361935i
$136$		0			0
$137$	0.617567			0.0527623			0.0263811	−	0.999652i	$-0.491602\pi$
$137$	0.617567			0.0527623			0.0263811	+	0.999652i	$0.491602\pi$
$138$		0			0
$139$	−5.69838	−	17.5378i	−0.483330	−	1.48754i	−0.834385	−	0.551182i	$-0.814177\pi$
$139$	−5.69838	−	17.5378i	−0.483330	−	1.48754i	0.351055	−	0.936355i	$-0.385823\pi$
$140$		0			0
$141$	0.905063	−	2.78550i	0.0762201	−	0.234581i
$142$		0			0
$143$	20.0290	−	6.50781i	1.67491	−	0.544210i
$144$		0			0
$145$	14.4821	+	14.7349i	1.20268	+	1.22367i
$146$		0			0
$147$	1.52577	−	1.10854i	0.125844	−	0.0914307i
$148$		0			0
$149$	−13.8926	+	19.1216i	−1.13813	+	1.56650i	−0.366510	+	0.930414i	$0.619447\pi$
$149$	−13.8926	+	19.1216i	−1.13813	+	1.56650i	−0.771619	+	0.636085i	$0.780553\pi$
$150$		0			0
$151$	14.4549	+	4.69668i	1.17632	+	0.382210i	0.830999	−	0.556274i	$-0.187769\pi$
$151$	14.4549	+	4.69668i	1.17632	+	0.382210i	0.345323	+	0.938484i	$0.387769\pi$
$152$		0			0
$153$	−12.7637	+	9.27340i	−1.03189	+	0.749710i
$154$		0			0
$155$	6.75827	+	13.5524i	0.542838	+	1.08856i
$156$		0			0
$157$	6.35713	+	19.5652i	0.507354	+	1.56148i	0.796776	+	0.604275i	$0.206537\pi$
$157$	6.35713	+	19.5652i	0.507354	+	1.56148i	−0.289422	+	0.957202i	$0.593463\pi$
$158$		0			0
$159$	1.23549	+	0.897636i	0.0979807	+	0.0711871i
$160$		0			0
$161$			1.90453i			0.150098i
$162$		0			0
$163$			15.6125i			1.22287i	0.791296	+	0.611433i	$0.209407\pi$
$163$			15.6125i			1.22287i	−0.791296	+	0.611433i	$0.790593\pi$
$164$		0			0
$165$	2.46411	−	1.22879i	0.191831	−	0.0956615i
$166$		0			0
$167$	−18.8443			−1.45821			−0.729107	−	0.684400i	$-0.760064\pi$
$167$	−18.8443			−1.45821			−0.729107	+	0.684400i	$0.760064\pi$
$168$		0			0
$169$	−14.2367	−	10.3436i	−1.09513	−	0.795661i
$170$		0			0
$171$	9.32938	−	3.03130i	0.713436	−	0.231809i
$172$		0			0
$173$		−	13.5531i		−	1.03043i	−0.857062	−	0.515213i	$-0.827713\pi$
$173$		−	13.5531i		−	1.03043i	0.857062	−	0.515213i	$-0.172287\pi$
$174$		0			0
$175$	−0.309856	+	17.9075i	−0.0234229	+	1.35368i
$176$		0			0
$177$	−0.988746	+	3.04305i	−0.0743187	+	0.228729i
$178$		0			0
$179$	5.15096	−	7.08969i	0.385001	−	0.529908i	−0.571900	−	0.820323i	$-0.693793\pi$
$179$	5.15096	−	7.08969i	0.385001	−	0.529908i	0.956901	+	0.290415i	$0.0937934\pi$
$180$		0			0
$181$	4.48481	+	6.17280i	0.333353	+	0.458821i	0.942485	−	0.334248i	$-0.108482\pi$
$181$	4.48481	+	6.17280i	0.333353	+	0.458821i	−0.609132	+	0.793069i	$0.708482\pi$
$182$		0			0
$183$	0.664422	+	2.04488i	0.0491155	+	0.151162i
$184$		0			0
$185$	12.3969	+	12.6133i	0.911442	+	0.927349i
$186$		0			0
$187$	19.7301	+	6.41069i	1.44281	+	0.468796i
$188$		0			0
$189$	−2.11065	−	6.49591i	−0.153527	−	0.472508i
$190$		0			0
$191$		−	2.59195i		−	0.187547i	−0.995594	−	0.0937736i	$-0.970107\pi$
$191$		−	2.59195i		−	0.187547i	0.995594	−	0.0937736i	$-0.0298930\pi$
$192$		0			0
$193$	12.6123	+	9.16337i	0.907853	+	0.659594i	0.940471	−	0.339874i	$-0.110384\pi$
$193$	12.6123	+	9.16337i	0.907853	+	0.659594i	−0.0326179	+	0.999468i	$0.510384\pi$
$194$		0			0
$195$	−3.54867	−	1.84698i	−0.254126	−	0.132265i
$196$		0			0
$197$	4.15387	+	5.71732i	0.295951	+	0.407342i	0.930936	−	0.365183i	$-0.118994\pi$
$197$	4.15387	+	5.71732i	0.295951	+	0.407342i	−0.634985	+	0.772525i	$0.718994\pi$
$198$		0			0
$199$	−4.99884	−	1.62422i	−0.354358	−	0.115138i	0.126428	−	0.991976i	$-0.459649\pi$
$199$	−4.99884	−	1.62422i	−0.354358	−	0.115138i	−0.480786	+	0.876838i	$0.659649\pi$
$200$		0			0
$201$	1.72367	+	1.25232i	0.121578	+	0.0883319i
$202$		0			0
$203$	−31.4767	−	10.2274i	−2.20923	−	0.717822i
$204$		0			0
$205$	−14.1880	+	1.92394i	−0.990931	+	0.134373i
$206$		0			0
$207$	1.46410	+	0.475715i	0.101762	+	0.0330645i
$208$		0			0
$209$	−10.4353	−	7.58172i	−0.721827	−	0.524438i
$210$		0			0
$211$	13.5045	+	4.38787i	0.929687	+	0.302074i	0.734435	−	0.678679i	$-0.237447\pi$
$211$	13.5045	+	4.38787i	0.929687	+	0.302074i	0.195253	+	0.980753i	$0.437447\pi$
$212$		0			0
$213$	−0.206304	−	0.283954i	−0.0141357	−	0.0194562i
$214$		0			0
$215$	−0.979437	+	1.88183i	−0.0667970	+	0.128340i
$216$		0			0
$217$	−19.6266	−	14.2595i	−1.33234	−	0.968001i
$218$		0			0
$219$			0.407606i			0.0275434i
$220$		0			0
$221$	−9.31406	−	28.6657i	−0.626532	−	1.92827i
$222$		0			0
$223$	10.8302	+	3.51893i	0.725241	+	0.235645i	0.648294	−	0.761390i	$-0.275483\pi$
$223$	10.8302	+	3.51893i	0.725241	+	0.235645i	0.0769470	+	0.997035i	$0.475483\pi$
$224$		0			0
$225$	13.6889	+	4.71115i	0.912595	+	0.314077i
$226$		0			0
$227$	3.31590	+	10.2053i	0.220084	+	0.677349i	0.998753	+	0.0499144i	$0.0158949\pi$
$227$	3.31590	+	10.2053i	0.220084	+	0.677349i	−0.778670	+	0.627434i	$0.784105\pi$
$228$		0			0
$229$	−3.56218	−	4.90292i	−0.235395	−	0.323994i	0.674934	−	0.737878i	$-0.264172\pi$
$229$	−3.56218	−	4.90292i	−0.235395	−	0.323994i	−0.910330	+	0.413884i	$0.864172\pi$
$230$		0			0
$231$	−2.59268	+	3.56852i	−0.170586	+	0.234791i
$232$		0			0
$233$	3.19060	−	9.81965i	0.209023	−	0.643307i	−0.790501	−	0.612461i	$-0.790180\pi$
$233$	3.19060	−	9.81965i	0.209023	−	0.643307i	0.999524	−	0.0308463i	$-0.00982023\pi$
$234$		0			0
$235$	−17.9612	−	9.34829i	−1.17166	−	0.609816i
$236$		0			0
$237$			0.517872i			0.0336394i
$238$		0			0
$239$	−19.7473	+	6.41627i	−1.27734	+	0.415034i	−0.867644	−	0.497186i	$-0.834367\pi$
$239$	−19.7473	+	6.41627i	−1.27734	+	0.415034i	−0.409700	+	0.912220i	$0.634367\pi$
$240$		0			0
$241$	−12.5913	−	9.14812i	−0.811078	−	0.589282i	0.103065	−	0.994675i	$-0.467135\pi$
$241$	−12.5913	−	9.14812i	−0.811078	−	0.589282i	−0.914143	+	0.405392i	$0.867135\pi$
$242$		0			0
$243$	−8.33035			−0.534392
$244$		0			0
$245$	−5.81861	−	11.6681i	−0.371737	−	0.745448i
$246$		0			0
$247$			18.7406i			1.19244i
$248$		0			0
$249$			0.707337i			0.0448257i
$250$		0			0
$251$	14.0545	+	10.2112i	0.887112	+	0.644525i	0.935123	−	0.354322i	$-0.115288\pi$
$251$	14.0545	+	10.2112i	0.887112	+	0.644525i	−0.0480113	+	0.998847i	$0.515288\pi$
$252$		0			0
$253$	−0.625532	−	1.92519i	−0.0393268	−	0.121036i
$254$		0			0
$255$	−1.75867	−	3.52667i	−0.110132	−	0.220849i
$256$		0			0
$257$	16.9702	−	12.3295i	1.05857	−	0.769096i	0.0847466	−	0.996403i	$-0.472992\pi$
$257$	16.9702	−	12.3295i	1.05857	−	0.769096i	0.973823	+	0.227307i	$0.0729919\pi$
$258$		0			0
$259$	−26.9445	−	8.75480i	−1.67425	−	0.543997i
$260$		0			0
$261$	−15.7245	+	21.6430i	−0.973325	+	1.33967i
$262$		0			0
$263$	−0.387478	+	0.281519i	−0.0238929	+	0.0173592i	−0.599668	−	0.800249i	$-0.704701\pi$
$263$	−0.387478	+	0.281519i	−0.0238929	+	0.0173592i	0.575775	+	0.817608i	$0.304701\pi$
$264$		0			0
$265$	7.52982	−	7.40066i	0.462553	−	0.454619i
$266$		0			0
$267$	−0.797842	+	0.259235i	−0.0488271	+	0.0158649i
$268$		0			0
$269$	4.63996	−	14.2803i	0.282903	−	0.870687i	−0.704116	−	0.710085i	$-0.748657\pi$
$269$	4.63996	−	14.2803i	0.282903	−	0.870687i	0.987019	−	0.160602i	$-0.0513435\pi$
$270$		0			0
$271$	7.22729	+	22.2433i	0.439027	+	1.35119i	0.888903	+	0.458095i	$0.151468\pi$
$271$	7.22729	+	22.2433i	0.439027	+	1.35119i	−0.449876	+	0.893091i	$0.648532\pi$
$272$		0			0
$273$	6.40862			0.387867
$274$		0			0
$275$	−5.56840	−	18.2035i	−0.335787	−	1.09771i
$276$		0			0
$277$	−7.21267	−	9.92739i	−0.433367	−	0.596479i	0.535355	−	0.844627i	$-0.320178\pi$
$277$	−7.21267	−	9.92739i	−0.433367	−	0.596479i	−0.968722	+	0.248148i	$0.920178\pi$
$278$		0			0
$279$	−15.8643	+	11.5261i	−0.949772	+	0.690050i
$280$		0			0
$281$	−1.94205	−	0.631011i	−0.115853	−	0.0376430i	0.250517	−	0.968112i	$-0.419399\pi$
$281$	−1.94205	−	0.631011i	−0.115853	−	0.0376430i	−0.366370	+	0.930469i	$0.619399\pi$
$282$		0			0
$283$	−13.9900	+	19.2556i	−0.831620	+	1.14463i	0.156000	+	0.987757i	$0.450140\pi$
$283$	−13.9900	+	19.2556i	−0.831620	+	1.14463i	−0.987619	+	0.156869i	$0.949860\pi$
$284$		0			0
$285$	0.362359	+	2.42334i	0.0214643	+	0.143546i
$286$		0			0
$287$	18.7380	−	13.2271i	1.10607	−	0.780769i
$288$		0			0
$289$	3.92178	−	12.0700i	0.230693	−	0.709999i
$290$		0			0
$291$	1.93119	+	1.40309i	0.113208	+	0.0822507i
$292$		0			0
$293$	−2.15585	+	6.63502i	−0.125946	+	0.387622i	−0.994072	−	0.108722i	$-0.965324\pi$
$293$	−2.15585	+	6.63502i	−0.125946	+	0.387622i	0.868126	+	0.496343i	$0.165324\pi$
$294$		0			0
$295$	19.6219	+	10.2126i	1.14243	+	0.594603i
$296$		0			0
$297$	4.26709	+	5.87314i	0.247602	+	0.340794i
$298$		0			0
$299$	−1.72870	+	2.37935i	−0.0999734	+	0.137602i
$300$		0			0
$301$		−	3.39843i		−	0.195882i
$302$		0			0
$303$	−3.56051	+	1.15688i	−0.204546	+	0.0664610i
$304$		0			0
$305$	14.7012	−	2.19825i	0.841789	−	0.125872i
$306$		0			0
$307$	19.0901	−	6.20273i	1.08953	−	0.354009i	0.291463	−	0.956582i	$-0.405858\pi$
$307$	19.0901	−	6.20273i	1.08953	−	0.354009i	0.798064	+	0.602573i	$0.205858\pi$
$308$		0			0
$309$	−0.525080	+	0.170609i	−0.0298708	+	0.00970561i
$310$		0			0
$311$	12.1391	+	16.7080i	0.688343	+	0.947422i	0.999996	−	0.00277352i	$-0.000882839\pi$
$311$	12.1391	+	16.7080i	0.688343	+	0.947422i	−0.311654	+	0.950196i	$0.600883\pi$
$312$		0			0
$313$	−8.34400	−	6.06227i	−0.471631	−	0.342660i	0.326446	−	0.945216i	$-0.394149\pi$
$313$	−8.34400	−	6.06227i	−0.471631	−	0.342660i	−0.798077	+	0.602556i	$0.794149\pi$
$314$		0			0
$315$	−22.9361	+	3.42960i	−1.29230	+	0.193236i
$316$		0			0
$317$	18.2630	−	13.2688i	1.02575	−	0.745252i	0.0582978	−	0.998299i	$-0.481433\pi$
$317$	18.2630	−	13.2688i	1.02575	−	0.745252i	0.967454	+	0.253047i	$0.0814327\pi$
$318$		0			0
$319$	35.1772			1.96955
$320$		0			0
$321$	3.85864	−	1.25375i	0.215368	−	0.0699775i
$322$		0			0
$323$	−10.8511	+	14.9352i	−0.603769	+	0.831016i
$324$		0			0
$325$	−16.6414	+	22.0908i	−0.923097	+	1.22538i
$326$		0			0
$327$		−	2.54766i		−	0.140886i
$328$		0			0
$329$	32.4366			1.78829
$330$		0			0
$331$		−	26.4785i		−	1.45539i	−0.685900	−	0.727696i	$-0.740591\pi$
$331$		−	26.4785i		−	1.45539i	0.685900	−	0.727696i	$-0.259409\pi$
$332$		0			0
$333$	−13.4605	+	18.5267i	−0.737628	+	1.01526i
$334$		0			0
$335$	10.5051	−	10.3249i	0.573955	−	0.564109i
$336$		0			0
$337$		−	1.99129i		−	0.108472i	−0.998528	−	0.0542362i	$-0.982728\pi$
$337$		−	1.99129i		−	0.108472i	0.998528	−	0.0542362i	$-0.0172724\pi$
$338$		0			0
$339$	0.583474	+	0.803083i	0.0316900	+	0.0436175i
$340$		0			0
$341$	24.5229	+	7.96799i	1.32799	+	0.431491i
$342$		0			0
$343$	−3.38778	−	2.46136i	−0.182923	−	0.132901i
$344$		0			0
$345$	−0.177532	+	0.341099i	−0.00955800	+	0.0183642i
$346$		0			0
$347$	−9.26301	−	28.5086i	−0.497265	−	1.53042i	−0.813397	−	0.581708i	$-0.802385\pi$
$347$	−9.26301	−	28.5086i	−0.497265	−	1.53042i	0.316133	−	0.948715i	$-0.397615\pi$
$348$		0			0
$349$	3.60942	+	11.1087i	0.193208	+	0.594633i	0.999993	+	0.00378744i	$0.00120558\pi$
$349$	3.60942	+	11.1087i	0.193208	+	0.594633i	−0.806785	+	0.590845i	$0.798794\pi$
$350$		0			0
$351$	3.25934	−	10.0312i	0.173971	−	0.535427i
$352$		0			0
$353$	14.7171	−	4.78187i	0.783312	−	0.254513i	0.110058	−	0.993925i	$-0.464896\pi$
$353$	14.7171	−	4.78187i	0.783312	−	0.254513i	0.673254	+	0.739412i	$0.264896\pi$
$354$		0			0
$355$	−2.17149	+	1.08287i	−0.115251	+	0.0574728i
$356$		0			0
$357$	5.10731	+	3.71068i	0.270308	+	0.196390i
$358$		0			0
$359$	2.22246	−	1.61471i	0.117297	−	0.0852211i	−0.527590	−	0.849499i	$-0.676904\pi$
$359$	2.22246	−	1.61471i	0.117297	−	0.0852211i	0.644887	+	0.764278i	$0.276904\pi$
$360$		0			0
$361$	−6.08514	+	4.42111i	−0.320270	+	0.232690i
$362$		0			0
$363$	0.349318	−	1.07509i	0.0183344	−	0.0564276i
$364$		0			0
$365$	2.77934	+	0.464885i	0.145477	+	0.0243332i
$366$		0			0
$367$	1.16714	+	0.379228i	0.0609243	+	0.0197955i	0.339321	−	0.940671i	$-0.389803\pi$
$367$	1.16714	+	0.379228i	0.0609243	+	0.0197955i	−0.278396	+	0.960466i	$0.589803\pi$
$368$		0			0
$369$	−5.48786	−	17.7087i	−0.285687	−	0.921877i
$370$		0			0
$371$	−5.22639	+	16.0852i	−0.271341	+	0.835101i
$372$		0			0
$373$	17.1372	−	23.5873i	0.887329	−	1.22130i	−0.0870073	−	0.996208i	$-0.527730\pi$
$373$	17.1372	−	23.5873i	0.887329	−	1.22130i	0.974337	−	0.225096i	$-0.0722697\pi$
$374$		0			0
$375$	−1.72475	+	3.17833i	−0.0890659	+	0.164128i
$376$		0			0
$377$	−30.0410	−	41.3479i	−1.54719	−	2.12953i
$378$		0			0
$379$	25.0058	−	18.1678i	1.28446	−	0.933218i	0.284786	−	0.958591i	$-0.408077\pi$
$379$	25.0058	−	18.1678i	1.28446	−	0.933218i	0.999678	+	0.0253732i	$0.00807740\pi$
$380$		0			0
$381$	1.46229	−	2.01268i	0.0749156	−	0.103113i
$382$		0			0
$383$	24.4170			1.24765			0.623826	−	0.781563i	$-0.285577\pi$
$383$	24.4170			1.24765			0.623826	+	0.781563i	$0.285577\pi$
$384$		0			0
$385$	21.3756	+	21.7487i	1.08940	+	1.10842i
$386$		0			0
$387$	−2.61254	−	0.848864i	−0.132803	−	0.0431502i
$388$		0			0
$389$	2.02804	+	6.24168i	0.102826	+	0.316466i	0.989214	−	0.146477i	$-0.0467935\pi$
$389$	2.02804	+	6.24168i	0.102826	+	0.316466i	−0.886388	+	0.462943i	$0.846793\pi$
$390$		0			0
$391$	−2.75536	+	0.895269i	−0.139344	+	0.0452757i
$392$		0			0
$393$	4.96412	−	3.60664i	0.250407	−	0.181931i
$394$		0			0
$395$	3.53122	+	0.590647i	0.177675	+	0.0297187i
$396$		0			0
$397$	−0.884344	+	2.72173i	−0.0443839	+	0.136600i	−0.970793	−	0.239919i	$-0.922879\pi$
$397$	−0.884344	+	2.72173i	−0.0443839	+	0.136600i	0.926409	+	0.376519i	$0.122879\pi$
$398$		0			0
$399$	−2.30717	−	3.17555i	−0.115503	−	0.158976i
$400$		0			0
$401$	2.33669			0.116689			0.0583443	−	0.998297i	$-0.481418\pi$
$401$	2.33669			0.116689			0.0583443	+	0.998297i	$0.481418\pi$
$402$		0			0
$403$	−11.5767	−	35.6293i	−0.576674	−	1.77482i
$404$		0			0
$405$	−2.97673	+	17.7966i	−0.147915	+	0.884318i
$406$		0			0
$407$	30.1123			1.49261
$408$		0			0
$409$	−4.06167			−0.200837			−0.100418	−	0.994945i	$-0.532018\pi$
$409$	−4.06167			−0.200837			−0.100418	+	0.994945i	$0.532018\pi$
$410$		0			0
$411$	−0.199745			−0.00985268
$412$		0			0
$413$	−35.4356			−1.74367
$414$		0			0
$415$	4.82312	+	0.806737i	0.236758	+	0.0396012i
$416$		0			0
$417$	1.84307	+	5.67240i	0.0902557	+	0.277779i
$418$		0			0
$419$	8.47842			0.414198			0.207099	−	0.978320i	$-0.433598\pi$
$419$	8.47842			0.414198			0.207099	+	0.978320i	$0.433598\pi$
$420$		0			0
$421$	−20.5080	−	28.2269i	−0.999501	−	1.37569i	−0.925631	−	0.378427i	$-0.876465\pi$
$421$	−20.5080	−	28.2269i	−0.999501	−	1.37569i	−0.0738694	−	0.997268i	$-0.523535\pi$
$422$		0			0
$423$	8.10204	−	24.9355i	0.393935	−	1.21241i
$424$		0			0
$425$	−26.0531	+	7.96956i	−1.26376	+	0.386581i
$426$		0			0
$427$	−19.2645	+	13.9965i	−0.932274	+	0.677336i
$428$		0			0
$429$	−6.47814	+	2.10488i	−0.312768	+	0.101624i
$430$		0			0
$431$	−5.42031	−	16.6820i	−0.261087	−	0.803543i	−0.992569	−	0.121682i	$-0.961171\pi$
$431$	−5.42031	−	16.6820i	−0.261087	−	0.803543i	0.731482	−	0.681861i	$-0.238829\pi$
$432$		0			0
$433$	31.1477	+	10.1205i	1.49686	+	0.486361i	0.939101	−	0.343640i	$-0.111660\pi$
$433$	31.1477	+	10.1205i	1.49686	+	0.486361i	0.557763	+	0.830001i	$0.311660\pi$
$434$		0			0
$435$	−4.68408	−	4.76583i	−0.224585	−	0.228504i
$436$		0			0
$437$	1.80135			0.0861702
$438$		0			0
$439$	−19.0863	+	26.2701i	−0.910941	+	1.25380i	0.0559035	+	0.998436i	$0.482196\pi$
$439$	−19.0863	+	26.2701i	−0.910941	+	1.25380i	−0.966844	+	0.255366i	$0.917804\pi$
$440$		0			0
$441$	13.6586	−	9.92352i	0.650407	−	0.472549i
$442$		0			0
$443$	−9.95829	−	13.7064i	−0.473133	−	0.651211i	0.504034	−	0.863684i	$-0.331848\pi$
$443$	−9.95829	−	13.7064i	−0.473133	−	0.651211i	−0.977167	+	0.212472i	$0.931848\pi$
$444$		0			0
$445$	0.857683	+	5.73591i	0.0406581	+	0.271908i
$446$		0			0
$447$	4.49341	−	6.18465i	0.212531	−	0.292524i
$448$		0			0
$449$	−3.22139	+	9.91442i	−0.152027	+	0.467891i	−0.997848	−	0.0655767i	$-0.979111\pi$
$449$	−3.22139	+	9.91442i	−0.152027	+	0.467891i	0.845821	+	0.533467i	$0.179111\pi$
$450$		0			0
$451$	−14.5969	+	19.5250i	−0.687343	+	0.919394i
$452$		0			0
$453$	−4.67526	−	1.51909i	−0.219663	−	0.0713729i
$454$		0			0
$455$	7.30921	−	43.6985i	0.342661	−	2.04862i
$456$		0			0
$457$	−11.3384	+	34.8962i	−0.530390	+	1.63237i	0.223014	+	0.974815i	$0.428411\pi$
$457$	−11.3384	+	34.8962i	−0.530390	+	1.63237i	−0.753404	+	0.657558i	$0.771589\pi$
$458$		0			0
$459$	8.40572	−	6.10711i	0.392345	−	0.285056i
$460$		0			0
$461$	−20.2256	+	14.6948i	−0.942000	+	0.684403i	−0.948901	−	0.315573i	$-0.897803\pi$
$461$	−20.2256	+	14.6948i	−0.942000	+	0.684403i	0.00690089	+	0.999976i	$0.497803\pi$
$462$		0			0
$463$	13.3896	+	9.72815i	0.622270	+	0.452105i	0.853714	−	0.520743i	$-0.174345\pi$
$463$	13.3896	+	9.72815i	0.622270	+	0.452105i	−0.231444	+	0.972848i	$0.574345\pi$
$464$		0			0
$465$	−2.18589	−	4.38337i	−0.101368	−	0.203274i
$466$		0			0
$467$	−34.9472	+	11.3550i	−1.61716	+	0.525449i	−0.971270	−	0.237979i	$-0.923515\pi$
$467$	−34.9472	+	11.3550i	−1.61716	+	0.525449i	−0.645894	+	0.763427i	$0.723515\pi$
$468$		0			0
$469$	−7.29151	+	22.4410i	−0.336691	+	1.03623i
$470$		0			0
$471$	−2.05614	−	6.32815i	−0.0947420	−	0.291586i
$472$		0			0
$473$	1.11620	+	3.43530i	0.0513228	+	0.157955i
$474$		0			0
$475$	16.9373	+	0.293069i	0.777138	+	0.0134469i
$476$		0			0
$477$	11.0600	+	8.03554i	0.506402	+	0.367922i
$478$		0			0
$479$	18.7223	+	6.08324i	0.855443	+	0.277950i	0.703724	−	0.710473i	$-0.251519\pi$
$479$	18.7223	+	6.08324i	0.855443	+	0.277950i	0.151719	+	0.988424i	$0.451519\pi$
$480$		0			0
$481$	−25.7156	−	35.3945i	−1.17253	−	1.61385i
$482$		0			0
$483$		−	0.615998i		−	0.0280289i
$484$		0			0
$485$	11.7698	−	11.5679i	0.534441	−	0.525273i
$486$		0			0
$487$	14.1204	−	19.4351i	0.639859	−	0.880690i	−0.358749	−	0.933434i	$-0.616797\pi$
$487$	14.1204	−	19.4351i	0.639859	−	0.880690i	0.998608	+	0.0527440i	$0.0167967\pi$
$488$		0			0
$489$		−	5.04968i		−	0.228355i
$490$		0			0
$491$	31.2785			1.41158			0.705788	−	0.708423i	$-0.250593\pi$
$491$	31.2785			1.41158			0.705788	+	0.708423i	$0.250593\pi$
$492$		0			0
$493$		−	50.3461i		−	2.26748i
$494$		0			0
$495$	22.0585	−	11.0000i	0.991455	−	0.494415i
$496$		0			0
$497$	2.28479	−	3.14475i	0.102487	−	0.141061i
$498$		0			0
$499$	7.75904	−	2.52107i	0.347342	−	0.112858i	−0.130150	−	0.991494i	$-0.541546\pi$
$499$	7.75904	−	2.52107i	0.347342	−	0.112858i	0.477492	+	0.878636i	$0.341546\pi$
$500$		0			0
$501$	6.09496			0.272303
$502$		0			0
$503$	11.8321	−	8.59652i	0.527567	−	0.383300i	−0.291880	−	0.956455i	$-0.594281\pi$
$503$	11.8321	−	8.59652i	0.527567	−	0.383300i	0.819447	+	0.573155i	$0.194281\pi$
$504$		0			0
$505$	3.82756	+	25.5975i	0.170324	+	1.13907i
$506$		0			0
$507$	4.60470	+	3.34551i	0.204502	+	0.148579i
$508$		0			0
$509$	10.4425	+	14.3728i	0.462854	+	0.637064i	0.975098	−	0.221777i	$-0.0711856\pi$
$509$	10.4425	+	14.3728i	0.462854	+	0.637064i	−0.512244	+	0.858840i	$0.671186\pi$
$510$		0			0
$511$	−4.29323	+	1.39496i	−0.189921	+	0.0617092i
$512$		0			0
$513$	−6.14398	+	1.99630i	−0.271263	+	0.0881388i
$514$		0			0
$515$	0.564463	+	3.77495i	0.0248732	+	0.166344i
$516$		0			0
$517$	−32.7884	+	10.6536i	−1.44203	+	0.468545i
$518$		0			0
$519$			4.38360i			0.192419i
$520$		0			0
$521$	15.9630	−	21.9711i	0.699350	−	0.962573i	−0.300611	−	0.953747i	$-0.597191\pi$
$521$	15.9630	−	21.9711i	0.699350	−	0.962573i	0.999961	−	0.00882616i	$-0.00280949\pi$
$522$		0			0
$523$	−15.6851	−	21.5887i	−0.685861	−	0.944006i	0.314125	−	0.949382i	$-0.398289\pi$
$523$	−15.6851	−	21.5887i	−0.685861	−	0.944006i	−0.999986	+	0.00537534i	$0.998289\pi$
$524$		0			0
$525$	0.100219	−	5.79197i	0.00437392	−	0.252782i
$526$		0			0
$527$	11.4039	−	35.0976i	0.496761	−	1.52887i
$528$		0			0
$529$	−18.3787	−	13.3529i	−0.799073	−	0.580561i
$530$		0			0
$531$	−8.85115	+	27.2410i	−0.384107	+	1.18216i
$532$		0			0
$533$	35.4156	+	0.483374i	1.53402	+	0.0209373i
$534$		0			0
$535$	−4.14806	−	27.7409i	−0.179336	−	1.19934i
$536$		0			0
$537$	−1.66602	+	2.29308i	−0.0718940	+	0.0989536i
$538$		0			0
$539$	−21.1133	−	6.86012i	−0.909414	−	0.295486i
$540$		0			0
$541$	28.9322	−	21.0205i	1.24389	−	0.903740i	0.246041	−	0.969260i	$-0.420870\pi$
$541$	28.9322	−	21.0205i	1.24389	−	0.903740i	0.997851	+	0.0655192i	$0.0208704\pi$
$542$		0			0
$543$	−1.45056	−	1.99652i	−0.0622494	−	0.0856790i
$544$		0			0
$545$	−17.3718	−	2.90568i	−0.744125	−	0.124466i
$546$		0			0
$547$	−4.34916			−0.185957			−0.0929783	−	0.995668i	$-0.529639\pi$
$547$	−4.34916			−0.185957			−0.0929783	+	0.995668i	$0.529639\pi$
$548$		0			0
$549$	5.94784	+	18.3056i	0.253848	+	0.781262i
$550$		0			0
$551$	−9.67330	+	29.7714i	−0.412097	+	1.26830i
$552$		0			0
$553$	−5.45465	+	1.77232i	−0.231955	+	0.0753669i
$554$		0			0
$555$	−4.00965	−	4.07963i	−0.170200	−	0.173171i
$556$		0			0
$557$	−4.75515	+	3.45482i	−0.201482	+	0.146385i	−0.683952	−	0.729527i	$-0.739740\pi$
$557$	−4.75515	+	3.45482i	−0.201482	+	0.146385i	0.482469	+	0.875913i	$0.339740\pi$
$558$		0			0
$559$	3.08469	−	4.24571i	0.130468	−	0.179574i
$560$		0			0
$561$	−6.38146	−	2.07346i	−0.269426	−	0.0875417i
$562$		0			0
$563$	−26.1178	+	18.9757i	−1.10073	+	0.799729i	−0.981179	−	0.193099i	$-0.938146\pi$
$563$	−26.1178	+	18.9757i	−1.10073	+	0.799729i	−0.119553	+	0.992828i	$0.538146\pi$
$564$		0			0
$565$	6.14145	−	3.06260i	0.258373	−	0.128844i
$566$		0			0
$567$	−8.93213	−	27.4903i	−0.375114	−	1.15448i
$568$		0			0
$569$	11.4547	+	8.32230i	0.480204	+	0.348889i	0.801405	−	0.598122i	$-0.204086\pi$
$569$	11.4547	+	8.32230i	0.480204	+	0.348889i	−0.321200	+	0.947011i	$0.604086\pi$
$570$		0			0
$571$			11.4233i			0.478051i	0.971013	+	0.239025i	$0.0768279\pi$
$571$			11.4233i			0.478051i	−0.971013	+	0.239025i	$0.923172\pi$
$572$		0			0
$573$			0.838337i			0.0350220i
$574$		0			0
$575$	2.12337	+	1.59957i	0.0885508	+	0.0667067i
$576$		0			0
$577$	−32.5144			−1.35359			−0.676796	−	0.736171i	$-0.736632\pi$
$577$	−32.5144			−1.35359			−0.676796	+	0.736171i	$0.736632\pi$
$578$		0			0
$579$	−4.07930	−	2.96379i	−0.169530	−	0.123171i
$580$		0			0
$581$	−7.45025	+	2.42073i	−0.309088	+	0.100429i
$582$		0			0
$583$		−	17.9762i		−	0.744500i
$584$		0			0
$585$	−31.7674	−	16.5340i	−1.31342	−	0.683596i
$586$		0			0
$587$	−8.54007	+	26.2836i	−0.352486	+	1.08484i	0.604966	+	0.796251i	$0.293187\pi$
$587$	−8.54007	+	26.2836i	−0.352486	+	1.08484i	−0.957453	+	0.288590i	$0.906813\pi$
$588$		0			0
$589$	−13.4870	+	18.5633i	−0.555723	+	0.764887i
$590$		0			0
$591$	−1.34352	−	1.84920i	−0.0552651	−	0.0760659i
$592$		0			0
$593$	11.7760	+	36.2428i	0.483583	+	1.48831i	0.834023	+	0.551730i	$0.186032\pi$
$593$	11.7760	+	36.2428i	0.483583	+	1.48831i	−0.350440	+	0.936585i	$0.613968\pi$
$594$		0			0
$595$	31.1270	−	30.5931i	1.27608	−	1.25419i
$596$		0			0
$597$	1.61682	+	0.525335i	0.0661719	+	0.0215005i
$598$		0			0
$599$	2.49613	+	7.68231i	0.101989	+	0.313891i	0.989012	−	0.147835i	$-0.0472305\pi$
$599$	2.49613	+	7.68231i	0.101989	+	0.313891i	−0.887023	+	0.461726i	$0.847230\pi$
$600$		0			0
$601$			20.0945i			0.819673i	0.912159	+	0.409837i	$0.134414\pi$
$601$			20.0945i			0.819673i	−0.912159	+	0.409837i	$0.865586\pi$
$602$		0			0
$603$	15.4301	+	11.2106i	0.628364	+	0.456533i
$604$		0			0
$605$	−6.93231	−	3.60806i	−0.281839	−	0.146689i
$606$		0			0
$607$	24.3362	+	33.4959i	0.987777	+	1.35956i	0.932533	+	0.361085i	$0.117594\pi$
$607$	24.3362	+	33.4959i	0.987777	+	1.35956i	0.0552439	+	0.998473i	$0.482406\pi$
$608$		0			0
$609$	10.1808	+	3.30793i	0.412545	+	0.134044i
$610$		0			0
$611$	40.5234	+	29.4420i	1.63940	+	1.19110i
$612$		0			0
$613$	43.0744	+	13.9957i	1.73976	+	0.565282i	0.994802	−	0.101828i	$-0.0324692\pi$
$613$	43.0744	+	13.9957i	1.73976	+	0.565282i	0.744959	+	0.667111i	$0.232469\pi$
$614$		0			0
$615$	4.58893	−	0.622274i	0.185044	−	0.0250925i
$616$		0			0
$617$	1.25193	+	0.406777i	0.0504008	+	0.0163762i	0.334109	−	0.942534i	$-0.391565\pi$
$617$	1.25193	+	0.406777i	0.0504008	+	0.0163762i	−0.283708	+	0.958911i	$0.591565\pi$
$618$		0			0
$619$	26.3363	+	19.1345i	1.05855	+	0.769079i	0.973819	−	0.227325i	$-0.0729980\pi$
$619$	26.3363	+	19.1345i	1.05855	+	0.769079i	0.0847277	+	0.996404i	$0.472998\pi$
$620$		0			0
$621$	−0.964202	−	0.313288i	−0.0386921	−	0.0125718i
$622$		0			0
$623$	−5.46094	−	7.51634i	−0.218788	−	0.301136i
$624$		0			0
$625$	19.7049	+	15.3856i	0.788198	+	0.615422i
$626$		0			0
$627$	3.37519	+	2.45222i	0.134792	+	0.0979322i
$628$		0			0
$629$		−	43.0971i		−	1.71839i
$630$		0			0
$631$	1.08512	+	3.33966i	0.0431979	+	0.132950i	0.970329	−	0.241786i	$-0.0777333\pi$
$631$	1.08512	+	3.33966i	0.0431979	+	0.132950i	−0.927132	+	0.374736i	$0.877733\pi$
$632$		0			0
$633$	−4.36787	−	1.41921i	−0.173607	−	0.0564084i
$634$		0			0
$635$	−12.0560	−	12.2665i	−0.478430	−	0.486780i
$636$		0			0
$637$	9.96704	+	30.6754i	0.394909	+	1.21540i
$638$		0			0
$639$	−1.84682	−	2.54192i	−0.0730589	−	0.100557i
$640$		0			0
$641$	14.2690	−	19.6396i	0.563593	−	0.775719i	−0.428185	−	0.903691i	$-0.640847\pi$
$641$	14.2690	−	19.6396i	0.563593	−	0.775719i	0.991778	+	0.127972i	$0.0408467\pi$
$642$		0			0
$643$	−14.0839	+	43.3457i	−0.555414	+	1.70939i	0.139434	+	0.990231i	$0.455472\pi$
$643$	−14.0839	+	43.3457i	−0.555414	+	1.70939i	−0.694848	+	0.719157i	$0.744528\pi$
$644$		0			0
$645$	0.316787	−	0.608656i	0.0124735	−	0.0239658i
$646$		0			0
$647$			30.8633i			1.21336i	0.794946	+	0.606680i	$0.207499\pi$
$647$			30.8633i			1.21336i	−0.794946	+	0.606680i	$0.792501\pi$
$648$		0			0
$649$	35.8200	−	11.6386i	1.40606	−	0.456856i
$650$		0			0
$651$	6.34799	+	4.61208i	0.248797	+	0.180762i
$652$		0			0
$653$	−17.1864			−0.672555			−0.336278	−	0.941763i	$-0.609168\pi$
$653$	−17.1864			−0.672555			−0.336278	+	0.941763i	$0.609168\pi$
$654$		0			0
$655$	−18.9309	−	37.9623i	−0.739692	−	1.48331i
$656$		0			0
$657$			3.64884i			0.142355i
$658$		0			0
$659$		−	13.0015i		−	0.506467i	−0.967405	−	0.253233i	$-0.918506\pi$
$659$		−	13.0015i		−	0.506467i	0.967405	−	0.253233i	$-0.0814941\pi$
$660$		0			0
$661$	−32.9969	−	23.9736i	−1.28343	−	0.932466i	−0.283779	−	0.958890i	$-0.591588\pi$
$661$	−32.9969	−	23.9736i	−1.28343	−	0.932466i	−0.999651	+	0.0264233i	$0.991588\pi$
$662$		0			0
$663$	3.01253	+	9.27160i	0.116997	+	0.360079i
$664$		0			0
$665$	−24.2845	+	12.1101i	−0.941713	+	0.469610i
$666$		0			0
$667$	−3.97437	+	2.88755i	−0.153888	+	0.111806i
$668$		0			0
$669$	−3.50289	−	1.13816i	−0.135429	−	0.0440037i
$670$		0			0
$671$	14.8764	−	20.4756i	0.574297	−	0.790452i
$672$		0			0
$673$	−21.2404	+	15.4320i	−0.818756	+	0.594861i	−0.916356	−	0.400365i	$-0.868883\pi$
$673$	−21.2404	+	15.4320i	−0.818756	+	0.594861i	0.0976002	+	0.995226i	$0.468883\pi$
$674$		0			0
$675$	−9.01502	−	3.10259i	−0.346988	−	0.119419i
$676$		0			0
$677$	−8.96082	+	2.91155i	−0.344392	+	0.111900i	−0.476106	−	0.879388i	$-0.657952\pi$
$677$	−8.96082	+	2.91155i	−0.344392	+	0.111900i	0.131714	+	0.991288i	$0.457952\pi$
$678$		0			0
$679$	−8.16935	+	25.1427i	−0.313511	+	0.964888i
$680$		0			0
$681$	−1.07249	−	3.30078i	−0.0410979	−	0.126486i
$682$		0			0
$683$	32.9208			1.25968			0.629840	−	0.776725i	$-0.283120\pi$
$683$	32.9208			1.25968			0.629840	+	0.776725i	$0.283120\pi$
$684$		0			0
$685$	−0.227814	+	1.36200i	−0.00870433	+	0.0520393i
$686$		0			0
$687$	1.15215	+	1.58579i	0.0439571	+	0.0605018i
$688$		0			0
$689$	−21.1296	+	15.3515i	−0.804973	+	0.584847i
$690$		0			0
$691$	−40.0174	−	13.0025i	−1.52234	−	0.494637i	−0.575897	−	0.817522i	$-0.695347\pi$
$691$	−40.0174	−	13.0025i	−1.52234	−	0.494637i	−0.946438	+	0.322886i	$0.895347\pi$
$692$		0			0
$693$	−23.2094	+	31.9450i	−0.881653	+	1.21349i
$694$		0			0
$695$	40.7805	−	6.09785i	1.54689	−	0.231305i
$696$		0			0
$697$	27.9444	+	20.8913i	1.05847	+	0.791316i
$698$		0			0
$699$	−1.03196	+	3.17605i	−0.0390324	+	0.120129i
$700$		0			0
$701$	5.63145	+	4.09149i	0.212697	+	0.154533i	0.689033	−	0.724730i	$-0.258035\pi$
$701$	5.63145	+	4.09149i	0.212697	+	0.154533i	−0.476336	+	0.879263i	$0.658035\pi$
$702$		0			0
$703$	−8.28050	+	25.4848i	−0.312305	+	0.961176i
$704$		0			0
$705$	5.80935	+	3.02360i	0.218793	+	0.113875i
$706$		0			0
$707$	−24.3704	−	33.5430i	−0.916544	−	1.26151i
$708$		0			0
$709$	20.4467	−	28.1424i	0.767891	−	1.05691i	−0.228626	−	0.973514i	$-0.573423\pi$
$709$	20.4467	−	28.1424i	0.767891	−	1.05691i	0.996516	−	0.0833965i	$-0.0265768\pi$
$710$		0			0
$711$			4.63594i			0.173861i
$712$		0			0
$713$	−3.42469	+	1.11275i	−0.128256	+	0.0416728i
$714$		0			0
$715$	6.96402	+	46.5732i	0.260440	+	1.74174i
$716$		0			0
$717$	6.38702	−	2.07527i	0.238528	−	0.0775023i
$718$		0			0
$719$	−20.2844	+	6.59080i	−0.756481	+	0.245796i	−0.661768	−	0.749709i	$-0.730193\pi$
$719$	−20.2844	+	6.59080i	−0.756481	+	0.245796i	−0.0947132	+	0.995505i	$0.530193\pi$
$720$		0			0
$721$	−3.59399	−	4.94670i	−0.133847	−	0.184225i
$722$		0			0
$723$	4.07251	+	2.95885i	0.151458	+	0.110041i
$724$		0			0
$725$	−37.8391	+	26.5038i	−1.40531	+	0.984326i
$726$		0			0
$727$	25.3473	−	18.4159i	0.940080	−	0.683008i	−0.00836025	−	0.999965i	$-0.502661\pi$
$727$	25.3473	−	18.4159i	0.940080	−	0.683008i	0.948440	+	0.316957i	$0.102661\pi$
$728$		0			0
$729$	−21.5139			−0.796813
$730$		0			0
$731$	4.91665	−	1.59752i	0.181849	−	0.0590862i
$732$		0			0
$733$	−21.4607	+	29.5381i	−0.792670	+	1.09102i	0.201101	+	0.979571i	$0.435548\pi$
$733$	−21.4607	+	29.5381i	−0.792670	+	1.09102i	−0.993771	+	0.111446i	$0.964452\pi$
$734$		0			0
$735$	1.88196	+	3.77391i	0.0694172	+	0.139203i
$736$		0			0
$737$		−	25.0792i		−	0.923806i
$738$		0			0
$739$	14.8588			0.546589			0.273294	−	0.961930i	$-0.411887\pi$
$739$	14.8588			0.546589			0.273294	+	0.961930i	$0.411887\pi$
$740$		0			0
$741$		−	6.06143i		−	0.222672i
$742$		0			0
$743$	3.22466	−	4.43836i	0.118301	−	0.162828i	−0.745760	−	0.666215i	$-0.767913\pi$
$743$	3.22466	−	4.43836i	0.118301	−	0.162828i	0.864061	+	0.503388i	$0.167913\pi$
$744$		0			0
$745$	−37.0464	−	37.6930i	−1.35728	−	1.38096i
$746$		0			0
$747$			6.33201i			0.231676i
$748$		0			0
$749$	26.4110	+	36.3517i	0.965038	+	1.32826i
$750$		0			0
$751$	−42.7462	−	13.8891i	−1.55983	−	0.506820i	−0.603069	−	0.797689i	$-0.706056\pi$
$751$	−42.7462	−	13.8891i	−1.55983	−	0.506820i	−0.956763	+	0.290869i	$0.906056\pi$
$752$		0			0
$753$	−4.54576	−	3.30269i	−0.165657	−	0.120357i
$754$		0			0
$755$	−15.6905	+	30.1467i	−0.571034	+	1.09715i
$756$		0			0
$757$	−14.8094	−	45.5787i	−0.538258	−	1.65659i	−0.736502	−	0.676435i	$-0.763524\pi$
$757$	−14.8094	−	45.5787i	−0.538258	−	1.65659i	0.198244	−	0.980153i	$-0.436476\pi$
$758$		0			0
$759$	0.202321	+	0.622680i	0.00734379	+	0.0226018i
$760$		0			0
$761$	−1.68629	+	5.18987i	−0.0611280	+	0.188132i	−0.976957	−	0.213436i	$-0.931535\pi$
$761$	−1.68629	+	5.18987i	−0.0611280	+	0.188132i	0.915829	+	0.401568i	$0.131535\pi$
$762$		0			0
$763$	26.8341	−	8.71892i	0.971459	−	0.315646i
$764$		0			0
$765$	−15.7434	−	31.5704i	−0.569204	−	1.14143i
$766$		0			0
$767$	−44.2702	−	32.1642i	−1.59851	−	1.16138i
$768$		0			0
$769$	−39.8395	+	28.9451i	−1.43665	+	1.04379i	−0.447919	+	0.894074i	$0.647835\pi$
$769$	−39.8395	+	28.9451i	−1.43665	+	1.04379i	−0.988730	+	0.149712i	$0.952165\pi$
$770$		0			0
$771$	−5.48880	+	3.98785i	−0.197674	+	0.143619i
$772$		0			0
$773$	3.79777	−	11.6883i	0.136596	−	0.420400i	−0.859239	−	0.511575i	$-0.829062\pi$
$773$	3.79777	−	11.6883i	0.136596	−	0.420400i	0.995835	+	0.0911748i	$0.0290622\pi$
$774$		0			0
$775$	−32.3820	+	9.90554i	−1.16319	+	0.355818i
$776$		0			0
$777$	8.71489	+	2.83164i	0.312645	+	0.101584i
$778$		0			0
$779$	−12.5105	−	17.7229i	−0.448234	−	0.634988i
$780$		0			0
$781$	−1.27670	+	3.92929i	−0.0456840	+	0.140601i
$782$		0			0
$783$	10.3556	−	14.2533i	0.370079	−	0.509370i
$784$		0			0
$785$	−45.4948	+	6.80278i	−1.62378	+	0.242802i
$786$		0			0
$787$	−18.0535	−	24.8485i	−0.643538	−	0.885754i	0.355260	−	0.934767i	$-0.384392\pi$
$787$	−18.0535	−	24.8485i	−0.643538	−	0.885754i	−0.998798	+	0.0490134i	$0.984392\pi$
$788$		0			0
$789$	0.125325	−	0.0910541i	0.00446170	−	0.00324161i
$790$		0			0
$791$	−6.46189	+	8.89403i	−0.229758	+	0.316235i
$792$		0			0
$793$	−36.7717			−1.30580
$794$		0			0
$795$	−2.43543	+	2.39366i	−0.0863759	+	0.0848942i
$796$		0			0
$797$	47.2707	+	15.3592i	1.67442	+	0.544051i	0.983815	−	0.179186i	$-0.0573464\pi$
$797$	47.2707	+	15.3592i	1.67442	+	0.544051i	0.690600	+	0.723237i	$0.257346\pi$
$798$		0			0
$799$	15.2476	+	46.9272i	0.539421	+	1.66017i
$800$		0			0
$801$	−7.14220	+	2.32064i	−0.252357	+	0.0819958i
$802$		0			0
$803$	3.88164	−	2.82018i	0.136980	−	0.0995219i
$804$		0			0
$805$	−4.20030	−	0.702562i	−0.148041	−	0.0247621i
$806$		0			0
$807$	−1.50074	+	4.61880i	−0.0528286	+	0.162590i
$808$		0			0
$809$	28.3917	+	39.0778i	0.998199	+	1.37390i	0.926424	+	0.376482i	$0.122866\pi$
$809$	28.3917	+	39.0778i	0.998199	+	1.37390i	0.0717745	+	0.997421i	$0.477134\pi$
$810$		0			0
$811$	−24.5513			−0.862114			−0.431057	−	0.902325i	$-0.641859\pi$
$811$	−24.5513			−0.862114			−0.431057	+	0.902325i	$0.641859\pi$
$812$		0			0
$813$	−2.33758	−	7.19434i	−0.0819826	−	0.252317i
$814$		0			0
$815$	−34.4323	−	5.75930i	−1.20611	−	0.201739i
$816$		0			0
$817$	−3.21432			−0.112455
$818$		0			0
$819$	57.3693			2.00465
$820$		0			0
$821$	1.55914			0.0544145			0.0272072	−	0.999630i	$-0.491339\pi$
$821$	1.55914			0.0544145			0.0272072	+	0.999630i	$0.491339\pi$
$822$		0			0
$823$	−22.0230			−0.767672			−0.383836	−	0.923401i	$-0.625397\pi$
$823$	−22.0230			−0.767672			−0.383836	+	0.923401i	$0.625397\pi$
$824$		0			0
$825$	1.80103	+	5.88771i	0.0627039	+	0.204984i
$826$		0			0
$827$	16.2756	+	50.0911i	0.565957	+	1.74184i	0.665090	+	0.746764i	$0.268393\pi$
$827$	16.2756	+	50.0911i	0.565957	+	1.74184i	−0.0991322	+	0.995074i	$0.531607\pi$
$828$		0			0
$829$	36.6349			1.27238			0.636191	−	0.771532i	$-0.280509\pi$
$829$	36.6349			1.27238			0.636191	+	0.771532i	$0.280509\pi$
$830$		0			0
$831$	2.33285	+	3.21090i	0.0809258	+	0.111385i
$832$		0			0
$833$	−9.81830	+	30.2176i	−0.340184	+	1.04698i
$834$		0			0
$835$	6.95147	−	41.5597i	0.240566	−	1.43823i
$836$		0			0
$837$	10.4477	−	7.59066i	0.361124	−	0.262372i
$838$		0			0
$839$	43.5611	−	14.1539i	1.50390	−	0.488645i	0.562745	−	0.826631i	$-0.309745\pi$
$839$	43.5611	−	14.1539i	1.50390	−	0.488645i	0.941151	+	0.337985i	$0.109745\pi$
$840$		0			0
$841$	−17.4193	−	53.6111i	−0.600665	−	1.84866i
$842$		0			0
$843$	0.628134	+	0.204093i	0.0216341	+	0.00702934i
$844$		0			0
$845$	28.0638	−	27.5825i	0.965426	−	0.948865i
$846$		0			0
$847$	12.5192			0.430165
$848$		0			0
$849$	4.52490	−	6.22800i	0.155294	−	0.213744i
$850$		0			0
$851$	−3.40212	+	2.47179i	−0.116623	+	0.0847317i
$852$		0			0
$853$	25.4247	+	34.9942i	0.870527	+	1.19818i	0.978956	+	0.204073i	$0.0654180\pi$
$853$	25.4247	+	34.9942i	0.870527	+	1.19818i	−0.108429	+	0.994104i	$0.534582\pi$
$854$		0			0
$855$	3.24380	+	21.6935i	0.110936	+	0.741902i
$856$		0			0
$857$	−2.89622	+	3.98630i	−0.0989330	+	0.136170i	−0.855613	−	0.517615i	$-0.826820\pi$
$857$	−2.89622	+	3.98630i	−0.0989330	+	0.136170i	0.756680	+	0.653785i	$0.226820\pi$
$858$		0			0
$859$	−7.54929	+	23.2343i	−0.257579	+	0.792745i	0.735732	+	0.677273i	$0.236838\pi$
$859$	−7.54929	+	23.2343i	−0.257579	+	0.792745i	−0.993311	+	0.115473i	$0.963162\pi$
$860$		0			0
$861$	−6.06060	+	4.27814i	−0.206545	+	0.145799i
$862$		0			0
$863$	−10.8977	−	3.54089i	−0.370963	−	0.120533i	0.117601	−	0.993061i	$-0.462479\pi$
$863$	−10.8977	−	3.54089i	−0.370963	−	0.120533i	−0.488565	+	0.872528i	$0.662479\pi$
$864$		0			0
$865$	29.8905	+	4.99962i	1.01631	+	0.169992i
$866$		0			0
$867$	−1.26845	+	3.90390i	−0.0430789	+	0.132583i
$868$		0			0
$869$	4.93171	−	3.58310i	0.167297	−	0.121548i
$870$		0			0
$871$	−29.4786	+	21.4174i	−0.998843	+	0.725702i
$872$		0			0
$873$	17.2878	+	12.5603i	0.585104	+	0.425103i
$874$		0			0
$875$	−39.3794	−	7.28926i	−1.33127	−	0.246422i
$876$		0			0
$877$	−42.8548	+	13.9244i	−1.44710	+	0.470193i	−0.924104	−	0.382140i	$-0.875187\pi$
$877$	−42.8548	+	13.9244i	−1.44710	+	0.470193i	−0.523000	+	0.852333i	$0.675187\pi$
$878$		0			0
$879$	0.697284	−	2.14602i	0.0235188	−	0.0723834i
$880$		0			0
$881$	12.4494	+	38.3154i	0.419432	+	1.29088i	0.908226	+	0.418479i	$0.137437\pi$
$881$	12.4494	+	38.3154i	0.419432	+	1.29088i	−0.488795	+	0.872399i	$0.662563\pi$
$882$		0			0
$883$	−5.49349	−	16.9072i	−0.184871	−	0.568974i	0.815075	−	0.579355i	$-0.196696\pi$
$883$	−5.49349	−	16.9072i	−0.184871	−	0.568974i	−0.999946	+	0.0103812i	$0.996696\pi$
$884$		0			0
$885$	−6.34648	−	3.30316i	−0.213335	−	0.111034i
$886$		0			0
$887$	45.4460	+	33.0184i	1.52593	+	1.10865i	0.958450	+	0.285261i	$0.0920803\pi$
$887$	45.4460	+	33.0184i	1.52593	+	1.10865i	0.567477	+	0.823390i	$0.307920\pi$
$888$		0			0
$889$	26.2036	+	8.51406i	0.878840	+	0.285552i
$890$		0			0
$891$	18.0580	+	24.8548i	0.604967	+	0.832666i
$892$		0			0
$893$		−	30.6793i		−	1.02664i
$894$		0			0
$895$	13.7357	+	13.9754i	0.459133	+	0.467146i
$896$		0			0
$897$	0.559128	−	0.769574i	0.0186688	−	0.0256953i
$898$		0			0
$899$		−	62.5763i		−	2.08704i
$900$		0			0
$901$	−25.7278			−0.857119
$902$		0			0
$903$			1.09918i			0.0365786i
$904$		0			0
$905$	−15.2681	+	7.61384i	−0.507528	+	0.253092i
$906$		0			0
$907$	7.28420	−	10.0258i	0.241868	−	0.332902i	−0.670775	−	0.741661i	$-0.734038\pi$
$907$	7.28420	−	10.0258i	0.241868	−	0.332902i	0.912642	+	0.408759i	$0.134038\pi$
$908$		0			0
$909$	−31.8733	+	10.3563i	−1.05717	+	0.343496i
$910$		0			0
$911$	38.8062			1.28571			0.642853	−	0.765989i	$-0.277750\pi$
$911$	38.8062			1.28571			0.642853	+	0.765989i	$0.277750\pi$
$912$		0			0
$913$	6.73599	−	4.89398i	0.222929	−	0.161967i
$914$		0			0
$915$	−4.75494	+	0.710999i	−0.157193	+	0.0235049i
$916$		0			0
$917$	54.9769	+	39.9431i	1.81550	+	1.31904i
$918$		0			0
$919$	6.32049	+	8.69940i	0.208494	+	0.286967i	0.900438	−	0.434984i	$-0.143246\pi$
$919$	6.32049	+	8.69940i	0.208494	+	0.286967i	−0.691945	+	0.721950i	$0.743246\pi$
$920$		0			0
$921$	−6.17446	+	2.00620i	−0.203455	+	0.0661066i
$922$		0			0
$923$	5.70884	−	1.85492i	0.187909	−	0.0610553i
$924$		0			0
$925$	−32.3909	+	22.6877i	−1.06501	+	0.745966i
$926$		0			0
$927$	−4.70047	+	1.52727i	−0.154384	+	0.0501623i
$928$		0			0
$929$			43.2661i			1.41952i	0.704446	+	0.709758i	$0.251196\pi$
$929$			43.2661i			1.41952i	−0.704446	+	0.709758i	$0.748804\pi$
$930$		0			0
$931$	11.6118	−	15.9822i	0.380561	−	0.523797i
$932$		0			0
$933$	−3.92624	−	5.40400i	−0.128539	−	0.176919i
$934$		0			0
$935$	−21.4166	+	41.1485i	−0.700396	+	1.34570i
$936$		0			0
$937$	−8.90743	+	27.4142i	−0.290993	+	0.895584i	0.693545	+	0.720413i	$0.256048\pi$
$937$	−8.90743	+	27.4142i	−0.290993	+	0.895584i	−0.984538	+	0.175171i	$0.943952\pi$
$938$		0			0
$939$	2.69877	+	1.96077i	0.0880710	+	0.0639873i
$940$		0			0
$941$	9.00551	−	27.7161i	0.293571	−	0.903520i	−0.690126	−	0.723689i	$-0.742445\pi$
$941$	9.00551	−	27.7161i	0.293571	−	0.903520i	0.983698	−	0.179831i	$-0.0575550\pi$
$942$		0			0
$943$	0.0464620	−	3.40416i	0.00151301	−	0.110855i
$944$		0			0
$945$	15.1049	−	2.25861i	0.491361	−	0.0734726i
$946$		0			0
$947$	−24.8016	+	34.1364i	−0.805942	+	1.10928i	0.185995	+	0.982551i	$0.440449\pi$
$947$	−24.8016	+	34.1364i	−0.805942	+	1.10928i	−0.991937	+	0.126733i	$0.959551\pi$
$948$		0			0
$949$	−6.62977	−	2.15414i	−0.215211	−	0.0699264i
$950$		0			0
$951$	−5.90695	+	4.29165i	−0.191546	+	0.139166i
$952$		0			0
$953$	−2.11739	−	2.91433i	−0.0685889	−	0.0944045i	0.773344	−	0.633986i	$-0.218582\pi$
$953$	−2.11739	−	2.91433i	−0.0685889	−	0.0944045i	−0.841933	+	0.539582i	$0.818582\pi$
$954$		0			0
$955$	5.71637	+	0.956146i	0.184977	+	0.0309402i
$956$		0			0
$957$	−11.3777			−0.367788
$958$		0			0
$959$	−0.683590	−	2.10387i	−0.0220743	−	0.0679376i
$960$		0			0
$961$	4.59462	−	14.1408i	0.148213	−	0.456154i
$962$		0			0
$963$	34.5422	−	11.2234i	1.11311	−	0.361670i
$964$		0			0
$965$	−24.8617	+	24.4353i	−0.800327	+	0.786599i
$966$		0			0
$967$	41.5195	−	30.1657i	1.33518	−	0.970063i	0.335570	−	0.942015i	$-0.391071\pi$
$967$	41.5195	−	30.1657i	1.33518	−	0.970063i	0.999607	−	0.0280476i	$-0.00892898\pi$
$968$		0			0
$969$	3.50965	−	4.83061i	0.112746	−	0.155182i
$970$		0			0
$971$	−51.3827	−	16.6953i	−1.64895	−	0.535776i	−0.670437	−	0.741966i	$-0.733894\pi$
$971$	−51.3827	−	16.6953i	−1.64895	−	0.535776i	−0.978512	+	0.206190i	$0.933894\pi$
$972$		0			0
$973$	−53.4387	+	38.8255i	−1.71317	+	1.24469i
$974$		0			0
$975$	5.38246	−	7.14502i	0.172377	−	0.228824i
$976$		0			0
$977$	−4.81936	−	14.8325i	−0.154185	−	0.474532i	0.843892	−	0.536512i	$-0.180259\pi$
$977$	−4.81936	−	14.8325i	−0.154185	−	0.474532i	−0.998077	+	0.0619800i	$0.980259\pi$
$978$		0			0
$979$	7.98888	+	5.80426i	0.255326	+	0.185505i
$980$		0			0
$981$		−	22.8064i		−	0.728154i
$982$		0			0
$983$		−	22.3814i		−	0.713856i	−0.934132	−	0.356928i	$-0.883824\pi$
$983$		−	22.3814i		−	0.713856i	0.934132	−	0.356928i	$-0.116176\pi$
$984$		0			0
$985$	−14.1415	+	7.05201i	−0.450584	+	0.224696i
$986$		0			0
$987$	−10.4912			−0.333939
$988$		0			0
$989$	−0.408098	−	0.296501i	−0.0129768	−	0.00942817i
$990$		0			0
$991$	17.4547	−	5.67138i	0.554467	−	0.180157i	−0.0183629	−	0.999831i	$-0.505845\pi$
$991$	17.4547	−	5.67138i	0.554467	−	0.180157i	0.572830	+	0.819674i	$0.305845\pi$
$992$		0			0
$993$			8.56417i			0.271776i
$994$		0			0
$995$	5.42613	−	10.4254i	0.172020	−	0.330508i
$996$		0			0
$997$	−7.85100	+	24.1629i	−0.248644	+	0.765246i	0.746372	+	0.665529i	$0.231794\pi$
$997$	−7.85100	+	24.1629i	−0.248644	+	0.765246i	−0.995016	+	0.0997174i	$0.968206\pi$
$998$		0			0
$999$	8.86455	−	12.2010i	0.280462	−	0.386023i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.bi.a.189.10	✓	80
5.4	even	2	inner	820.2.bi.a.189.11	yes	80
41.23	even	10	inner	820.2.bi.a.269.11	yes	80
205.64	even	10	inner	820.2.bi.a.269.10	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.bi.a.189.10	✓	80	1.1	even	1	trivial
820.2.bi.a.189.11	yes	80	5.4	even	2	inner
820.2.bi.a.269.10	yes	80	205.64	even	10	inner
820.2.bi.a.269.11	yes	80	41.23	even	10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.bi (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q-0.323438 q^{3} +(-0.368890 + 2.20543i) q^{5} +(-1.10691 - 3.40672i) q^{7} -2.89539 q^{9} +(2.23783 + 3.08011i) q^{11} +(1.70933 - 5.26078i) q^{13} +(0.119313 - 0.713321i) q^{15} +(4.40830 - 3.20282i) q^{17} +(-3.22215 + 1.04694i) q^{19} +(0.358017 + 1.10186i) q^{21} +(-0.505667 - 0.164301i) q^{23} +(-4.72784 - 1.62712i) q^{25} +1.90679 q^{27} +(5.43089 - 7.47498i) q^{29} +(5.47917 - 3.98085i) q^{31} +(-0.723801 - 0.996227i) q^{33} +(7.92160 - 1.18451i) q^{35} +(4.64893 - 6.39870i) q^{37} +(-0.552863 + 1.70154i) q^{39} +(1.89538 + 6.11617i) q^{41} +(0.902310 + 0.293178i) q^{43} +(1.06808 - 6.38557i) q^{45} +(-2.79826 + 8.61215i) q^{47} +(-4.71735 + 3.42736i) q^{49} +(-1.42581 + 1.03591i) q^{51} +(-3.81986 - 2.77529i) q^{53} +(-7.61849 + 3.79916i) q^{55} +(1.04217 - 0.338621i) q^{57} +(3.05698 - 9.40843i) q^{59} +(-2.05425 - 6.32232i) q^{61} +(3.20493 + 9.86376i) q^{63} +(10.9717 + 5.71045i) q^{65} +(-5.32921 - 3.87190i) q^{67} +(0.163552 + 0.0531412i) q^{69} +(0.637848 + 0.877922i) q^{71} -1.26023i q^{73} +(1.52916 + 0.526274i) q^{75} +(8.01599 - 11.0331i) q^{77} -1.60115i q^{79} +8.06943 q^{81} -2.18693i q^{83} +(5.43741 + 10.9037i) q^{85} +(-1.75656 + 2.41770i) q^{87} +(2.46675 - 0.801496i) q^{89} -19.8140 q^{91} +(-1.77217 + 1.28756i) q^{93} +(-1.12033 - 7.49244i) q^{95} +(-5.97081 - 4.33805i) q^{97} +(-6.47940 - 8.91812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 68 q^{9} + 10 q^{15} - 26 q^{21} + 10 q^{25} - 20 q^{29} + 4 q^{31} + 15 q^{35} - 8 q^{39} + 4 q^{41} - 4 q^{45} + 18 q^{49} + 52 q^{51} - 36 q^{59} - 42 q^{61} - 15 q^{65} + 30 q^{69} - 20 q^{75}+ \cdots + 80 q^{99}+O(q^{100}) \) 80 * q + 68 * q^9 + 10 * q^15 - 26 * q^21 + 10 * q^25 - 20 * q^29 + 4 * q^31 + 15 * q^35 - 8 * q^39 + 4 * q^41 - 4 * q^45 + 18 * q^49 + 52 * q^51 - 36 * q^59 - 42 * q^61 - 15 * q^65 + 30 * q^69 - 20 * q^75 + 32 * q^81 + 10 * q^89 - 132 * q^91 + 50 * q^95 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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