LMFDB - Embedded newform 820.2.x.a.273.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(273,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 6, 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("820.273"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.x (of order $8$, 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:	$84$
Relative dimension:	$21$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			273.9
Character	$\chi$	$=$	820.273
Dual form			820.2.x.a.817.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.741636 - 0.307196i) q^{3} +(2.17900 - 0.501977i) q^{5} +(-1.54758 + 3.73618i) q^{7} +(-1.66567 - 1.66567i) q^{9} +(-0.868860 - 2.09761i) q^{11} +(-5.82833 - 2.41417i) q^{13} +(-1.77023 - 0.297094i) q^{15} +(-5.90256 + 2.44492i) q^{17} +(2.66729 - 6.43941i) q^{19} +(2.29548 - 2.29548i) q^{21} +(2.33878 - 2.33878i) q^{23} +(4.49604 - 2.18761i) q^{25} +(1.64522 + 3.97191i) q^{27} +(-2.84330 - 6.86433i) q^{29} +5.79995i q^{31} +1.82258i q^{33} +(-1.49669 + 8.91797i) q^{35} +(4.56684 - 4.56684i) q^{37} +(3.58088 + 3.58088i) q^{39} +(-6.30515 - 1.11584i) q^{41} -5.36561i q^{43} +(-4.46560 - 2.79335i) q^{45} +(-5.03559 + 2.08581i) q^{47} +(-6.61431 - 6.61431i) q^{49} +5.12863 q^{51} +(1.87498 - 4.52660i) q^{53} +(-2.94619 - 4.13454i) q^{55} +(-3.95632 + 3.95632i) q^{57} +10.6611i q^{59} +(-7.29537 - 7.29537i) q^{61} +(8.80097 - 3.64548i) q^{63} +(-13.9118 - 2.33479i) q^{65} +(-4.61341 + 1.91094i) q^{67} +(-2.45298 + 1.01606i) q^{69} +(-6.45817 + 2.67506i) q^{71} +11.6632i q^{73} +(-4.00645 + 0.241246i) q^{75} +9.18169 q^{77} +(7.85772 - 3.25478i) q^{79} +3.61570i q^{81} +(-2.07996 - 2.07996i) q^{83} +(-11.6344 + 8.29042i) q^{85} +5.96429i q^{87} +(1.43272 + 3.45889i) q^{89} +(18.0396 - 18.0396i) q^{91} +(1.78172 - 4.30145i) q^{93} +(2.57958 - 15.3704i) q^{95} +(1.15021 + 2.77685i) q^{97} +(-2.04669 + 4.94115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) $ 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.741636	−	0.307196i	−0.428184	−	0.177360i	0.158175	−	0.987411i	$-0.449439\pi$
$3$	−0.741636	−	0.307196i	−0.428184	−	0.177360i	−0.586359	+	0.810052i	$0.699439\pi$
$4$		0			0
$5$	2.17900	−	0.501977i	0.974476	−	0.224491i
$5$	2.17900	−	0.501977i	0.974476	−	0.224491i
$6$		0			0
$7$	−1.54758	+	3.73618i	−0.584929	+	1.41214i	0.303368	+	0.952874i	$0.401889\pi$
$7$	−1.54758	+	3.73618i	−0.584929	+	1.41214i	−0.888297	+	0.459270i	$0.848111\pi$
$8$		0			0
$9$	−1.66567	−	1.66567i	−0.555222	−	0.555222i
$10$		0			0
$11$	−0.868860	−	2.09761i	−0.261971	−	0.632454i	0.737089	−	0.675795i	$-0.236200\pi$
$11$	−0.868860	−	2.09761i	−0.261971	−	0.632454i	−0.999060	+	0.0433414i	$0.986200\pi$
$12$		0			0
$13$	−5.82833	−	2.41417i	−1.61649	−	0.669572i	−0.622866	−	0.782328i	$-0.714032\pi$
$13$	−5.82833	−	2.41417i	−1.61649	−	0.669572i	−0.993623	+	0.112757i	$0.964032\pi$
$14$		0			0
$15$	−1.77023	−	0.297094i	−0.457071	−	0.0767094i
$16$		0			0
$17$	−5.90256	+	2.44492i	−1.43158	+	0.592981i	−0.957742	−	0.287630i	$-0.907133\pi$
$17$	−5.90256	+	2.44492i	−1.43158	+	0.592981i	−0.473840	+	0.880611i	$0.657133\pi$
$18$		0			0
$19$	2.66729	−	6.43941i	0.611918	−	1.47730i	−0.248972	−	0.968511i	$-0.580093\pi$
$19$	2.66729	−	6.43941i	0.611918	−	1.47730i	0.860890	−	0.508791i	$-0.169907\pi$
$20$		0			0
$21$	2.29548	−	2.29548i	0.500914	−	0.500914i
$22$		0			0
$23$	2.33878	−	2.33878i	0.487669	−	0.487669i	−0.419901	−	0.907570i	$-0.637935\pi$
$23$	2.33878	−	2.33878i	0.487669	−	0.487669i	0.907570	+	0.419901i	$0.137935\pi$
$24$		0			0
$25$	4.49604	−	2.18761i	0.899208	−	0.437522i
$26$		0			0
$27$	1.64522	+	3.97191i	0.316623	+	0.764395i
$28$		0			0
$29$	−2.84330	−	6.86433i	−0.527987	−	1.27467i	−0.932840	−	0.360292i	$-0.882677\pi$
$29$	−2.84330	−	6.86433i	−0.527987	−	1.27467i	0.404852	−	0.914382i	$-0.367323\pi$
$30$		0			0
$31$			5.79995i			1.04170i	0.853648	+	0.520851i	$0.174385\pi$
$31$			5.79995i			1.04170i	−0.853648	+	0.520851i	$0.825615\pi$
$32$		0			0
$33$			1.82258i			0.317270i
$34$		0			0
$35$	−1.49669	+	8.91797i	−0.252986	+	1.50741i
$36$		0			0
$37$	4.56684	−	4.56684i	0.750783	−	0.750783i	−0.223842	−	0.974625i	$-0.571860\pi$
$37$	4.56684	−	4.56684i	0.750783	−	0.750783i	0.974625	+	0.223842i	$0.0718600\pi$
$38$		0			0
$39$	3.58088	+	3.58088i	0.573400	+	0.573400i
$40$		0			0
$41$	−6.30515	−	1.11584i	−0.984699	−	0.174265i
$41$	−6.30515	−	1.11584i	−0.984699	−	0.174265i
$42$		0			0
$43$		−	5.36561i		−	0.818248i	−0.912479	−	0.409124i	$-0.865834\pi$
$43$		−	5.36561i		−	0.818248i	0.912479	−	0.409124i	$-0.134166\pi$
$44$		0			0
$45$	−4.46560	−	2.79335i	−0.665693	−	0.416408i
$46$		0			0
$47$	−5.03559	+	2.08581i	−0.734516	+	0.304246i	−0.718406	−	0.695624i	$-0.755128\pi$
$47$	−5.03559	+	2.08581i	−0.734516	+	0.304246i	−0.0161095	+	0.999870i	$0.505128\pi$
$48$		0			0
$49$	−6.61431	−	6.61431i	−0.944901	−	0.944901i
$50$		0			0
$51$	5.12863			0.718151
$52$		0			0
$53$	1.87498	−	4.52660i	0.257548	−	0.621777i	−0.741227	−	0.671255i	$-0.765756\pi$
$53$	1.87498	−	4.52660i	0.257548	−	0.621777i	0.998775	+	0.0494778i	$0.0157557\pi$
$54$		0			0
$55$	−2.94619	−	4.13454i	−0.397265	−	0.557501i
$56$		0			0
$57$	−3.95632	+	3.95632i	−0.524027	+	0.524027i
$58$		0			0
$59$			10.6611i			1.38795i	0.719999	+	0.693976i	$0.244142\pi$
$59$			10.6611i			1.38795i	−0.719999	+	0.693976i	$0.755858\pi$
$60$		0			0
$61$	−7.29537	−	7.29537i	−0.934076	−	0.934076i	0.0638810	−	0.997958i	$-0.479652\pi$
$61$	−7.29537	−	7.29537i	−0.934076	−	0.934076i	−0.997958	+	0.0638810i	$0.979652\pi$
$62$		0			0
$63$	8.80097	−	3.64548i	1.10882	−	0.459287i
$64$		0			0
$65$	−13.9118	−	2.33479i	−1.72554	−	0.289595i
$66$		0			0
$67$	−4.61341	+	1.91094i	−0.563617	+	0.233458i	−0.646255	−	0.763122i	$-0.723666\pi$
$67$	−4.61341	+	1.91094i	−0.563617	+	0.233458i	0.0826374	+	0.996580i	$0.473666\pi$
$68$		0			0
$69$	−2.45298	+	1.01606i	−0.295305	+	0.122319i
$70$		0			0
$71$	−6.45817	+	2.67506i	−0.766444	+	0.317471i	−0.731431	−	0.681915i	$-0.761147\pi$
$71$	−6.45817	+	2.67506i	−0.766444	+	0.317471i	−0.0350128	+	0.999387i	$0.511147\pi$
$72$		0			0
$73$			11.6632i			1.36507i	0.730852	+	0.682536i	$0.239123\pi$
$73$			11.6632i			1.36507i	−0.730852	+	0.682536i	$0.760877\pi$
$74$		0			0
$75$	−4.00645	+	0.241246i	−0.462625	+	0.0278567i
$76$		0			0
$77$	9.18169			1.04635
$78$		0			0
$79$	7.85772	−	3.25478i	0.884063	−	0.366191i	0.105992	−	0.994367i	$-0.466198\pi$
$79$	7.85772	−	3.25478i	0.884063	−	0.366191i	0.778071	+	0.628176i	$0.216198\pi$
$80$		0			0
$81$			3.61570i			0.401744i
$82$		0			0
$83$	−2.07996	−	2.07996i	−0.228305	−	0.228305i	0.583679	−	0.811984i	$-0.301613\pi$
$83$	−2.07996	−	2.07996i	−0.228305	−	0.228305i	−0.811984	+	0.583679i	$0.801613\pi$
$84$		0			0
$85$	−11.6344	+	8.29042i	−1.26192	+	0.899222i
$86$		0			0
$87$			5.96429i			0.639439i
$88$		0			0
$89$	1.43272	+	3.45889i	0.151868	+	0.366641i	0.981443	−	0.191754i	$-0.0614175\pi$
$89$	1.43272	+	3.45889i	0.151868	+	0.366641i	−0.829575	+	0.558395i	$0.811417\pi$
$90$		0			0
$91$	18.0396	−	18.0396i	1.89106	−	1.89106i
$92$		0			0
$93$	1.78172	−	4.30145i	0.184756	−	0.446040i
$94$		0			0
$95$	2.57958	−	15.3704i	0.264659	−	1.57696i
$96$		0			0
$97$	1.15021	+	2.77685i	0.116786	+	0.281946i	0.971454	−	0.237229i	$-0.0762392\pi$
$97$	1.15021	+	2.77685i	0.116786	+	0.281946i	−0.854668	+	0.519175i	$0.826239\pi$
$98$		0			0
$99$	−2.04669	+	4.94115i	−0.205700	+	0.496604i
$100$		0			0
$101$	2.08050	+	0.861770i	0.207017	+	0.0857493i	0.483783	−	0.875188i	$-0.339263\pi$
$101$	2.08050	+	0.861770i	0.207017	+	0.0857493i	−0.276765	+	0.960937i	$0.589263\pi$
$102$		0			0
$103$	4.64935			0.458115			0.229057	−	0.973413i	$-0.426436\pi$
$103$	4.64935			0.458115			0.229057	+	0.973413i	$0.426436\pi$
$104$		0			0
$105$	3.84956	−	6.15411i	0.375679	−	0.600580i
$106$		0			0
$107$	−7.40215	−	7.40215i	−0.715593	−	0.715593i	0.252107	−	0.967699i	$-0.418877\pi$
$107$	−7.40215	−	7.40215i	−0.715593	−	0.715593i	−0.967699	+	0.252107i	$0.918877\pi$
$108$		0			0
$109$	−9.97525	−	4.13189i	−0.955456	−	0.395763i	−0.150177	−	0.988659i	$-0.547984\pi$
$109$	−9.97525	−	4.13189i	−0.955456	−	0.395763i	−0.805279	+	0.592896i	$0.797984\pi$
$110$		0			0
$111$	−4.78984	+	1.98402i	−0.454632	+	0.188315i
$112$		0			0
$113$	−3.45580	+	3.45580i	−0.325095	+	0.325095i	−0.850718	−	0.525623i	$-0.823832\pi$
$113$	−3.45580	+	3.45580i	−0.325095	+	0.325095i	0.525623	+	0.850718i	$0.323832\pi$
$114$		0			0
$115$	3.92217	−	6.27019i	0.365744	−	0.584699i
$116$		0			0
$117$	5.68684	+	13.7293i	0.525749	+	1.26927i
$118$		0			0
$119$		−	25.8367i		−	2.36845i
$120$		0			0
$121$	4.13311	−	4.13311i	0.375738	−	0.375738i
$122$		0			0
$123$	4.33335	+	2.76446i	0.390725	+	0.249263i
$124$		0			0
$125$	8.69872	−	7.02370i	0.778037	−	0.628218i
$126$		0			0
$127$	14.7330	+	14.7330i	1.30734	+	1.30734i	0.923325	+	0.384019i	$0.125460\pi$
$127$	14.7330	+	14.7330i	1.30734	+	1.30734i	0.384019	+	0.923325i	$0.374540\pi$
$128$		0			0
$129$	−1.64829	+	3.97933i	−0.145124	+	0.350361i
$130$		0			0
$131$	1.70792	−	1.70792i	0.149222	−	0.149222i	−0.628549	−	0.777770i	$-0.716351\pi$
$131$	1.70792	−	1.70792i	0.149222	−	0.149222i	0.777770	+	0.628549i	$0.216351\pi$
$132$		0			0
$133$	19.9310	+	19.9310i	1.72823	+	1.72823i
$134$		0			0
$135$	5.57873	+	7.82892i	0.480141	+	0.673806i
$136$		0			0
$137$	−3.11339	+	1.28961i	−0.265995	+	0.110179i	−0.511695	−	0.859167i	$-0.670982\pi$
$137$	−3.11339	+	1.28961i	−0.265995	+	0.110179i	0.245700	+	0.969346i	$0.420982\pi$
$138$		0			0
$139$			7.52848i			0.638557i	0.947661	+	0.319279i	$0.103441\pi$
$139$			7.52848i			0.638557i	−0.947661	+	0.319279i	$0.896559\pi$
$140$		0			0
$141$	4.37533			0.368469
$142$		0			0
$143$			14.3232i			1.19776i
$144$		0			0
$145$	−9.64127	−	13.5301i	−0.800664	−	1.12361i
$146$		0			0
$147$	2.87352	+	6.93730i	0.237004	+	0.572179i
$148$		0			0
$149$	3.49692	−	8.44230i	0.286478	−	0.691620i	−0.713481	−	0.700675i	$-0.752882\pi$
$149$	3.49692	−	8.44230i	0.286478	−	0.691620i	0.999959	+	0.00905484i	$0.00288229\pi$
$150$		0			0
$151$	1.89223	+	4.56824i	0.153987	+	0.371758i	0.981981	−	0.188979i	$-0.0605179\pi$
$151$	1.89223	+	4.56824i	0.153987	+	0.371758i	−0.827994	+	0.560737i	$0.810518\pi$
$152$		0			0
$153$	13.9041	+	5.75927i	1.12408	+	0.465610i
$154$		0			0
$155$	2.91144	+	12.6381i	0.233852	+	1.01511i
$156$		0			0
$157$	−13.1773	−	5.45822i	−1.05166	−	0.435613i	−0.211178	−	0.977448i	$-0.567730\pi$
$157$	−13.1773	−	5.45822i	−1.05166	−	0.435613i	−0.840485	+	0.541835i	$0.817730\pi$
$158$		0			0
$159$	−2.78111	+	2.78111i	−0.220556	+	0.220556i
$160$		0			0
$161$	5.11866	+	12.3575i	0.403407	+	0.973910i
$162$		0			0
$163$	−11.4479	+	11.4479i	−0.896671	+	0.896671i	−0.995140	−	0.0984693i	$-0.968605\pi$
$163$	−11.4479	+	11.4479i	−0.896671	+	0.896671i	0.0984693	+	0.995140i	$0.468605\pi$
$164$		0			0
$165$	0.914890	+	3.97138i	0.0712241	+	0.309172i
$166$		0			0
$167$	3.91750	−	9.45768i	0.303145	−	0.731857i	−0.696749	−	0.717315i	$-0.745371\pi$
$167$	3.91750	−	9.45768i	0.303145	−	0.731857i	0.999894	−	0.0145421i	$-0.00462906\pi$
$168$		0			0
$169$	18.9488	+	18.9488i	1.45760	+	1.45760i
$170$		0			0
$171$	−15.1687	+	6.28308i	−1.15998	+	0.480479i
$172$		0			0
$173$	13.3113			1.01204			0.506021	−	0.862521i	$-0.331116\pi$
$173$	13.3113			1.01204			0.506021	+	0.862521i	$0.331116\pi$
$174$		0			0
$175$	1.21534	+	20.1835i	0.0918708	+	1.52573i
$176$		0			0
$177$	3.27503	−	7.90663i	0.246166	−	0.594298i
$178$		0			0
$179$	−11.5135	−	4.76907i	−0.860563	−	0.356457i	−0.0916351	−	0.995793i	$-0.529209\pi$
$179$	−11.5135	−	4.76907i	−0.860563	−	0.356457i	−0.768928	+	0.639336i	$0.779209\pi$
$180$		0			0
$181$	3.50448	+	1.45160i	0.260486	+	0.107897i	0.509105	−	0.860705i	$-0.329977\pi$
$181$	3.50448	+	1.45160i	0.260486	+	0.107897i	−0.248619	+	0.968601i	$0.579977\pi$
$182$		0			0
$183$	3.16940	+	7.65162i	0.234289	+	0.565624i
$184$		0			0
$185$	7.65867	−	12.2436i	0.563076	−	0.900164i
$186$		0			0
$187$	10.2570	+	10.2570i	0.750066	+	0.750066i
$188$		0			0
$189$	−17.3859			−1.26464
$190$		0			0
$191$	3.86268	−	9.32533i	0.279493	−	0.674757i	−0.720328	−	0.693633i	$-0.756009\pi$
$191$	3.86268	−	9.32533i	0.279493	−	0.674757i	0.999822	+	0.0188763i	$0.00600888\pi$
$192$		0			0
$193$	−7.71773	−	3.19679i	−0.555535	−	0.230110i	0.0872107	−	0.996190i	$-0.472205\pi$
$193$	−7.71773	−	3.19679i	−0.555535	−	0.230110i	−0.642745	+	0.766080i	$0.722205\pi$
$194$		0			0
$195$	9.60024	+	6.00520i	0.687487	+	0.430041i
$196$		0			0
$197$	−1.47748			−0.105266			−0.0526331	−	0.998614i	$-0.516761\pi$
$197$	−1.47748			−0.105266			−0.0526331	+	0.998614i	$0.516761\pi$
$198$		0			0
$199$	7.12402	+	2.95087i	0.505009	+	0.209181i	0.620618	−	0.784113i	$-0.286882\pi$
$199$	7.12402	+	2.95087i	0.505009	+	0.209181i	−0.115609	+	0.993295i	$0.536882\pi$
$200$		0			0
$201$	4.00850			0.282738
$202$		0			0
$203$	30.0466			2.10886
$204$		0			0
$205$	−14.2990	+	0.733631i	−0.998686	+	0.0512390i
$206$		0			0
$207$	−7.79124			−0.541528
$208$		0			0
$209$	−15.8249			−1.09463
$210$		0			0
$211$	11.4492	+	4.74240i	0.788193	+	0.326480i	0.740217	−	0.672368i	$-0.234723\pi$
$211$	11.4492	+	4.74240i	0.788193	+	0.326480i	0.0479763	+	0.998848i	$0.484723\pi$
$212$		0			0
$213$	5.61138			0.384486
$214$		0			0
$215$	−2.69341	−	11.6916i	−0.183689	−	0.797363i
$216$		0			0
$217$	−21.6697	−	8.97587i	−1.47103	−	0.609322i
$218$		0			0
$219$	3.58288	−	8.64984i	0.242109	−	0.584502i
$220$		0			0
$221$	40.3046			2.71118
$222$		0			0
$223$	−16.6542	−	16.6542i	−1.11525	−	1.11525i	−0.992429	−	0.122822i	$-0.960806\pi$
$223$	−16.6542	−	16.6542i	−1.11525	−	1.11525i	−0.122822	−	0.992429i	$-0.539194\pi$
$224$		0			0
$225$	−11.1327	−	3.84507i	−0.742181	−	0.256338i
$226$		0			0
$227$	4.15296	+	10.0261i	0.275642	+	0.665458i	0.999705	−	0.0242750i	$-0.00772773\pi$
$227$	4.15296	+	10.0261i	0.275642	+	0.665458i	−0.724063	+	0.689733i	$0.757728\pi$
$228$		0			0
$229$	5.61997	+	2.32787i	0.371378	+	0.153830i	0.560563	−	0.828112i	$-0.310585\pi$
$229$	5.61997	+	2.32787i	0.371378	+	0.153830i	−0.189185	+	0.981941i	$0.560585\pi$
$230$		0			0
$231$	−6.80947	−	2.82058i	−0.448030	−	0.185580i
$232$		0			0
$233$	7.13748	−	17.2314i	0.467592	−	1.12887i	−0.497620	−	0.867395i	$-0.665793\pi$
$233$	7.13748	−	17.2314i	0.467592	−	1.12887i	0.965211	−	0.261471i	$-0.0842075\pi$
$234$		0			0
$235$	−9.92549	+	7.07271i	−0.647468	+	0.461373i
$236$		0			0
$237$	−6.82743			−0.443489
$238$		0			0
$239$	−3.60092	+	1.49155i	−0.232924	+	0.0964804i	−0.496093	−	0.868269i	$-0.665232\pi$
$239$	−3.60092	+	1.49155i	−0.232924	+	0.0964804i	0.263169	+	0.964750i	$0.415232\pi$
$240$		0			0
$241$	−5.26946	−	5.26946i	−0.339436	−	0.339436i	0.516719	−	0.856155i	$-0.327153\pi$
$241$	−5.26946	−	5.26946i	−0.339436	−	0.339436i	−0.856155	+	0.516719i	$0.827153\pi$
$242$		0			0
$243$	6.04639	−	14.5973i	0.387876	−	0.936415i
$244$		0			0
$245$	−17.7328	−	11.0923i	−1.13290	−	0.708662i
$246$		0			0
$247$	−31.0917	+	31.0917i	−1.97832	+	1.97832i
$248$		0			0
$249$	0.903617	+	2.18153i	0.0572644	+	0.138249i
$250$		0			0
$251$	15.0929	−	15.0929i	0.952653	−	0.952653i	−0.0462758	−	0.998929i	$-0.514735\pi$
$251$	15.0929	−	15.0929i	0.952653	−	0.952653i	0.998929	+	0.0462758i	$0.0147353\pi$
$252$		0			0
$253$	−6.93791	−	2.87378i	−0.436183	−	0.180673i
$254$		0			0
$255$	11.1753	−	2.57445i	0.699821	−	0.161218i
$256$		0			0
$257$	13.7687	+	5.70319i	0.858869	+	0.355755i	0.768265	−	0.640132i	$-0.221120\pi$
$257$	13.7687	+	5.70319i	0.858869	+	0.355755i	0.0906042	+	0.995887i	$0.471120\pi$
$258$		0			0
$259$	9.99499	+	24.1301i	0.621059	+	1.49937i
$260$		0			0
$261$	−6.69769	+	16.1697i	−0.414577	+	1.00088i
$262$		0			0
$263$	−0.0784272	−	0.189340i	−0.00483603	−	0.0116752i	0.921443	−	0.388513i	$-0.127011\pi$
$263$	−0.0784272	−	0.189340i	−0.00483603	−	0.0116752i	−0.926279	+	0.376838i	$0.877011\pi$
$264$		0			0
$265$	1.81332	−	10.8046i	0.111392	−	0.663724i
$266$		0			0
$267$		−	3.00536i		−	0.183925i
$268$		0			0
$269$	−3.41414			−0.208164			−0.104082	−	0.994569i	$-0.533190\pi$
$269$	−3.41414			−0.208164			−0.104082	+	0.994569i	$0.533190\pi$
$270$		0			0
$271$		−	15.8371i		−	0.962036i	−0.876711	−	0.481018i	$-0.840267\pi$
$271$		−	15.8371i		−	0.962036i	0.876711	−	0.481018i	$-0.159733\pi$
$272$		0			0
$273$	−18.9205	+	7.83713i	−1.14512	+	0.474324i
$274$		0			0
$275$	−8.49518	−	7.53022i	−0.512279	−	0.454090i
$276$		0			0
$277$	12.6783	+	12.6783i	0.761763	+	0.761763i	0.976641	−	0.214878i	$-0.0689354\pi$
$277$	12.6783	+	12.6783i	0.761763	+	0.761763i	−0.214878	+	0.976641i	$0.568935\pi$
$278$		0			0
$279$	9.66078	−	9.66078i	0.578376	−	0.578376i
$280$		0			0
$281$	7.03038	−	16.9728i	0.419397	−	1.01251i	−0.563126	−	0.826371i	$-0.690401\pi$
$281$	7.03038	−	16.9728i	0.419397	−	1.01251i	0.982523	−	0.186143i	$-0.0595987\pi$
$282$		0			0
$283$	−15.6840	−	15.6840i	−0.932315	−	0.932315i	0.0655348	−	0.997850i	$-0.479125\pi$
$283$	−15.6840	−	15.6840i	−0.932315	−	0.932315i	−0.997850	+	0.0655348i	$0.979125\pi$
$284$		0			0
$285$	−6.63482	+	10.6068i	−0.393013	+	0.628291i
$286$		0			0
$287$	13.9267	−	21.8303i	0.822066	−	1.28860i
$288$		0			0
$289$	16.8418	−	16.8418i	0.990694	−	0.990694i
$290$		0			0
$291$		−	2.41275i		−	0.141438i
$292$		0			0
$293$	−11.0614	−	26.7045i	−0.646212	−	1.56009i	−0.818162	−	0.574988i	$-0.805007\pi$
$293$	−11.0614	−	26.7045i	−0.646212	−	1.56009i	0.171950	−	0.985106i	$-0.444993\pi$
$294$		0			0
$295$	5.35160	+	23.2304i	0.311582	+	1.35253i
$296$		0			0
$297$	6.90207	−	6.90207i	0.400499	−	0.400499i
$298$		0			0
$299$	−19.2774	+	7.98495i	−1.11484	+	0.461782i
$300$		0			0
$301$	20.0469	+	8.30369i	1.15548	+	0.478617i
$302$		0			0
$303$	−1.27824	−	1.27824i	−0.0734330	−	0.0734330i
$304$		0			0
$305$	−19.5587	−	12.2345i	−1.11993	−	0.700544i
$306$		0			0
$307$	−2.43042			−0.138711			−0.0693556	−	0.997592i	$-0.522094\pi$
$307$	−2.43042			−0.138711			−0.0693556	+	0.997592i	$0.522094\pi$
$308$		0			0
$309$	−3.44813	−	1.42826i	−0.196157	−	0.0812510i
$310$		0			0
$311$	−9.73781	+	23.5091i	−0.552180	+	1.33308i	0.363658	+	0.931533i	$0.381528\pi$
$311$	−9.73781	+	23.5091i	−0.552180	+	1.33308i	−0.915838	+	0.401548i	$0.868472\pi$
$312$		0			0
$313$	11.5048	+	27.7751i	0.650291	+	1.56994i	0.812356	+	0.583161i	$0.198184\pi$
$313$	11.5048	+	27.7751i	0.650291	+	1.56994i	−0.162066	+	0.986780i	$0.551816\pi$
$314$		0			0
$315$	17.3473	−	12.3614i	0.977411	−	0.696484i
$316$		0			0
$317$	2.55288	−	6.16319i	0.143384	−	0.346159i	−0.835830	−	0.548988i	$-0.815013\pi$
$317$	2.55288	−	6.16319i	0.143384	−	0.346159i	0.979214	+	0.202828i	$0.0650134\pi$
$318$		0			0
$319$	−11.9283	+	11.9283i	−0.667855	+	0.667855i
$320$		0			0
$321$	3.21579	+	7.76361i	0.179488	+	0.433323i
$322$		0			0
$323$			44.5303i			2.47773i
$324$		0			0
$325$	−31.4857	+	1.89589i	−1.74651	+	0.105165i
$326$		0			0
$327$	6.12871	+	6.12871i	0.338919	+	0.338919i
$328$		0			0
$329$		−	22.0418i		−	1.21520i
$330$		0			0
$331$	23.5050	−	9.73608i	1.29195	−	0.535143i	0.372384	−	0.928079i	$-0.378540\pi$
$331$	23.5050	−	9.73608i	1.29195	−	0.535143i	0.919566	+	0.392935i	$0.128540\pi$
$332$		0			0
$333$	−15.2136			−0.833702
$334$		0			0
$335$	−9.09335	+	6.47974i	−0.496823	+	0.354026i
$336$		0			0
$337$		−	2.41226i		−	0.131404i	−0.997839	−	0.0657022i	$-0.979071\pi$
$337$		−	2.41226i		−	0.131404i	0.997839	−	0.0657022i	$-0.0209287\pi$
$338$		0			0
$339$	3.62456	−	1.50134i	0.196859	−	0.0815416i
$340$		0			0
$341$	12.1660	−	5.03934i	0.658828	−	0.272896i
$342$		0			0
$343$	8.79512	−	3.64306i	0.474892	−	0.196707i
$344$		0			0
$345$	−4.83500	+	3.44533i	−0.260308	+	0.185490i
$346$		0			0
$347$	−4.63313	+	1.91911i	−0.248719	+	0.103023i	−0.503560	−	0.863960i	$-0.667977\pi$
$347$	−4.63313	+	1.91911i	−0.248719	+	0.103023i	0.254841	+	0.966983i	$0.417977\pi$
$348$		0			0
$349$	9.85858	+	9.85858i	0.527718	+	0.527718i	0.919891	−	0.392173i	$-0.128277\pi$
$349$	9.85858	+	9.85858i	0.527718	+	0.527718i	−0.392173	+	0.919891i	$0.628277\pi$
$350$		0			0
$351$		−	27.1215i		−	1.44764i
$352$		0			0
$353$	10.9615	−	10.9615i	0.583423	−	0.583423i	−0.352419	−	0.935842i	$-0.614641\pi$
$353$	10.9615	−	10.9615i	0.583423	−	0.583423i	0.935842	+	0.352419i	$0.114641\pi$
$354$		0			0
$355$	−12.7295	+	9.07080i	−0.675612	+	0.481428i
$356$		0			0
$357$	−7.93694	+	19.1615i	−0.420068	+	1.01413i
$358$		0			0
$359$	−29.9598			−1.58122			−0.790608	−	0.612323i	$-0.790235\pi$
$359$	−29.9598			−1.58122			−0.790608	+	0.612323i	$0.790235\pi$
$360$		0			0
$361$	−20.9165	−	20.9165i	−1.10087	−	1.10087i
$362$		0			0
$363$	−4.33494	+	1.79559i	−0.227525	+	0.0942441i
$364$		0			0
$365$	5.85464	+	25.4140i	0.306446	+	1.33023i
$366$		0			0
$367$		−	16.4696i		−	0.859705i	−0.902899	−	0.429852i	$-0.858566\pi$
$367$		−	16.4696i		−	0.859705i	0.902899	−	0.429852i	$-0.141434\pi$
$368$		0			0
$369$	8.64365	+	12.3609i	0.449971	+	0.643482i
$370$		0			0
$371$	14.0105	+	14.0105i	0.727391	+	0.727391i
$372$		0			0
$373$	−15.8668	+	15.8668i	−0.821553	+	0.821553i	−0.986331	−	0.164778i	$-0.947309\pi$
$373$	−15.8668	+	15.8668i	−0.821553	+	0.821553i	0.164778	+	0.986331i	$0.447309\pi$
$374$		0			0
$375$	−8.60894	+	2.53682i	−0.444564	+	0.131001i
$376$		0			0
$377$			46.8718i			2.41402i
$378$		0			0
$379$			21.3874i			1.09860i	0.835626	+	0.549299i	$0.185105\pi$
$379$			21.3874i			1.09860i	−0.835626	+	0.549299i	$0.814895\pi$
$380$		0			0
$381$	−6.40062	−	15.4525i	−0.327914	−	0.791654i
$382$		0			0
$383$	−11.2561	−	27.1745i	−0.575158	−	1.38855i	−0.897114	−	0.441799i	$-0.854340\pi$
$383$	−11.2561	−	27.1745i	−0.575158	−	1.38855i	0.321956	−	0.946755i	$-0.395660\pi$
$384$		0			0
$385$	20.0068	−	4.60899i	1.01964	−	0.234896i
$386$		0			0
$387$	−8.93731	+	8.93731i	−0.454309	+	0.454309i
$388$		0			0
$389$	20.3117	−	20.3117i	1.02984	−	1.02984i	0.0303030	−	0.999541i	$-0.490353\pi$
$389$	20.3117	−	20.3117i	1.02984	−	1.02984i	0.999541	−	0.0303030i	$-0.00964721\pi$
$390$		0			0
$391$	−8.08665	+	19.5229i	−0.408960	+	0.987316i
$392$		0			0
$393$	−1.79132	+	0.741990i	−0.0903603	+	0.0374284i
$394$		0			0
$395$	15.4881	−	11.0365i	0.779292	−	0.555308i
$396$		0			0
$397$	17.6338	+	7.30414i	0.885013	+	0.366584i	0.778439	−	0.627720i	$-0.216012\pi$
$397$	17.6338	+	7.30414i	0.885013	+	0.366584i	0.106574	+	0.994305i	$0.466012\pi$
$398$		0			0
$399$	−8.65881	−	20.9042i	−0.433483	−	1.04652i
$400$		0			0
$401$	−23.0950	−	23.0950i	−1.15331	−	1.15331i	−0.985885	−	0.167425i	$-0.946455\pi$
$401$	−23.0950	−	23.0950i	−1.15331	−	1.15331i	−0.167425	−	0.985885i	$-0.553545\pi$
$402$		0			0
$403$	14.0021	−	33.8040i	0.697494	−	1.68390i
$404$		0			0
$405$	1.81500	+	7.87859i	0.0901879	+	0.391490i
$406$		0			0
$407$	−13.5474	−	5.61151i	−0.671519	−	0.278152i
$408$		0			0
$409$	18.0140			0.890733			0.445367	−	0.895348i	$-0.353073\pi$
$409$	18.0140			0.890733			0.445367	+	0.895348i	$0.353073\pi$
$410$		0			0
$411$	2.70516			0.133436
$412$		0			0
$413$	−39.8316	−	16.4988i	−1.95999	−	0.811853i
$414$		0			0
$415$	−5.57631	−	3.48813i	−0.273730	−	0.171225i
$416$		0			0
$417$	2.31272	−	5.58339i	0.113254	−	0.273420i
$418$		0			0
$419$	−13.7219	−	13.7219i	−0.670358	−	0.670358i	0.287441	−	0.957798i	$-0.407196\pi$
$419$	−13.7219	−	13.7219i	−0.670358	−	0.670358i	−0.957798	+	0.287441i	$0.907196\pi$
$420$		0			0
$421$	−14.5852	−	35.2118i	−0.710838	−	1.71612i	−0.697895	−	0.716200i	$-0.745880\pi$
$421$	−14.5852	−	35.2118i	−0.710838	−	1.71612i	−0.0129430	−	0.999916i	$-0.504120\pi$
$422$		0			0
$423$	11.8619	+	4.91334i	0.576743	+	0.238895i
$424$		0			0
$425$	−21.1896	+	23.9050i	−1.02785	+	1.15956i
$426$		0			0
$427$	38.5470	−	15.9667i	1.86542	−	0.772682i
$428$		0			0
$429$	4.40002	−	10.6226i	0.212435	−	0.512863i
$430$		0			0
$431$	−15.9189	+	15.9189i	−0.766786	+	0.766786i	−0.977539	−	0.210753i	$-0.932408\pi$
$431$	−15.9189	+	15.9189i	−0.766786	+	0.766786i	0.210753	+	0.977539i	$0.432408\pi$
$432$		0			0
$433$	5.19835	−	5.19835i	0.249817	−	0.249817i	−0.571079	−	0.820895i	$-0.693475\pi$
$433$	5.19835	−	5.19835i	0.249817	−	0.249817i	0.820895	+	0.571079i	$0.193475\pi$
$434$		0			0
$435$	2.99393	+	12.9961i	0.143548	+	0.623118i
$436$		0			0
$437$	−8.82214	−	21.2985i	−0.422020	−	1.01885i
$438$		0			0
$439$	−0.921123	−	2.22379i	−0.0439628	−	0.106136i	0.900373	−	0.435119i	$-0.143294\pi$
$439$	−0.921123	−	2.22379i	−0.0439628	−	0.106136i	−0.944336	+	0.328984i	$0.893294\pi$
$440$		0			0
$441$			22.0344i			1.04926i
$442$		0			0
$443$		−	1.32131i		−	0.0627773i	−0.999507	−	0.0313887i	$-0.990007\pi$
$443$		−	1.32131i		−	0.0627773i	0.999507	−	0.0313887i	$-0.00999296\pi$
$444$		0			0
$445$	4.85816	+	6.81770i	0.230299	+	0.323190i
$446$		0			0
$447$	−5.18688	+	5.18688i	−0.245331	+	0.245331i
$448$		0			0
$449$	−7.75719	−	7.75719i	−0.366084	−	0.366084i	0.499963	−	0.866047i	$-0.333347\pi$
$449$	−7.75719	−	7.75719i	−0.366084	−	0.366084i	−0.866047	+	0.499963i	$0.833347\pi$
$450$		0			0
$451$	3.13769	+	14.1953i	0.147748	+	0.668429i
$452$		0			0
$453$		−	3.96925i		−	0.186492i
$454$		0			0
$455$	30.2527	−	48.3636i	1.41827	−	2.26732i
$456$		0			0
$457$	6.19516	−	2.56612i	0.289797	−	0.120038i	−0.233049	−	0.972465i	$-0.574870\pi$
$457$	6.19516	−	2.56612i	0.289797	−	0.120038i	0.522846	+	0.852427i	$0.324870\pi$
$458$		0			0
$459$	−19.4220	−	19.4220i	−0.906543	−	0.906543i
$460$		0			0
$461$	−4.23637			−0.197308			−0.0986538	−	0.995122i	$-0.531454\pi$
$461$	−4.23637			−0.197308			−0.0986538	+	0.995122i	$0.531454\pi$
$462$		0			0
$463$	7.24763	−	17.4973i	0.336826	−	0.813170i	−0.661190	−	0.750218i	$-0.729948\pi$
$463$	7.24763	−	17.4973i	0.336826	−	0.813170i	0.998017	−	0.0629520i	$-0.0200515\pi$
$464$		0			0
$465$	1.72313	−	10.2672i	0.0799083	−	0.476131i
$466$		0			0
$467$	−12.2749	+	12.2749i	−0.568016	+	0.568016i	−0.931572	−	0.363557i	$-0.881562\pi$
$467$	−12.2749	+	12.2749i	−0.568016	+	0.568016i	0.363557	+	0.931572i	$0.381562\pi$
$468$		0			0
$469$		−	20.1938i		−	0.932465i
$470$		0			0
$471$	8.09602	+	8.09602i	0.373045	+	0.373045i
$472$		0			0
$473$	−11.2550	+	4.66196i	−0.517504	+	0.214357i
$474$		0			0
$475$	−2.09466	−	34.7868i	−0.0961098	−	1.59613i
$476$		0			0
$477$	−10.6629	+	4.41672i	−0.488220	+	0.202228i
$478$		0			0
$479$	26.8771	−	11.1329i	1.22805	−	0.508673i	0.328086	−	0.944648i	$-0.393596\pi$
$479$	26.8771	−	11.1329i	1.22805	−	0.508673i	0.899959	+	0.435975i	$0.143596\pi$
$480$		0			0
$481$	−37.6422	+	15.5919i	−1.71634	+	0.710929i
$482$		0			0
$483$		−	10.7372i		−	0.488560i
$484$		0			0
$485$	3.90021	+	5.47336i	0.177100	+	0.248533i
$486$		0			0
$487$	−7.57636			−0.343317			−0.171659	−	0.985156i	$-0.554913\pi$
$487$	−7.57636			−0.343317			−0.171659	+	0.985156i	$0.554913\pi$
$488$		0			0
$489$	12.0070	−	4.97344i	0.542973	−	0.224907i
$490$		0			0
$491$			28.0432i			1.26557i	0.774327	+	0.632786i	$0.218089\pi$
$491$			28.0432i			1.26557i	−0.774327	+	0.632786i	$0.781911\pi$
$492$		0			0
$493$	33.5655	+	33.5655i	1.51171	+	1.51171i
$494$		0			0
$495$	−1.97939	+	11.7941i	−0.0889669	+	0.530107i
$496$		0			0
$497$		−	28.2688i		−	1.26803i
$498$		0			0
$499$	5.13521	+	12.3975i	0.229884	+	0.554988i	0.996163	−	0.0875196i	$-0.0278940\pi$
$499$	5.13521	+	12.3975i	0.229884	+	0.554988i	−0.766279	+	0.642508i	$0.777894\pi$
$500$		0			0
$501$	−5.81072	+	5.81072i	−0.259604	+	0.259604i
$502$		0			0
$503$	4.39737	−	10.6162i	0.196069	−	0.473353i	−0.795015	−	0.606590i	$-0.792537\pi$
$503$	4.39737	−	10.6162i	0.196069	−	0.473353i	0.991084	+	0.133237i	$0.0425371\pi$
$504$		0			0
$505$	4.96598	+	0.833432i	0.220983	+	0.0370872i
$506$		0			0
$507$	−8.23214	−	19.8742i	−0.365602	−	0.882642i
$508$		0			0
$509$	−0.888935	+	2.14608i	−0.0394014	+	0.0951233i	−0.942355	−	0.334614i	$-0.891394\pi$
$509$	−0.888935	+	2.14608i	−0.0394014	+	0.0951233i	0.902954	+	0.429738i	$0.141394\pi$
$510$		0			0
$511$	−43.5758	−	18.0497i	−1.92768	−	0.798470i
$512$		0			0
$513$	29.9650			1.32299
$514$		0			0
$515$	10.1309	−	2.33387i	0.446422	−	0.102842i
$516$		0			0
$517$	8.75043	+	8.75043i	0.384844	+	0.384844i
$518$		0			0
$519$	−9.87218	−	4.08919i	−0.433340	−	0.179496i
$520$		0			0
$521$	−37.7095	+	15.6198i	−1.65208	+	0.684315i	−0.997432	−	0.0716155i	$-0.977185\pi$
$521$	−37.7095	+	15.6198i	−1.65208	+	0.684315i	−0.654651	+	0.755931i	$0.727185\pi$
$522$		0			0
$523$	−7.01605	+	7.01605i	−0.306791	+	0.306791i	−0.843663	−	0.536873i	$-0.819606\pi$
$523$	−7.01605	+	7.01605i	−0.306791	+	0.306791i	0.536873	+	0.843663i	$0.319606\pi$
$524$		0			0
$525$	5.29895	−	15.3422i	0.231265	−	0.669587i
$526$		0			0
$527$	−14.1804	−	34.2346i	−0.617709	−	1.49128i
$528$		0			0
$529$			12.0603i			0.524359i
$530$		0			0
$531$	17.7577	−	17.7577i	0.770621	−	0.770621i
$532$		0			0
$533$	34.0547	+	21.7252i	1.47507	+	0.941023i
$534$		0			0
$535$	−19.8450	−	12.4135i	−0.857972	−	0.536684i
$536$		0			0
$537$	7.07383	+	7.07383i	0.305258	+	0.305258i
$538$		0			0
$539$	−8.12735	+	19.6212i	−0.350070	+	0.845143i
$540$		0			0
$541$	−25.0077	+	25.0077i	−1.07516	+	1.07516i	−0.0782280	+	0.996935i	$0.524926\pi$
$541$	−25.0077	+	25.0077i	−1.07516	+	1.07516i	−0.996935	+	0.0782280i	$0.975074\pi$
$542$		0			0
$543$	−2.15313	−	2.15313i	−0.0923994	−	0.0923994i
$544$		0			0
$545$	−23.8101	−	3.99601i	−1.01991	−	0.171170i
$546$		0			0
$547$	−2.08817	+	0.864950i	−0.0892839	+	0.0369826i	−0.426878	−	0.904309i	$-0.640387\pi$
$547$	−2.08817	+	0.864950i	−0.0892839	+	0.0369826i	0.337594	+	0.941292i	$0.390387\pi$
$548$		0			0
$549$			24.3033i			1.03724i
$550$		0			0
$551$	−51.7861			−2.20616
$552$		0			0
$553$			34.3949i			1.46262i
$554$		0			0
$555$	−9.44112	+	6.72756i	−0.400753	+	0.285569i
$556$		0			0
$557$	−10.6122	−	25.6200i	−0.449651	−	1.08555i	−0.972453	−	0.233100i	$-0.925113\pi$
$557$	−10.6122	−	25.6200i	−0.449651	−	1.08555i	0.522802	−	0.852454i	$-0.324887\pi$
$558$		0			0
$559$	−12.9535	+	31.2726i	−0.547875	+	1.32269i
$560$		0			0
$561$	−4.45606	−	10.7579i	−0.188135	−	0.454198i
$562$		0			0
$563$	12.8051	+	5.30406i	0.539673	+	0.223540i	0.635834	−	0.771826i	$-0.280656\pi$
$563$	12.8051	+	5.30406i	0.539673	+	0.223540i	−0.0961612	+	0.995366i	$0.530656\pi$
$564$		0			0
$565$	−5.79545	+	9.26491i	−0.243816	+	0.389778i
$566$		0			0
$567$	−13.5089	−	5.59557i	−0.567321	−	0.234992i
$568$		0			0
$569$	23.7930	−	23.7930i	0.997455	−	0.997455i	−0.00254162	−	0.999997i	$-0.500809\pi$
$569$	23.7930	−	23.7930i	0.997455	−	0.997455i	0.999997	+	0.00254162i	$0.000809024\pi$
$570$		0			0
$571$	7.19779	+	17.3770i	0.301218	+	0.727205i	0.999930	+	0.0118020i	$0.00375678\pi$
$571$	7.19779	+	17.3770i	0.301218	+	0.727205i	−0.698712	+	0.715403i	$0.746243\pi$
$572$		0			0
$573$	−5.72940	+	5.72940i	−0.239349	+	0.239349i
$574$		0			0
$575$	5.39890	−	15.6316i	0.225150	−	0.651881i
$576$		0			0
$577$	0.400455	−	0.966784i	0.0166712	−	0.0402477i	−0.915325	−	0.402717i	$-0.868066\pi$
$577$	0.400455	−	0.966784i	0.0166712	−	0.0402477i	0.931996	+	0.362469i	$0.118066\pi$
$578$		0			0
$579$	4.74171	+	4.74171i	0.197059	+	0.197059i
$580$		0			0
$581$	10.9900	−	4.55220i	0.455941	−	0.188857i
$582$		0			0
$583$	−11.1242			−0.460715
$584$		0			0
$585$	19.2834	+	27.0613i	0.797269	+	1.11885i
$586$		0			0
$587$	−5.00464	+	12.0823i	−0.206563	+	0.498688i	−0.992878	−	0.119139i	$-0.961987\pi$
$587$	−5.00464	+	12.0823i	−0.206563	+	0.498688i	0.786314	+	0.617827i	$0.211987\pi$
$588$		0			0
$589$	37.3482	+	15.4701i	1.53891	+	0.637436i
$590$		0			0
$591$	1.09575	+	0.453876i	0.0450733	+	0.0186700i
$592$		0			0
$593$	−12.7963	−	30.8930i	−0.525480	−	1.26862i	−0.934457	−	0.356077i	$-0.884114\pi$
$593$	−12.7963	−	30.8930i	−0.525480	−	1.26862i	0.408976	−	0.912545i	$-0.365886\pi$
$594$		0			0
$595$	−12.9694	−	56.2982i	−0.531695	−	2.30800i
$596$		0			0
$597$	−4.37694	−	4.37694i	−0.179136	−	0.179136i
$598$		0			0
$599$	−22.0182			−0.899641			−0.449820	−	0.893119i	$-0.648512\pi$
$599$	−22.0182			−0.899641			−0.449820	+	0.893119i	$0.648512\pi$
$600$		0			0
$601$	6.27711	−	15.1543i	0.256049	−	0.618156i	−0.742622	−	0.669711i	$-0.766418\pi$
$601$	6.27711	−	15.1543i	0.256049	−	0.618156i	0.998670	+	0.0515554i	$0.0164179\pi$
$602$		0			0
$603$	10.8674	+	4.50141i	0.442554	+	0.183312i
$604$		0			0
$605$	6.93131	−	11.0808i	0.281798	−	0.450497i
$606$		0			0
$607$	−28.0844			−1.13991			−0.569955	−	0.821676i	$-0.693039\pi$
$607$	−28.0844			−1.13991			−0.569955	+	0.821676i	$0.693039\pi$
$608$		0			0
$609$	−22.2836	−	9.23019i	−0.902979	−	0.374026i
$610$		0			0
$611$	34.3846			1.39105
$612$		0			0
$613$	−35.7762			−1.44499			−0.722493	−	0.691378i	$-0.757004\pi$
$613$	−35.7762			−1.44499			−0.722493	+	0.691378i	$0.757004\pi$
$614$		0			0
$615$	10.8300	+	3.84851i	0.436709	+	0.155187i
$616$		0			0
$617$	15.9301			0.641323			0.320662	−	0.947194i	$-0.396095\pi$
$617$	15.9301			0.641323			0.320662	+	0.947194i	$0.396095\pi$
$618$		0			0
$619$	−1.25274			−0.0503518			−0.0251759	−	0.999683i	$-0.508015\pi$
$619$	−1.25274			−0.0503518			−0.0251759	+	0.999683i	$0.508015\pi$
$620$		0			0
$621$	13.1372	+	5.44161i	0.527178	+	0.218364i
$622$		0			0
$623$	−15.1403			−0.606582
$624$		0			0
$625$	15.4287	−	19.6711i	0.617149	−	0.786846i
$626$		0			0
$627$	11.7363	+	4.86134i	0.468703	+	0.194143i
$628$		0			0
$629$	−15.7905	+	38.1216i	−0.629608	+	1.52001i
$630$		0			0
$631$	23.4794			0.934700			0.467350	−	0.884072i	$-0.345209\pi$
$631$	23.4794			0.934700			0.467350	+	0.884072i	$0.345209\pi$
$632$		0			0
$633$	−7.03427	−	7.03427i	−0.279587	−	0.279587i
$634$		0			0
$635$	39.4988	+	24.7075i	1.56746	+	0.980489i
$636$		0			0
$637$	22.5823	+	54.5185i	0.894743	+	2.16010i
$638$		0			0
$639$	15.2129	+	6.30139i	0.601813	+	0.249279i
$640$		0			0
$641$	10.3487	+	4.28659i	0.408751	+	0.169310i	0.577578	−	0.816336i	$-0.303998\pi$
$641$	10.3487	+	4.28659i	0.408751	+	0.169310i	−0.168827	+	0.985646i	$0.553998\pi$
$642$		0			0
$643$	−13.4099	+	32.3743i	−0.528834	+	1.27672i	0.403454	+	0.915000i	$0.367809\pi$
$643$	−13.4099	+	32.3743i	−0.528834	+	1.27672i	−0.932288	+	0.361717i	$0.882191\pi$
$644$		0			0
$645$	−1.59409	+	9.49835i	−0.0627673	+	0.373997i
$646$		0			0
$647$	31.5710			1.24118			0.620592	−	0.784133i	$-0.286892\pi$
$647$	31.5710			1.24118			0.620592	+	0.784133i	$0.286892\pi$
$648$		0			0
$649$	22.3628	−	9.26296i	0.877815	−	0.363603i
$650$		0			0
$651$	13.3137	+	13.3137i	0.521804	+	0.521804i
$652$		0			0
$653$	−9.26076	+	22.3575i	−0.362402	+	0.874915i	0.632546	+	0.774522i	$0.282010\pi$
$653$	−9.26076	+	22.3575i	−0.362402	+	0.874915i	−0.994948	+	0.100392i	$0.967990\pi$
$654$		0			0
$655$	2.86422	−	4.57889i	0.111914	−	0.178912i
$656$		0			0
$657$	19.4270	−	19.4270i	0.757918	−	0.757918i
$658$		0			0
$659$	12.8278	+	30.9690i	0.499699	+	1.20638i	0.949646	+	0.313325i	$0.101443\pi$
$659$	12.8278	+	30.9690i	0.499699	+	1.20638i	−0.449946	+	0.893056i	$0.648557\pi$
$660$		0			0
$661$	18.1588	−	18.1588i	0.706294	−	0.706294i	−0.259460	−	0.965754i	$-0.583545\pi$
$661$	18.1588	−	18.1588i	0.706294	−	0.706294i	0.965754	+	0.259460i	$0.0835447\pi$
$662$		0			0
$663$	−29.8913	−	12.3814i	−1.16088	−	0.480854i
$664$		0			0
$665$	53.4343	+	33.4246i	2.07209	+	1.29615i
$666$		0			0
$667$	−22.7040	−	9.40429i	−0.879101	−	0.364136i
$668$		0			0
$669$	7.23528	+	17.4675i	0.279732	+	0.675333i
$670$		0			0
$671$	−8.96421	+	21.6415i	−0.346059	+	0.835461i
$672$		0			0
$673$	5.17009	+	12.4817i	0.199292	+	0.481134i	0.991656	−	0.128915i	$-0.0411496\pi$
$673$	5.17009	+	12.4817i	0.199292	+	0.481134i	−0.792363	+	0.610049i	$0.791150\pi$
$674$		0			0
$675$	16.0860	+	14.2588i	0.619149	+	0.548820i
$676$		0			0
$677$		−	24.9353i		−	0.958341i	−0.877722	−	0.479171i	$-0.840937\pi$
$677$		−	24.9353i		−	0.958341i	0.877722	−	0.479171i	$-0.159063\pi$
$678$		0			0
$679$	−12.1548			−0.466460
$680$		0			0
$681$		−	8.71152i		−	0.333826i
$682$		0			0
$683$	11.0219	−	4.56544i	0.421743	−	0.174692i	−0.161710	−	0.986838i	$-0.551701\pi$
$683$	11.0219	−	4.56544i	0.421743	−	0.174692i	0.583453	+	0.812147i	$0.301701\pi$
$684$		0			0
$685$	−6.13670	+	4.37289i	−0.234471	+	0.167080i
$686$		0			0
$687$	−3.45286	−	3.45286i	−0.131735	−	0.131735i
$688$		0			0
$689$	−21.8560	+	21.8560i	−0.832648	+	0.832648i
$690$		0			0
$691$	−8.34307	+	20.1420i	−0.317385	+	0.766236i	0.682006	+	0.731347i	$0.261108\pi$
$691$	−8.34307	+	20.1420i	−0.317385	+	0.766236i	−0.999391	+	0.0348894i	$0.988892\pi$
$692$		0			0
$693$	−15.2936	−	15.2936i	−0.580956	−	0.580956i
$694$		0			0
$695$	3.77912	+	16.4045i	0.143350	+	0.622259i
$696$		0			0
$697$	39.9447	−	8.82929i	1.51301	−	0.334433i
$698$		0			0
$699$	−10.5868	+	10.5868i	−0.400430	+	0.400430i
$700$		0			0
$701$		−	51.4034i		−	1.94148i	−0.240137	−	0.970739i	$-0.577192\pi$
$701$		−	51.4034i		−	1.94148i	0.240137	−	0.970739i	$-0.422808\pi$
$702$		0			0
$703$	−17.2266	−	41.5888i	−0.649715	−	1.56855i
$704$		0			0
$705$	9.53381	−	2.19631i	0.359064	−	0.0827178i
$706$		0			0
$707$	−6.43946	+	6.43946i	−0.242181	+	0.242181i
$708$		0			0
$709$	38.8799	−	16.1046i	1.46017	−	0.604821i	0.495574	−	0.868566i	$-0.334958\pi$
$709$	38.8799	−	16.1046i	1.46017	−	0.604821i	0.964592	+	0.263745i	$0.0849579\pi$
$710$		0			0
$711$	−18.5097	−	7.66697i	−0.694168	−	0.287534i
$712$		0			0
$713$	13.5648	+	13.5648i	0.508005	+	0.508005i
$714$		0			0
$715$	7.18989	+	31.2101i	0.268887	+	1.16719i
$716$		0			0
$717$	3.12877			0.116846
$718$		0			0
$719$	−19.2440	−	7.97113i	−0.717680	−	0.297273i	−0.00620185	−	0.999981i	$-0.501974\pi$
$719$	−19.2440	−	7.97113i	−0.717680	−	0.297273i	−0.711479	+	0.702708i	$0.751974\pi$
$720$		0			0
$721$	−7.19523	+	17.3708i	−0.267964	+	0.646923i
$722$		0			0
$723$	2.28927	+	5.52678i	0.0851388	+	0.205543i
$724$		0			0
$725$	−27.8000	−	24.6423i	−1.03247	−	0.915191i
$726$		0			0
$727$	9.52055	−	22.9846i	0.353098	−	0.852453i	−0.643137	−	0.765751i	$-0.722367\pi$
$727$	9.52055	−	22.9846i	0.353098	−	0.852453i	0.996234	−	0.0867019i	$-0.0276328\pi$
$728$		0			0
$729$	−1.29838	+	1.29838i	−0.0480883	+	0.0480883i
$730$		0			0
$731$	13.1185	+	31.6708i	0.485205	+	1.17139i
$732$		0			0
$733$		−	29.8571i		−	1.10280i	−0.834241	−	0.551399i	$-0.814094\pi$
$733$		−	29.8571i		−	1.10280i	0.834241	−	0.551399i	$-0.185906\pi$
$734$		0			0
$735$	9.74375	+	13.6739i	0.359404	+	0.504369i
$736$		0			0
$737$	8.01681	+	8.01681i	0.295303	+	0.295303i
$738$		0			0
$739$		−	47.0589i		−	1.73109i	−0.500830	−	0.865545i	$-0.666972\pi$
$739$		−	47.0589i		−	1.73109i	0.500830	−	0.865545i	$-0.333028\pi$
$740$		0			0
$741$	32.6100	−	13.5075i	1.19796	−	0.496210i
$742$		0			0
$743$	−41.0683			−1.50665			−0.753325	−	0.657648i	$-0.771551\pi$
$743$	−41.0683			−1.50665			−0.753325	+	0.657648i	$0.771551\pi$
$744$		0			0
$745$	3.38192	−	20.1511i	0.123904	−	0.738279i
$746$		0			0
$747$			6.92902i			0.253520i
$748$		0			0
$749$	39.1112	−	16.2004i	1.42909	−	0.591949i
$750$		0			0
$751$	12.5950	−	5.21703i	0.459599	−	0.190372i	−0.140857	−	0.990030i	$-0.544986\pi$
$751$	12.5950	−	5.21703i	0.459599	−	0.190372i	0.600456	+	0.799658i	$0.294986\pi$
$752$		0			0
$753$	−15.8299	+	6.55695i	−0.576873	+	0.238949i
$754$		0			0
$755$	6.41630	+	9.00431i	0.233513	+	0.327700i
$756$		0			0
$757$	−28.7528	+	11.9098i	−1.04504	+	0.432869i	−0.838118	−	0.545489i	$-0.816344\pi$
$757$	−28.7528	+	11.9098i	−1.04504	+	0.432869i	−0.206920	+	0.978358i	$0.566344\pi$
$758$		0			0
$759$	4.26260	+	4.26260i	0.154722	+	0.154722i
$760$		0			0
$761$			15.0665i			0.546161i	0.961991	+	0.273081i	$0.0880426\pi$
$761$			15.0665i			0.546161i	−0.961991	+	0.273081i	$0.911957\pi$
$762$		0			0
$763$	30.8749	−	30.8749i	1.11775	−	1.11775i
$764$		0			0
$765$	33.1880	+	5.56989i	1.19992	+	0.201380i
$766$		0			0
$767$	25.7376	−	62.1362i	0.929333	−	2.24361i
$768$		0			0
$769$	−4.54226			−0.163798			−0.0818991	−	0.996641i	$-0.526099\pi$
$769$	−4.54226			−0.163798			−0.0818991	+	0.996641i	$0.526099\pi$
$770$		0			0
$771$	−8.45939	−	8.45939i	−0.304657	−	0.304657i
$772$		0			0
$773$	−41.3044	+	17.1089i	−1.48562	+	0.615363i	−0.970358	−	0.241671i	$-0.922304\pi$
$773$	−41.3044	+	17.1089i	−1.48562	+	0.615363i	−0.515260	+	0.857034i	$0.672304\pi$
$774$		0			0
$775$	12.6880	+	26.0768i	0.455767	+	0.936706i
$776$		0			0
$777$		−	20.9661i		−	0.752156i
$778$		0			0
$779$	−24.0030	+	37.6252i	−0.859996	+	1.34806i
$780$		0			0
$781$	11.2225	+	11.2225i	0.401572	+	0.401572i
$782$		0			0
$783$	22.5867	−	22.5867i	0.807181	−	0.807181i
$784$		0			0
$785$	−31.4532	−	5.27873i	−1.12261	−	0.188406i
$786$		0			0
$787$		−	31.4406i		−	1.12074i	−0.828243	−	0.560368i	$-0.810660\pi$
$787$		−	31.4406i		−	1.12074i	0.828243	−	0.560368i	$-0.189340\pi$
$788$		0			0
$789$			0.164514i			0.00585685i
$790$		0			0
$791$	−7.56338	−	18.2596i	−0.268923	−	0.649238i
$792$		0			0
$793$	24.9076	+	60.1321i	0.884493	+	2.13536i
$794$		0			0
$795$	−4.66397	+	7.45607i	−0.165414	+	0.264440i
$796$		0			0
$797$	0.705448	−	0.705448i	0.0249883	−	0.0249883i	−0.694502	−	0.719491i	$-0.744375\pi$
$797$	0.705448	−	0.705448i	0.0249883	−	0.0249883i	0.719491	+	0.694502i	$0.244375\pi$
$798$		0			0
$799$	24.6232	−	24.6232i	0.871107	−	0.871107i
$800$		0			0
$801$	3.37492	−	8.14777i	0.119247	−	0.287887i
$802$		0			0
$803$	24.4648	−	10.1337i	0.863345	−	0.357609i
$804$		0			0
$805$	17.3567	+	24.3575i	0.611744	+	0.858491i
$806$		0			0
$807$	2.53205	+	1.04881i	0.0891325	+	0.0369199i
$808$		0			0
$809$	−3.52212	−	8.50315i	−0.123831	−	0.298955i	0.849792	−	0.527119i	$-0.176728\pi$
$809$	−3.52212	−	8.50315i	−0.123831	−	0.298955i	−0.973623	+	0.228164i	$0.926728\pi$
$810$		0			0
$811$	16.4192	+	16.4192i	0.576557	+	0.576557i	0.933953	−	0.357396i	$-0.116335\pi$
$811$	16.4192	+	16.4192i	0.576557	+	0.576557i	−0.357396	+	0.933953i	$0.616335\pi$
$812$		0			0
$813$	−4.86509	+	11.7454i	−0.170626	+	0.411928i
$814$		0			0
$815$	−19.1984	+	30.6916i	−0.672490	+	1.07508i
$816$		0			0
$817$	−34.5513	−	14.3116i	−1.20880	−	0.500701i
$818$		0			0
$819$	−60.0958			−2.09992
$820$		0			0
$821$	−13.0829			−0.456596			−0.228298	−	0.973591i	$-0.573316\pi$
$821$	−13.0829			−0.456596			−0.228298	+	0.973591i	$0.573316\pi$
$822$		0			0
$823$	10.7634	+	4.45835i	0.375189	+	0.155408i	0.562306	−	0.826929i	$-0.309914\pi$
$823$	10.7634	+	4.45835i	0.375189	+	0.155408i	−0.187117	+	0.982338i	$0.559914\pi$
$824$		0			0
$825$	3.98708	+	8.19437i	0.138812	+	0.285291i
$826$		0			0
$827$	−17.3903	+	41.9838i	−0.604718	+	1.45992i	0.263956	+	0.964535i	$0.414973\pi$
$827$	−17.3903	+	41.9838i	−0.604718	+	1.45992i	−0.868674	+	0.495384i	$0.835027\pi$
$828$		0			0
$829$	−6.78221	−	6.78221i	−0.235556	−	0.235556i	0.579451	−	0.815007i	$-0.303267\pi$
$829$	−6.78221	−	6.78221i	−0.235556	−	0.235556i	−0.815007	+	0.579451i	$0.803267\pi$
$830$		0			0
$831$	−5.50795	−	13.2974i	−0.191069	−	0.461281i
$832$		0			0
$833$	55.2128	+	22.8699i	1.91301	+	0.792395i
$834$		0			0
$835$	3.78868	−	22.5747i	0.131113	−	0.781230i
$836$		0			0
$837$	−23.0369	+	9.54219i	−0.796272	+	0.329826i
$838$		0			0
$839$	−2.79958	+	6.75879i	−0.0966523	+	0.233339i	−0.964809	−	0.262950i	$-0.915305\pi$
$839$	−2.79958	+	6.75879i	−0.0966523	+	0.233339i	0.868157	+	0.496289i	$0.165305\pi$
$840$		0			0
$841$	−18.5286	+	18.5286i	−0.638916	+	0.638916i
$842$		0			0
$843$	−10.4280	+	10.4280i	−0.359158	+	0.359158i
$844$		0			0
$845$	50.8013	+	31.7776i	1.74762	+	1.09318i
$846$		0			0
$847$	9.04575	+	21.8384i	0.310816	+	0.750375i
$848$		0			0
$849$	6.81375	+	16.4499i	0.233847	+	0.564558i
$850$		0			0
$851$		−	21.3616i		−	0.732267i
$852$		0			0
$853$		−	16.0968i		−	0.551145i	−0.961280	−	0.275572i	$-0.911133\pi$
$853$		−	16.0968i		−	0.551145i	0.961280	−	0.275572i	$-0.0888674\pi$
$854$		0			0
$855$	−29.8986	+	21.3051i	−1.02251	+	0.728621i
$856$		0			0
$857$	−7.36223	+	7.36223i	−0.251489	+	0.251489i	−0.821581	−	0.570092i	$-0.806908\pi$
$857$	−7.36223	+	7.36223i	−0.251489	+	0.251489i	0.570092	+	0.821581i	$0.306908\pi$
$858$		0			0
$859$	9.58283	+	9.58283i	0.326962	+	0.326962i	0.851430	−	0.524468i	$-0.175736\pi$
$859$	9.58283	+	9.58283i	0.326962	+	0.326962i	−0.524468	+	0.851430i	$0.675736\pi$
$860$		0			0
$861$	−17.0347	+	11.9120i	−0.580542	+	0.405958i
$862$		0			0
$863$		−	8.23461i		−	0.280309i	−0.990130	−	0.140155i	$-0.955240\pi$
$863$		−	8.23461i		−	0.280309i	0.990130	−	0.140155i	$-0.0447600\pi$
$864$		0			0
$865$	29.0054	−	6.68198i	0.986212	−	0.227194i
$866$		0			0
$867$	−17.6642	+	7.31676i	−0.599908	+	0.248490i
$868$		0			0
$869$	−13.6545	−	13.6545i	−0.463198	−	0.463198i
$870$		0			0
$871$	31.5018			1.06740
$872$		0			0
$873$	2.70944	−	6.54116i	0.0917006	−	0.221385i
$874$		0			0
$875$	12.7799	+	43.3697i	0.432038	+	1.46616i
$876$		0			0
$877$	36.4594	−	36.4594i	1.23115	−	1.23115i	0.267623	−	0.963524i	$-0.413762\pi$
$877$	36.4594	−	36.4594i	1.23115	−	1.23115i	0.963524	−	0.267623i	$-0.0862381\pi$
$878$		0			0
$879$			23.2030i			0.782619i
$880$		0			0
$881$	41.3441	+	41.3441i	1.39292	+	1.39292i	0.818706	+	0.574213i	$0.194692\pi$
$881$	41.3441	+	41.3441i	1.39292	+	1.39292i	0.574213	+	0.818706i	$0.305308\pi$
$882$		0			0
$883$	−25.1279	+	10.4083i	−0.845622	+	0.350268i	−0.763068	−	0.646318i	$-0.776308\pi$
$883$	−25.1279	+	10.4083i	−0.845622	+	0.350268i	−0.0825543	+	0.996587i	$0.526308\pi$
$884$		0			0
$885$	3.16734	−	18.8725i	0.106469	−	0.634392i
$886$		0			0
$887$	40.0070	−	16.5714i	1.34330	−	0.556414i	0.408882	−	0.912587i	$-0.365919\pi$
$887$	40.0070	−	16.5714i	1.34330	−	0.556414i	0.934420	+	0.356173i	$0.115919\pi$
$888$		0			0
$889$	−77.8457	+	32.2447i	−2.61086	+	1.08145i
$890$		0			0
$891$	7.58434	−	3.14154i	0.254085	−	0.105245i
$892$		0			0
$893$			37.9896i			1.27127i
$894$		0			0
$895$	−27.4819	−	4.61224i	−0.918619	−	0.154170i
$896$		0			0
$897$	16.7498			0.559258
$898$		0			0
$899$	39.8128	−	16.4910i	1.32783	−	0.550005i
$900$		0			0
$901$			31.3027i			1.04285i
$902$		0			0
$903$	−12.3166	−	12.3166i	−0.409872	−	0.409872i
$904$		0			0
$905$	8.36492	+	1.40387i	0.278059	+	0.0466662i
$906$		0			0
$907$		−	39.8764i		−	1.32407i	−0.749471	−	0.662037i	$-0.769692\pi$
$907$		−	39.8764i		−	1.32407i	0.749471	−	0.662037i	$-0.230308\pi$
$908$		0			0
$909$	−2.02999	−	4.90083i	−0.0673306	−	0.162550i
$910$		0			0
$911$	14.8501	−	14.8501i	0.492005	−	0.492005i	−0.416932	−	0.908938i	$-0.636895\pi$
$911$	14.8501	−	14.8501i	0.492005	−	0.492005i	0.908938	+	0.416932i	$0.136895\pi$
$912$		0			0
$913$	−2.55575	+	6.17013i	−0.0845831	+	0.204202i
$914$		0			0
$915$	10.7471	+	15.0819i	0.355287	+	0.498591i
$916$		0			0
$917$	3.73796	+	9.02424i	0.123438	+	0.298007i
$918$		0			0
$919$	2.09210	−	5.05077i	0.0690119	−	0.166609i	−0.885610	−	0.464429i	$-0.846259\pi$
$919$	2.09210	−	5.05077i	0.0690119	−	0.166609i	0.954622	+	0.297820i	$0.0962595\pi$
$920$		0			0
$921$	1.80248	+	0.746613i	0.0593939	+	0.0246017i
$922$		0			0
$923$	44.0984			1.45152
$924$		0			0
$925$	10.5422	−	30.5231i	0.346626	−	1.00359i
$926$		0			0
$927$	−7.74427	−	7.74427i	−0.254355	−	0.254355i
$928$		0			0
$929$	33.0991	+	13.7101i	1.08594	+	0.449813i	0.852591	−	0.522579i	$-0.175030\pi$
$929$	33.0991	+	13.7101i	1.08594	+	0.449813i	0.233354	+	0.972392i	$0.425030\pi$
$930$		0			0
$931$	−60.2345	+	24.9499i	−1.97410	+	0.817701i
$932$		0			0
$933$	14.4438	−	14.4438i	0.472869	−	0.472869i
$934$		0			0
$935$	27.4987	+	17.2012i	0.899304	+	0.562539i
$936$		0			0
$937$	18.6611	+	45.0518i	0.609631	+	1.47178i	0.863403	+	0.504515i	$0.168329\pi$
$937$	18.6611	+	45.0518i	0.609631	+	1.47178i	−0.253772	+	0.967264i	$0.581671\pi$
$938$		0			0
$939$		−	24.1333i		−	0.787559i
$940$		0			0
$941$	−34.5386	+	34.5386i	−1.12593	+	1.12593i	−0.135094	+	0.990833i	$0.543134\pi$
$941$	−34.5386	+	34.5386i	−1.12593	+	1.12593i	−0.990833	+	0.135094i	$0.956866\pi$
$942$		0			0
$943$	−17.3560	+	12.1366i	−0.565190	+	0.395223i
$944$		0			0
$945$	−37.8838	+	8.72731i	−1.23236	+	0.283899i
$946$		0			0
$947$	−13.9238	−	13.9238i	−0.452464	−	0.452464i	0.443707	−	0.896172i	$-0.353663\pi$
$947$	−13.9238	−	13.9238i	−0.452464	−	0.452464i	−0.896172	+	0.443707i	$0.853663\pi$
$948$		0			0
$949$	28.1570	−	67.9769i	0.914014	−	2.20662i
$950$		0			0
$951$	−3.78661	+	3.78661i	−0.122789	+	0.122789i
$952$		0			0
$953$	−10.7779	−	10.7779i	−0.349132	−	0.349132i	0.510654	−	0.859786i	$-0.329403\pi$
$953$	−10.7779	−	10.7779i	−0.349132	−	0.349132i	−0.859786	+	0.510654i	$0.829403\pi$
$954$		0			0
$955$	3.73566	−	22.2588i	0.120883	−	0.720278i
$956$		0			0
$957$	12.5108	−	5.18213i	0.404415	−	0.167514i
$958$		0			0
$959$		−	13.6279i		−	0.440069i
$960$		0			0
$961$	−2.63943			−0.0851429
$962$		0			0
$963$			24.6590i			0.794625i
$964$		0			0
$965$	−18.4216	−	3.09167i	−0.593013	−	0.0995243i
$966$		0			0
$967$	4.12311	+	9.95408i	0.132590	+	0.320102i	0.976206	−	0.216846i	$-0.0695771\pi$
$967$	4.12311	+	9.95408i	0.132590	+	0.320102i	−0.843615	+	0.536948i	$0.819577\pi$
$968$		0			0
$969$	13.6795	−	33.0253i	0.439450	−	1.06093i
$970$		0			0
$971$	−17.7917	−	42.9529i	−0.570962	−	1.37842i	−0.900737	−	0.434365i	$-0.856973\pi$
$971$	−17.7917	−	42.9529i	−0.570962	−	1.37842i	0.329775	−	0.944059i	$-0.393027\pi$
$972$		0			0
$973$	−28.1278	−	11.6509i	−0.901734	−	0.373511i
$974$		0			0
$975$	23.9333	+	8.26621i	0.766480	+	0.264731i
$976$		0			0
$977$	−28.7981	−	11.9285i	−0.921332	−	0.381628i	−0.128948	−	0.991651i	$-0.541160\pi$
$977$	−28.7981	−	11.9285i	−0.921332	−	0.381628i	−0.792384	+	0.610023i	$0.791160\pi$
$978$		0			0
$979$	6.01057	−	6.01057i	0.192099	−	0.192099i
$980$		0			0
$981$	9.73309	+	23.4978i	0.310754	+	0.750226i
$982$		0			0
$983$	−10.4931	+	10.4931i	−0.334679	+	0.334679i	−0.854360	−	0.519681i	$-0.826051\pi$
$983$	−10.4931	+	10.4931i	−0.334679	+	0.334679i	0.519681	+	0.854360i	$0.326051\pi$
$984$		0			0
$985$	−3.21943	+	0.741661i	−0.102579	+	0.0236313i
$986$		0			0
$987$	−6.77115	+	16.3470i	−0.215528	+	0.520331i
$988$		0			0
$989$	−12.5490	−	12.5490i	−0.399034	−	0.399034i
$990$		0			0
$991$	33.7166	−	13.9659i	1.07104	−	0.443641i	0.223685	−	0.974661i	$-0.428191\pi$
$991$	33.7166	−	13.9659i	1.07104	−	0.443641i	0.847359	+	0.531020i	$0.178191\pi$
$992$		0			0
$993$	−20.4230			−0.648105
$994$		0			0
$995$	17.0045	+	2.85383i	0.539078	+	0.0904725i
$996$		0			0
$997$	15.4638	−	37.3330i	0.489744	−	1.18235i	−0.465105	−	0.885255i	$-0.653983\pi$
$997$	15.4638	−	37.3330i	0.489744	−	1.18235i	0.954849	−	0.297091i	$-0.0960165\pi$
$998$		0			0
$999$	25.6525	+	10.6256i	0.811610	+	0.336180i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.x.a.273.9	✓	84
5.2	odd	4		820.2.y.a.437.9	yes	84
41.38	odd	8		820.2.y.a.653.9	yes	84
205.202	even	8	inner	820.2.x.a.817.9	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.9	✓	84	1.1	even	1	trivial
820.2.x.a.817.9	yes	84	205.202	even	8	inner
820.2.y.a.437.9	yes	84	5.2	odd	4
820.2.y.a.653.9	yes	84	41.38	odd	8

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.x (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.741636 - 0.307196i) q^{3} +(2.17900 - 0.501977i) q^{5} +(-1.54758 + 3.73618i) q^{7} +(-1.66567 - 1.66567i) q^{9} +(-0.868860 - 2.09761i) q^{11} +(-5.82833 - 2.41417i) q^{13} +(-1.77023 - 0.297094i) q^{15} +(-5.90256 + 2.44492i) q^{17} +(2.66729 - 6.43941i) q^{19} +(2.29548 - 2.29548i) q^{21} +(2.33878 - 2.33878i) q^{23} +(4.49604 - 2.18761i) q^{25} +(1.64522 + 3.97191i) q^{27} +(-2.84330 - 6.86433i) q^{29} +5.79995i q^{31} +1.82258i q^{33} +(-1.49669 + 8.91797i) q^{35} +(4.56684 - 4.56684i) q^{37} +(3.58088 + 3.58088i) q^{39} +(-6.30515 - 1.11584i) q^{41} -5.36561i q^{43} +(-4.46560 - 2.79335i) q^{45} +(-5.03559 + 2.08581i) q^{47} +(-6.61431 - 6.61431i) q^{49} +5.12863 q^{51} +(1.87498 - 4.52660i) q^{53} +(-2.94619 - 4.13454i) q^{55} +(-3.95632 + 3.95632i) q^{57} +10.6611i q^{59} +(-7.29537 - 7.29537i) q^{61} +(8.80097 - 3.64548i) q^{63} +(-13.9118 - 2.33479i) q^{65} +(-4.61341 + 1.91094i) q^{67} +(-2.45298 + 1.01606i) q^{69} +(-6.45817 + 2.67506i) q^{71} +11.6632i q^{73} +(-4.00645 + 0.241246i) q^{75} +9.18169 q^{77} +(7.85772 - 3.25478i) q^{79} +3.61570i q^{81} +(-2.07996 - 2.07996i) q^{83} +(-11.6344 + 8.29042i) q^{85} +5.96429i q^{87} +(1.43272 + 3.45889i) q^{89} +(18.0396 - 18.0396i) q^{91} +(1.78172 - 4.30145i) q^{93} +(2.57958 - 15.3704i) q^{95} +(1.15021 + 2.77685i) q^{97} +(-2.04669 + 4.94115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 8 q^{9} + 20 q^{15} - 12 q^{17} - 8 q^{21} + 12 q^{27} - 28 q^{29} + 20 q^{35} + 24 q^{37} + 16 q^{39} + 20 q^{45} - 4 q^{47} + 24 q^{49} + 28 q^{53} + 16 q^{55} - 8 q^{57} + 4 q^{61} + 72 q^{63}+ \cdots - 48 q^{99}+O(q^{100}) \) 84 * q - 8 * q^9 + 20 * q^15 - 12 * q^17 - 8 * q^21 + 12 * q^27 - 28 * q^29 + 20 * q^35 + 24 * q^37 + 16 * q^39 + 20 * q^45 - 4 * q^47 + 24 * q^49 + 28 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 32 * q^65 + 16 * q^67 - 16 * q^69 + 8 * q^71 - 44 * q^75 + 72 * q^77 - 80 * q^83 - 60 * q^85 - 16 * q^89 - 40 * q^91 - 60 * q^93 - 52 * q^95 - 72 * q^97 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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