LMFDB - Embedded newform 820.2.y.a.653.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(137,820)] 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, 2, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.137"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.y (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			653.9
Character	$\chi$	$=$	820.653
Dual form			820.2.y.a.437.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.307196 - 0.741636i) q^{3} +(0.501977 + 2.17900i) q^{5} +(-3.73618 + 1.54758i) q^{7} +(1.66567 - 1.66567i) q^{9} +(-0.868860 + 2.09761i) q^{11} +(-2.41417 - 5.82833i) q^{13} +(1.46182 - 1.04166i) q^{15} +(-2.44492 + 5.90256i) q^{17} +(-2.66729 - 6.43941i) q^{19} +(2.29548 + 2.29548i) q^{21} +(-2.33878 + 2.33878i) q^{23} +(-4.49604 + 2.18761i) q^{25} +(-3.97191 - 1.64522i) q^{27} +(2.84330 - 6.86433i) q^{29} -5.79995i q^{31} +1.82258 q^{33} +(-5.24764 - 7.36427i) q^{35} +(4.56684 - 4.56684i) q^{37} +(-3.58088 + 3.58088i) q^{39} +(-6.30515 + 1.11584i) q^{41} -5.36561 q^{43} +(4.46560 + 2.79335i) q^{45} +(-2.08581 + 5.03559i) q^{47} +(6.61431 - 6.61431i) q^{49} +5.12863 q^{51} +(-4.52660 + 1.87498i) q^{53} +(-5.00683 - 0.840288i) q^{55} +(-3.95632 + 3.95632i) q^{57} +10.6611i q^{59} +(-7.29537 + 7.29537i) q^{61} +(-3.64548 + 8.80097i) q^{63} +(11.4880 - 8.18616i) q^{65} +(-1.91094 + 4.61341i) q^{67} +(2.45298 + 1.01606i) q^{69} +(-6.45817 - 2.67506i) q^{71} +11.6632 q^{73} +(3.00357 + 2.66240i) q^{75} -9.18169i q^{77} +(-7.85772 - 3.25478i) q^{79} -3.61570i q^{81} +(-2.07996 - 2.07996i) q^{83} +(-14.0890 - 2.36452i) q^{85} -5.96429 q^{87} +(-1.43272 + 3.45889i) q^{89} +(18.0396 + 18.0396i) q^{91} +(-4.30145 + 1.78172i) q^{93} +(12.6925 - 9.04444i) q^{95} +(-2.77685 - 1.15021i) q^{97} +(2.04669 + 4.94115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) $ 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Character values

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

$n$	$411$	$621$	$657$
$\chi(n)$	$1$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.307196	−	0.741636i	−0.177360	−	0.428184i	0.810052	−	0.586359i	$-0.199439\pi$
$3$	−0.307196	−	0.741636i	−0.177360	−	0.428184i	−0.987411	+	0.158175i	$0.949439\pi$
$4$		0			0
$5$	0.501977	+	2.17900i	0.224491	+	0.974476i
$5$	0.501977	+	2.17900i	0.224491	+	0.974476i
$6$		0			0
$7$	−3.73618	+	1.54758i	−1.41214	+	0.584929i	−0.952874	−	0.303368i	$-0.901889\pi$
$7$	−3.73618	+	1.54758i	−1.41214	+	0.584929i	−0.459270	+	0.888297i	$0.651889\pi$
$8$		0			0
$9$	1.66567	−	1.66567i	0.555222	−	0.555222i
$10$		0			0
$11$	−0.868860	+	2.09761i	−0.261971	+	0.632454i	−0.999060	−	0.0433414i	$-0.986200\pi$
$11$	−0.868860	+	2.09761i	−0.261971	+	0.632454i	0.737089	+	0.675795i	$0.236200\pi$
$12$		0			0
$13$	−2.41417	−	5.82833i	−0.669572	−	1.61649i	−0.782328	−	0.622866i	$-0.785968\pi$
$13$	−2.41417	−	5.82833i	−0.669572	−	1.61649i	0.112757	−	0.993623i	$-0.464032\pi$
$14$		0			0
$15$	1.46182	−	1.04166i	0.377439	−	0.268956i
$16$		0			0
$17$	−2.44492	+	5.90256i	−0.592981	+	1.43158i	0.287630	+	0.957742i	$0.407133\pi$
$17$	−2.44492	+	5.90256i	−0.592981	+	1.43158i	−0.880611	+	0.473840i	$0.842867\pi$
$18$		0			0
$19$	−2.66729	−	6.43941i	−0.611918	−	1.47730i	−0.860890	−	0.508791i	$-0.830093\pi$
$19$	−2.66729	−	6.43941i	−0.611918	−	1.47730i	0.248972	−	0.968511i	$-0.419907\pi$
$20$		0			0
$21$	2.29548	+	2.29548i	0.500914	+	0.500914i
$22$		0			0
$23$	−2.33878	+	2.33878i	−0.487669	+	0.487669i	−0.907570	−	0.419901i	$-0.862065\pi$
$23$	−2.33878	+	2.33878i	−0.487669	+	0.487669i	0.419901	+	0.907570i	$0.362065\pi$
$24$		0			0
$25$	−4.49604	+	2.18761i	−0.899208	+	0.437522i
$26$		0			0
$27$	−3.97191	−	1.64522i	−0.764395	−	0.316623i
$28$		0			0
$29$	2.84330	−	6.86433i	0.527987	−	1.27467i	−0.404852	−	0.914382i	$-0.632677\pi$
$29$	2.84330	−	6.86433i	0.527987	−	1.27467i	0.932840	−	0.360292i	$-0.117323\pi$
$30$		0			0
$31$		−	5.79995i		−	1.04170i	−0.853648	−	0.520851i	$-0.825615\pi$
$31$		−	5.79995i		−	1.04170i	0.853648	−	0.520851i	$-0.174385\pi$
$32$		0			0
$33$	1.82258			0.317270
$34$		0			0
$35$	−5.24764	−	7.36427i	−0.887013	−	1.24479i
$36$		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
$43$	−5.36561			−0.818248			−0.409124	−	0.912479i	$-0.634166\pi$
$43$	−5.36561			−0.818248			−0.409124	+	0.912479i	$0.634166\pi$
$44$		0			0
$45$	4.46560	+	2.79335i	0.665693	+	0.416408i
$46$		0			0
$47$	−2.08581	+	5.03559i	−0.304246	+	0.734516i	0.695624	+	0.718406i	$0.255128\pi$
$47$	−2.08581	+	5.03559i	−0.304246	+	0.734516i	−0.999870	+	0.0161095i	$0.994872\pi$
$48$		0			0
$49$	6.61431	−	6.61431i	0.944901	−	0.944901i
$50$		0			0
$51$	5.12863			0.718151
$52$		0			0
$53$	−4.52660	+	1.87498i	−0.621777	+	0.257548i	−0.671255	−	0.741227i	$-0.734244\pi$
$53$	−4.52660	+	1.87498i	−0.621777	+	0.257548i	0.0494778	+	0.998775i	$0.484244\pi$
$54$		0			0
$55$	−5.00683	−	0.840288i	−0.675121	−	0.113304i
$56$		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	−0.997958	−	0.0638810i	$-0.979652\pi$
$61$	−7.29537	+	7.29537i	−0.934076	+	0.934076i	0.0638810	+	0.997958i	$0.479652\pi$
$62$		0			0
$63$	−3.64548	+	8.80097i	−0.459287	+	1.10882i
$64$		0			0
$65$	11.4880	−	8.18616i	1.42492	−	1.01537i
$66$		0			0
$67$	−1.91094	+	4.61341i	−0.233458	+	0.563617i	−0.996580	−	0.0826374i	$-0.973666\pi$
$67$	−1.91094	+	4.61341i	−0.233458	+	0.563617i	0.763122	+	0.646255i	$0.223666\pi$
$68$		0			0
$69$	2.45298	+	1.01606i	0.295305	+	0.122319i
$70$		0			0
$71$	−6.45817	−	2.67506i	−0.766444	−	0.317471i	−0.0350128	−	0.999387i	$-0.511147\pi$
$71$	−6.45817	−	2.67506i	−0.766444	−	0.317471i	−0.731431	+	0.681915i	$0.761147\pi$
$72$		0			0
$73$	11.6632			1.36507			0.682536	−	0.730852i	$-0.260877\pi$
$73$	11.6632			1.36507			0.682536	+	0.730852i	$0.260877\pi$
$74$		0			0
$75$	3.00357	+	2.66240i	0.346823	+	0.307428i
$76$		0			0
$77$		−	9.18169i		−	1.04635i
$78$		0			0
$79$	−7.85772	−	3.25478i	−0.884063	−	0.366191i	−0.105992	−	0.994367i	$-0.533802\pi$
$79$	−7.85772	−	3.25478i	−0.884063	−	0.366191i	−0.778071	+	0.628176i	$0.783802\pi$
$80$		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
$85$	−14.0890	−	2.36452i	−1.52816	−	0.256469i
$86$		0			0
$87$	−5.96429			−0.639439
$88$		0			0
$89$	−1.43272	+	3.45889i	−0.151868	+	0.366641i	−0.981443	−	0.191754i	$-0.938583\pi$
$89$	−1.43272	+	3.45889i	−0.151868	+	0.366641i	0.829575	+	0.558395i	$0.188583\pi$
$90$		0			0
$91$	18.0396	+	18.0396i	1.89106	+	1.89106i
$92$		0			0
$93$	−4.30145	+	1.78172i	−0.446040	+	0.184756i
$94$		0			0
$95$	12.6925	−	9.04444i	1.30222	−	0.927940i
$96$		0			0
$97$	−2.77685	−	1.15021i	−0.281946	−	0.116786i	0.237229	−	0.971454i	$-0.423761\pi$
$97$	−2.77685	−	1.15021i	−0.281946	−	0.116786i	−0.519175	+	0.854668i	$0.673761\pi$
$98$		0			0
$99$	2.04669	+	4.94115i	0.205700	+	0.496604i
$100$		0			0
$101$	2.08050	−	0.861770i	0.207017	−	0.0857493i	−0.276765	−	0.960937i	$-0.589263\pi$
$101$	2.08050	−	0.861770i	0.207017	−	0.0857493i	0.483783	+	0.875188i	$0.339263\pi$
$102$		0			0
$103$			4.64935i			0.458115i	0.973413	+	0.229057i	$0.0735643\pi$
$103$			4.64935i			0.458115i	−0.973413	+	0.229057i	$0.926436\pi$
$104$		0			0
$105$	−3.84956	+	6.15411i	−0.375679	+	0.600580i
$106$		0			0
$107$	7.40215	+	7.40215i	0.715593	+	0.715593i	0.967699	−	0.252107i	$-0.0811234\pi$
$107$	7.40215	+	7.40215i	0.715593	+	0.715593i	−0.252107	+	0.967699i	$0.581123\pi$
$108$		0			0
$109$	9.97525	−	4.13189i	0.955456	−	0.395763i	0.150177	−	0.988659i	$-0.452016\pi$
$109$	9.97525	−	4.13189i	0.955456	−	0.395763i	0.805279	+	0.592896i	$0.202016\pi$
$110$		0			0
$111$	−4.78984	−	1.98402i	−0.454632	−	0.188315i
$112$		0			0
$113$	3.45580	−	3.45580i	0.325095	−	0.325095i	−0.525623	−	0.850718i	$-0.676168\pi$
$113$	3.45580	−	3.45580i	0.325095	−	0.325095i	0.850718	+	0.525623i	$0.176168\pi$
$114$		0			0
$115$	−6.27019	−	3.92217i	−0.584699	−	0.365744i
$116$		0			0
$117$	−13.7293	−	5.68684i	−1.26927	−	0.525749i
$118$		0			0
$119$		−	25.8367i		−	2.36845i
$120$		0			0
$121$	4.13311	+	4.13311i	0.375738	+	0.375738i
$122$		0			0
$123$	2.76446	+	4.33335i	0.249263	+	0.390725i
$124$		0			0
$125$	−7.02370	−	8.69872i	−0.628218	−	0.778037i
$126$		0			0
$127$	−14.7330	−	14.7330i	−1.30734	−	1.30734i	−0.923325	−	0.384019i	$-0.874540\pi$
$127$	−14.7330	−	14.7330i	−1.30734	−	1.30734i	−0.384019	−	0.923325i	$-0.625460\pi$
$128$		0			0
$129$	1.64829	+	3.97933i	0.145124	+	0.350361i
$130$		0			0
$131$	1.70792	+	1.70792i	0.149222	+	0.149222i	0.777770	−	0.628549i	$-0.216351\pi$
$131$	1.70792	+	1.70792i	0.149222	+	0.149222i	−0.628549	+	0.777770i	$0.716351\pi$
$132$		0			0
$133$	19.9310	+	19.9310i	1.72823	+	1.72823i
$134$		0			0
$135$	1.59112	−	9.48064i	0.136942	−	0.815963i
$136$		0			0
$137$	−1.28961	+	3.11339i	−0.110179	+	0.265995i	−0.969346	−	0.245700i	$-0.920982\pi$
$137$	−1.28961	+	3.11339i	−0.110179	+	0.265995i	0.859167	+	0.511695i	$0.170982\pi$
$138$		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
$143$	14.3232			1.19776
$144$		0			0
$145$	16.3846	+	2.74980i	1.36067	+	0.228359i
$146$		0			0
$147$	−6.93730	−	2.87352i	−0.572179	−	0.237004i
$148$		0			0
$149$	−3.49692	−	8.44230i	−0.286478	−	0.691620i	0.713481	−	0.700675i	$-0.247118\pi$
$149$	−3.49692	−	8.44230i	−0.286478	−	0.691620i	−0.999959	+	0.00905484i	$0.997118\pi$
$150$		0			0
$151$	1.89223	−	4.56824i	0.153987	−	0.371758i	−0.827994	−	0.560737i	$-0.810518\pi$
$151$	1.89223	−	4.56824i	0.153987	−	0.371758i	0.981981	+	0.188979i	$0.0605179\pi$
$152$		0			0
$153$	5.75927	+	13.9041i	0.465610	+	1.12408i
$154$		0			0
$155$	12.6381	−	2.91144i	1.01511	−	0.233852i
$156$		0			0
$157$	5.45822	+	13.1773i	0.435613	+	1.05166i	0.977448	+	0.211178i	$0.0677299\pi$
$157$	5.45822	+	13.1773i	0.435613	+	1.05166i	−0.541835	+	0.840485i	$0.682270\pi$
$158$		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	−0.0984693	−	0.995140i	$-0.531395\pi$
$163$	11.4479	−	11.4479i	0.896671	−	0.896671i	0.995140	+	0.0984693i	$0.0313946\pi$
$164$		0			0
$165$	0.914890	+	3.97138i	0.0712241	+	0.309172i
$166$		0			0
$167$	9.45768	−	3.91750i	0.731857	−	0.303145i	0.0145421	−	0.999894i	$-0.495371\pi$
$167$	9.45768	−	3.91750i	0.731857	−	0.303145i	0.717315	+	0.696749i	$0.245371\pi$
$168$		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
$173$			13.3113i			1.01204i	0.862521	+	0.506021i	$0.168884\pi$
$173$			13.3113i			1.01204i	−0.862521	+	0.506021i	$0.831116\pi$
$174$		0			0
$175$	13.4125	−	15.1313i	1.01389	−	1.14382i
$176$		0			0
$177$	7.90663	−	3.27503i	0.594298	−	0.246166i
$178$		0			0
$179$	11.5135	−	4.76907i	0.860563	−	0.356457i	0.0916351	−	0.995793i	$-0.470791\pi$
$179$	11.5135	−	4.76907i	0.860563	−	0.356457i	0.768928	+	0.639336i	$0.220791\pi$
$180$		0			0
$181$	3.50448	−	1.45160i	0.260486	−	0.107897i	−0.248619	−	0.968601i	$-0.579977\pi$
$181$	3.50448	−	1.45160i	0.260486	−	0.107897i	0.509105	+	0.860705i	$0.329977\pi$
$182$		0			0
$183$	7.65162	+	3.16940i	0.565624	+	0.234289i
$184$		0			0
$185$	12.2436	+	7.65867i	0.900164	+	0.563076i
$186$		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	0.999822	−	0.0188763i	$-0.00600888\pi$
$191$	3.86268	+	9.32533i	0.279493	+	0.674757i	−0.720328	+	0.693633i	$0.756009\pi$
$192$		0			0
$193$	−3.19679	−	7.71773i	−0.230110	−	0.555535i	0.766080	−	0.642745i	$-0.222205\pi$
$193$	−3.19679	−	7.71773i	−0.230110	−	0.555535i	−0.996190	+	0.0872107i	$0.972205\pi$
$194$		0			0
$195$	−9.60024	−	6.00520i	−0.687487	−	0.430041i
$196$		0			0
$197$			1.47748i			0.105266i	0.998614	+	0.0526331i	$0.0167614\pi$
$197$			1.47748i			0.105266i	−0.998614	+	0.0526331i	$0.983239\pi$
$198$		0			0
$199$	−7.12402	+	2.95087i	−0.505009	+	0.209181i	−0.620618	−	0.784113i	$-0.713118\pi$
$199$	−7.12402	+	2.95087i	−0.505009	+	0.209181i	0.115609	+	0.993295i	$0.463118\pi$
$200$		0			0
$201$	4.00850			0.282738
$202$		0			0
$203$			30.0466i			2.10886i
$204$		0			0
$205$	−5.59644	−	13.1788i	−0.390873	−	0.920445i
$206$		0			0
$207$			7.79124i			0.541528i
$208$		0			0
$209$	15.8249			1.09463
$210$		0			0
$211$	11.4492	−	4.74240i	0.788193	−	0.326480i	0.0479763	−	0.998848i	$-0.484723\pi$
$211$	11.4492	−	4.74240i	0.788193	−	0.326480i	0.740217	+	0.672368i	$0.234723\pi$
$212$		0			0
$213$			5.61138i			0.384486i
$214$		0			0
$215$	−2.69341	−	11.6916i	−0.183689	−	0.797363i
$216$		0			0
$217$	8.97587	+	21.6697i	0.609322	+	1.47103i
$218$		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
$225$	−3.84507	+	11.1327i	−0.256338	+	0.742181i
$226$		0			0
$227$	−10.0261	−	4.15296i	−0.665458	−	0.275642i	0.0242750	−	0.999705i	$-0.492272\pi$
$227$	−10.0261	−	4.15296i	−0.665458	−	0.275642i	−0.689733	+	0.724063i	$0.742272\pi$
$228$		0			0
$229$	−5.61997	+	2.32787i	−0.371378	+	0.153830i	−0.560563	−	0.828112i	$-0.689415\pi$
$229$	−5.61997	+	2.32787i	−0.371378	+	0.153830i	0.189185	+	0.981941i	$0.439415\pi$
$230$		0			0
$231$	−6.80947	+	2.82058i	−0.448030	+	0.185580i
$232$		0			0
$233$	−17.2314	+	7.13748i	−1.12887	+	0.467592i	−0.867395	−	0.497620i	$-0.834207\pi$
$233$	−17.2314	+	7.13748i	−1.12887	+	0.467592i	−0.261471	+	0.965211i	$0.584207\pi$
$234$		0			0
$235$	−12.0195	−	2.01722i	−0.784069	−	0.131589i
$236$		0			0
$237$			6.82743i			0.443489i
$238$		0			0
$239$	3.60092	+	1.49155i	0.232924	+	0.0964804i	0.496093	−	0.868269i	$-0.334768\pi$
$239$	3.60092	+	1.49155i	0.232924	+	0.0964804i	−0.263169	+	0.964750i	$0.584768\pi$
$240$		0			0
$241$	−5.26946	+	5.26946i	−0.339436	+	0.339436i	−0.856155	−	0.516719i	$-0.827153\pi$
$241$	−5.26946	+	5.26946i	−0.339436	+	0.339436i	0.516719	+	0.856155i	$0.327153\pi$
$242$		0			0
$243$	−14.5973	+	6.04639i	−0.936415	+	0.387876i
$244$		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	0.998929	−	0.0462758i	$-0.0147353\pi$
$251$	15.0929	+	15.0929i	0.952653	+	0.952653i	−0.0462758	+	0.998929i	$0.514735\pi$
$252$		0			0
$253$	−2.87378	−	6.93791i	−0.180673	−	0.436183i
$254$		0			0
$255$	2.57445	+	11.1753i	0.161218	+	0.699821i
$256$		0			0
$257$	−5.70319	−	13.7687i	−0.355755	−	0.858869i	−0.995887	−	0.0906042i	$-0.971120\pi$
$257$	−5.70319	−	13.7687i	−0.355755	−	0.858869i	0.640132	−	0.768265i	$-0.278880\pi$
$258$		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
$263$	−0.189340	−	0.0784272i	−0.0116752	−	0.00483603i	0.376838	−	0.926279i	$-0.377011\pi$
$263$	−0.189340	−	0.0784272i	−0.0116752	−	0.00483603i	−0.388513	+	0.921443i	$0.627011\pi$
$264$		0			0
$265$	−6.35782	−	8.92225i	−0.390558	−	0.548090i
$266$		0			0
$267$	3.00536			0.183925
$268$		0			0
$269$	3.41414			0.208164			0.104082	−	0.994569i	$-0.466810\pi$
$269$	3.41414			0.208164			0.104082	+	0.994569i	$0.466810\pi$
$270$		0			0
$271$			15.8371i			0.962036i	0.876711	+	0.481018i	$0.159733\pi$
$271$			15.8371i			0.962036i	−0.876711	+	0.481018i	$0.840267\pi$
$272$		0			0
$273$	7.83713	−	18.9205i	0.474324	−	1.14512i
$274$		0			0
$275$	−0.682329	−	11.3317i	−0.0411460	−	0.683326i
$276$		0			0
$277$	−12.6783	−	12.6783i	−0.761763	−	0.761763i	0.214878	−	0.976641i	$-0.431065\pi$
$277$	−12.6783	−	12.6783i	−0.761763	−	0.761763i	−0.976641	+	0.214878i	$0.931065\pi$
$278$		0			0
$279$	−9.66078	−	9.66078i	−0.578376	−	0.578376i
$280$		0			0
$281$	7.03038	+	16.9728i	0.419397	+	1.01251i	0.982523	+	0.186143i	$0.0595987\pi$
$281$	7.03038	+	16.9728i	0.419397	+	1.01251i	−0.563126	+	0.826371i	$0.690401\pi$
$282$		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
$285$	−10.6068	−	6.63482i	−0.628291	−	0.393013i
$286$		0			0
$287$	21.8303	−	13.9267i	1.28860	−	0.822066i
$288$		0			0
$289$	−16.8418	−	16.8418i	−0.990694	−	0.990694i
$290$		0			0
$291$			2.41275i			0.141438i
$292$		0			0
$293$	−26.7045	−	11.0614i	−1.56009	−	0.646212i	−0.574988	−	0.818162i	$-0.694993\pi$
$293$	−26.7045	−	11.0614i	−1.56009	−	0.646212i	−0.985106	+	0.171950i	$0.944993\pi$
$294$		0			0
$295$	−23.2304	+	5.35160i	−1.35253	+	0.311582i
$296$		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
$307$			2.43042i			0.138711i	0.997592	+	0.0693556i	$0.0220943\pi$
$307$			2.43042i			0.138711i	−0.997592	+	0.0693556i	$0.977906\pi$
$308$		0			0
$309$	3.44813	−	1.42826i	0.196157	−	0.0812510i
$310$		0			0
$311$	−9.73781	−	23.5091i	−0.552180	−	1.33308i	−0.915838	−	0.401548i	$-0.868472\pi$
$311$	−9.73781	−	23.5091i	−0.552180	−	1.33308i	0.363658	−	0.931533i	$-0.381528\pi$
$312$		0			0
$313$	27.7751	+	11.5048i	1.56994	+	0.650291i	0.986780	−	0.162066i	$-0.0518156\pi$
$313$	27.7751	+	11.5048i	1.56994	+	0.650291i	0.583161	+	0.812356i	$0.301816\pi$
$314$		0			0
$315$	−21.0072	−	3.52561i	−1.18362	−	0.198645i
$316$		0			0
$317$	6.16319	−	2.55288i	0.346159	−	0.143384i	−0.202828	−	0.979214i	$-0.565013\pi$
$317$	6.16319	−	2.55288i	0.346159	−	0.143384i	0.548988	+	0.835830i	$0.315013\pi$
$318$		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
$323$	44.5303			2.47773
$324$		0			0
$325$	23.6043	+	20.9231i	1.30933	+	1.16061i
$326$		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	0.919566	−	0.392935i	$-0.128540\pi$
$331$	23.5050	+	9.73608i	1.29195	+	0.535143i	0.372384	+	0.928079i	$0.378540\pi$
$332$		0			0
$333$		−	15.2136i		−	0.833702i
$334$		0			0
$335$	−11.0118	−	1.84810i	−0.601641	−	0.100972i
$336$		0			0
$337$	2.41226			0.131404			0.0657022	−	0.997839i	$-0.479071\pi$
$337$	2.41226			0.131404			0.0657022	+	0.997839i	$0.479071\pi$
$338$		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
$343$	−3.64306	+	8.79512i	−0.196707	+	0.474892i
$344$		0			0
$345$	−0.982648	+	5.85508i	−0.0529040	+	0.315227i
$346$		0			0
$347$	−1.91911	+	4.63313i	−0.103023	+	0.248719i	−0.966983	−	0.254841i	$-0.917977\pi$
$347$	−1.91911	+	4.63313i	−0.103023	+	0.248719i	0.863960	+	0.503560i	$0.167977\pi$
$348$		0			0
$349$	−9.85858	+	9.85858i	−0.527718	+	0.527718i	−0.919891	−	0.392173i	$-0.871723\pi$
$349$	−9.85858	+	9.85858i	−0.527718	+	0.527718i	0.392173	+	0.919891i	$0.371723\pi$
$350$		0			0
$351$			27.1215i			1.44764i
$352$		0			0
$353$	−10.9615	+	10.9615i	−0.583423	+	0.583423i	−0.935842	−	0.352419i	$-0.885359\pi$
$353$	−10.9615	+	10.9615i	−0.583423	+	0.583423i	0.352419	+	0.935842i	$0.385359\pi$
$354$		0			0
$355$	2.58710	−	15.4151i	0.137309	−	0.818151i
$356$		0			0
$357$	−19.1615	+	7.93694i	−1.01413	+	0.420068i
$358$		0			0
$359$	29.9598			1.58122			0.790608	−	0.612323i	$-0.209765\pi$
$359$	29.9598			1.58122			0.790608	+	0.612323i	$0.209765\pi$
$360$		0			0
$361$	−20.9165	+	20.9165i	−1.10087	+	1.10087i
$362$		0			0
$363$	1.79559	−	4.33494i	0.0942441	−	0.227525i
$364$		0			0
$365$	5.85464	+	25.4140i	0.306446	+	1.33023i
$366$		0			0
$367$	16.4696			0.859705			0.429852	−	0.902899i	$-0.358566\pi$
$367$	16.4696			0.859705			0.429852	+	0.902899i	$0.358566\pi$
$368$		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	−0.164778	−	0.986331i	$-0.552691\pi$
$373$	15.8668	−	15.8668i	0.821553	−	0.821553i	0.986331	+	0.164778i	$0.0526907\pi$
$374$		0			0
$375$	−4.29364	+	7.88124i	−0.221722	+	0.406985i
$376$		0			0
$377$	−46.8718			−2.41402
$378$		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
$383$	−27.1745	−	11.2561i	−1.38855	−	0.575158i	−0.441799	−	0.897114i	$-0.645660\pi$
$383$	−27.1745	−	11.2561i	−1.38855	−	0.575158i	−0.946755	+	0.321956i	$0.895660\pi$
$384$		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	−0.999541	−	0.0303030i	$-0.990353\pi$
$389$	−20.3117	−	20.3117i	−1.02984	−	1.02984i	−0.0303030	−	0.999541i	$-0.509647\pi$
$390$		0			0
$391$	−8.08665	−	19.5229i	−0.408960	−	0.987316i
$392$		0			0
$393$	0.741990	−	1.79132i	0.0374284	−	0.0903603i
$394$		0			0
$395$	3.14775	−	18.7558i	0.158380	−	0.943705i
$396$		0			0
$397$	−7.30414	−	17.6338i	−0.366584	−	0.885013i	−0.994305	−	0.106574i	$-0.966012\pi$
$397$	−7.30414	−	17.6338i	−0.366584	−	0.885013i	0.627720	−	0.778439i	$-0.283988\pi$
$398$		0			0
$399$	8.65881	−	20.9042i	0.433483	−	1.04652i
$400$		0			0
$401$	−23.0950	+	23.0950i	−1.15331	+	1.15331i	−0.167425	+	0.985885i	$0.553545\pi$
$401$	−23.0950	+	23.0950i	−1.15331	+	1.15331i	−0.985885	+	0.167425i	$0.946455\pi$
$402$		0			0
$403$	−33.8040	+	14.0021i	−1.68390	+	0.697494i
$404$		0			0
$405$	7.87859	−	1.81500i	0.391490	−	0.0901879i
$406$		0			0
$407$	5.61151	+	13.5474i	0.278152	+	0.671519i
$408$		0			0
$409$	−18.0140			−0.890733			−0.445367	−	0.895348i	$-0.646927\pi$
$409$	−18.0140			−0.890733			−0.445367	+	0.895348i	$0.646927\pi$
$410$		0			0
$411$	2.70516			0.133436
$412$		0			0
$413$	−16.4988	−	39.8316i	−0.811853	−	1.95999i
$414$		0			0
$415$	3.48813	−	5.57631i	0.171225	−	0.273730i
$416$		0			0
$417$	5.58339	−	2.31272i	0.273420	−	0.113254i
$418$		0			0
$419$	13.7219	−	13.7219i	0.670358	−	0.670358i	−0.287441	−	0.957798i	$-0.592804\pi$
$419$	13.7219	−	13.7219i	0.670358	−	0.670358i	0.957798	+	0.287441i	$0.0928044\pi$
$420$		0			0
$421$	−14.5852	+	35.2118i	−0.710838	+	1.71612i	−0.0129430	+	0.999916i	$0.504120\pi$
$421$	−14.5852	+	35.2118i	−0.710838	+	1.71612i	−0.697895	+	0.716200i	$0.745880\pi$
$422$		0			0
$423$	4.91334	+	11.8619i	0.238895	+	0.576743i
$424$		0			0
$425$	−1.92004	−	31.8867i	−0.0931354	−	1.54673i
$426$		0			0
$427$	15.9667	−	38.5470i	0.772682	−	1.86542i
$428$		0			0
$429$	−4.40002	−	10.6226i	−0.212435	−	0.512863i
$430$		0			0
$431$	−15.9189	−	15.9189i	−0.766786	−	0.766786i	0.210753	−	0.977539i	$-0.432408\pi$
$431$	−15.9189	−	15.9189i	−0.766786	−	0.766786i	−0.977539	+	0.210753i	$0.932408\pi$
$432$		0			0
$433$	−5.19835	+	5.19835i	−0.249817	+	0.249817i	−0.820895	−	0.571079i	$-0.806525\pi$
$433$	−5.19835	+	5.19835i	−0.249817	+	0.249817i	0.571079	+	0.820895i	$0.306525\pi$
$434$		0			0
$435$	−2.99393	−	12.9961i	−0.143548	−	0.623118i
$436$		0			0
$437$	21.2985	+	8.82214i	1.01885	+	0.422020i
$438$		0			0
$439$	0.921123	−	2.22379i	0.0439628	−	0.106136i	−0.900373	−	0.435119i	$-0.856706\pi$
$439$	0.921123	−	2.22379i	0.0439628	−	0.106136i	0.944336	+	0.328984i	$0.106706\pi$
$440$		0			0
$441$		−	22.0344i		−	1.04926i
$442$		0			0
$443$	−1.32131			−0.0627773			−0.0313887	−	0.999507i	$-0.509993\pi$
$443$	−1.32131			−0.0627773			−0.0313887	+	0.999507i	$0.509993\pi$
$444$		0			0
$445$	−8.25608	−	1.38560i	−0.391376	−	0.0656840i
$446$		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	$-0.666653\pi$
$449$	7.75719	−	7.75719i	0.366084	−	0.366084i	0.866047	+	0.499963i	$0.166653\pi$
$450$		0			0
$451$	3.13769	−	14.1953i	0.147748	−	0.668429i
$452$		0			0
$453$	−3.96925			−0.186492
$454$		0			0
$455$	−30.2527	+	48.3636i	−1.41827	+	2.26732i
$456$		0			0
$457$	2.56612	−	6.19516i	0.120038	−	0.289797i	−0.852427	−	0.522846i	$-0.824870\pi$
$457$	2.56612	−	6.19516i	0.120038	−	0.289797i	0.972465	+	0.233049i	$0.0748702\pi$
$458$		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
$463$	−17.4973	+	7.24763i	−0.813170	+	0.336826i	−0.750218	−	0.661190i	$-0.770052\pi$
$463$	−17.4973	+	7.24763i	−0.813170	+	0.336826i	−0.0629520	+	0.998017i	$0.520052\pi$
$464$		0			0
$465$	−6.04159	−	8.47847i	−0.280172	−	0.393179i
$466$		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
$473$	4.66196	−	11.2550i	0.214357	−	0.517504i
$474$		0			0
$475$	26.0791	+	23.1168i	1.19659	+	1.06067i
$476$		0			0
$477$	−4.41672	+	10.6629i	−0.202228	+	0.488220i
$478$		0			0
$479$	−26.8771	−	11.1329i	−1.22805	−	0.508673i	−0.328086	−	0.944648i	$-0.606404\pi$
$479$	−26.8771	−	11.1329i	−1.22805	−	0.508673i	−0.899959	+	0.435975i	$0.856404\pi$
$480$		0			0
$481$	−37.6422	−	15.5919i	−1.71634	−	0.710929i
$482$		0			0
$483$	−10.7372			−0.488560
$484$		0			0
$485$	1.11239	−	6.62812i	0.0505108	−	0.300967i
$486$		0			0
$487$			7.57636i			0.343317i	0.985156	+	0.171659i	$0.0549126\pi$
$487$			7.57636i			0.343317i	−0.985156	+	0.171659i	$0.945087\pi$
$488$		0			0
$489$	−12.0070	−	4.97344i	−0.542973	−	0.224907i
$490$		0			0
$491$		−	28.0432i		−	1.26557i	−0.774327	−	0.632786i	$-0.781911\pi$
$491$		−	28.0432i		−	1.26557i	0.774327	−	0.632786i	$-0.218089\pi$
$492$		0			0
$493$	33.5655	+	33.5655i	1.51171	+	1.51171i
$494$		0			0
$495$	−9.73935	+	6.94007i	−0.437751	+	0.311933i
$496$		0			0
$497$	28.2688			1.26803
$498$		0			0
$499$	−5.13521	+	12.3975i	−0.229884	+	0.554988i	−0.996163	−	0.0875196i	$-0.972106\pi$
$499$	−5.13521	+	12.3975i	−0.229884	+	0.554988i	0.766279	+	0.642508i	$0.222106\pi$
$500$		0			0
$501$	−5.81072	−	5.81072i	−0.259604	−	0.259604i
$502$		0			0
$503$	−10.6162	+	4.39737i	−0.473353	+	0.196069i	−0.606590	−	0.795015i	$-0.707463\pi$
$503$	−10.6162	+	4.39737i	−0.473353	+	0.196069i	0.133237	+	0.991084i	$0.457463\pi$
$504$		0			0
$505$	2.92215	+	4.10080i	0.130034	+	0.182483i
$506$		0			0
$507$	19.8742	+	8.23214i	0.882642	+	0.365602i
$508$		0			0
$509$	0.888935	+	2.14608i	0.0394014	+	0.0951233i	0.942355	−	0.334614i	$-0.108606\pi$
$509$	0.888935	+	2.14608i	0.0394014	+	0.0951233i	−0.902954	+	0.429738i	$0.858606\pi$
$510$		0			0
$511$	−43.5758	+	18.0497i	−1.92768	+	0.798470i
$512$		0			0
$513$			29.9650i			1.32299i
$514$		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	−0.654651	−	0.755931i	$-0.727185\pi$
$521$	−37.7095	−	15.6198i	−1.65208	−	0.684315i	−0.997432	+	0.0716155i	$0.977185\pi$
$522$		0			0
$523$	7.01605	−	7.01605i	0.306791	−	0.306791i	−0.536873	−	0.843663i	$-0.680394\pi$
$523$	7.01605	−	7.01605i	0.306791	−	0.306791i	0.843663	+	0.536873i	$0.180394\pi$
$524$		0			0
$525$	−15.3422	−	5.29895i	−0.669587	−	0.231265i
$526$		0			0
$527$	34.2346	+	14.1804i	1.49128	+	0.617709i
$528$		0			0
$529$			12.0603i			0.524359i
$530$		0			0
$531$	17.7577	+	17.7577i	0.770621	+	0.770621i
$532$		0			0
$533$	21.7252	+	34.0547i	0.941023	+	1.47507i
$534$		0			0
$535$	−12.4135	+	19.8450i	−0.536684	+	0.857972i
$536$		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	−0.996935	−	0.0782280i	$-0.975074\pi$
$541$	−25.0077	−	25.0077i	−1.07516	−	1.07516i	−0.0782280	−	0.996935i	$-0.524926\pi$
$542$		0			0
$543$	−2.15313	−	2.15313i	−0.0923994	−	0.0923994i
$544$		0			0
$545$	14.0107	+	19.6619i	0.600152	+	0.842224i
$546$		0			0
$547$	−0.864950	+	2.08817i	−0.0369826	+	0.0892839i	−0.941292	−	0.337594i	$-0.890387\pi$
$547$	−0.864950	+	2.08817i	−0.0369826	+	0.0892839i	0.904309	+	0.426878i	$0.140387\pi$
$548$		0			0
$549$			24.3033i			1.03724i
$550$		0			0
$551$	−51.7861			−2.20616
$552$		0			0
$553$	34.3949			1.46262
$554$		0			0
$555$	1.91878	−	11.4330i	0.0814475	−	0.485303i
$556$		0			0
$557$	25.6200	+	10.6122i	1.08555	+	0.449651i	0.852454	−	0.522802i	$-0.175113\pi$
$557$	25.6200	+	10.6122i	1.08555	+	0.449651i	0.233100	+	0.972453i	$0.425113\pi$
$558$		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
$563$	5.30406	+	12.8051i	0.223540	+	0.539673i	0.995366	−	0.0961612i	$-0.0306564\pi$
$563$	5.30406	+	12.8051i	0.223540	+	0.539673i	−0.771826	+	0.635834i	$0.780656\pi$
$564$		0			0
$565$	9.26491	+	5.79545i	0.389778	+	0.243816i
$566$		0			0
$567$	5.59557	+	13.5089i	0.234992	+	0.567321i
$568$		0			0
$569$	−23.7930	−	23.7930i	−0.997455	−	0.997455i	0.00254162	−	0.999997i	$-0.499191\pi$
$569$	−23.7930	−	23.7930i	−0.997455	−	0.997455i	−0.999997	+	0.00254162i	$0.999191\pi$
$570$		0			0
$571$	7.19779	−	17.3770i	0.301218	−	0.727205i	−0.698712	−	0.715403i	$-0.746243\pi$
$571$	7.19779	−	17.3770i	0.301218	−	0.727205i	0.999930	−	0.0118020i	$-0.00375678\pi$
$572$		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
$577$	0.966784	−	0.400455i	0.0402477	−	0.0166712i	−0.362469	−	0.931996i	$-0.618066\pi$
$577$	0.966784	−	0.400455i	0.0402477	−	0.0166712i	0.402717	+	0.915325i	$0.368066\pi$
$578$		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
$583$		−	11.1242i		−	0.460715i
$584$		0			0
$585$	5.49984	−	32.7706i	0.227390	−	1.35490i
$586$		0			0
$587$	−12.0823	+	5.00464i	−0.498688	+	0.206563i	−0.617827	−	0.786314i	$-0.711987\pi$
$587$	−12.0823	+	5.00464i	−0.498688	+	0.206563i	0.119139	+	0.992878i	$0.461987\pi$
$588$		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
$593$	−30.8930	−	12.7963i	−1.26862	−	0.525480i	−0.356077	−	0.934457i	$-0.615886\pi$
$593$	−30.8930	−	12.7963i	−1.26862	−	0.525480i	−0.912545	+	0.408976i	$0.865886\pi$
$594$		0			0
$595$	56.2982	−	12.9694i	2.30800	−	0.531695i
$596$		0			0
$597$	4.37694	+	4.37694i	0.179136	+	0.179136i
$598$		0			0
$599$	22.0182			0.899641			0.449820	−	0.893119i	$-0.351488\pi$
$599$	22.0182			0.899641			0.449820	+	0.893119i	$0.351488\pi$
$600$		0			0
$601$	6.27711	+	15.1543i	0.256049	+	0.618156i	0.998670	−	0.0515554i	$-0.0164179\pi$
$601$	6.27711	+	15.1543i	0.256049	+	0.618156i	−0.742622	+	0.669711i	$0.766418\pi$
$602$		0			0
$603$	4.50141	+	10.8674i	0.183312	+	0.442554i
$604$		0			0
$605$	−6.93131	+	11.0808i	−0.281798	+	0.450497i
$606$		0			0
$607$			28.0844i			1.13991i	0.821676	+	0.569955i	$0.193039\pi$
$607$			28.0844i			1.13991i	−0.821676	+	0.569955i	$0.806961\pi$
$608$		0			0
$609$	22.2836	−	9.23019i	0.902979	−	0.374026i
$610$		0			0
$611$	34.3846			1.39105
$612$		0			0
$613$		−	35.7762i		−	1.44499i	−0.691378	−	0.722493i	$-0.742996\pi$
$613$		−	35.7762i		−	1.44499i	0.691378	−	0.722493i	$-0.257004\pi$
$614$		0			0
$615$	−8.05465	+	8.19899i	−0.324795	+	0.330615i
$616$		0			0
$617$		−	15.9301i		−	0.641323i	−0.947194	−	0.320662i	$-0.896095\pi$
$617$		−	15.9301i		−	0.641323i	0.947194	−	0.320662i	$-0.103905\pi$
$618$		0			0
$619$	1.25274			0.0503518			0.0251759	−	0.999683i	$-0.491985\pi$
$619$	1.25274			0.0503518			0.0251759	+	0.999683i	$0.491985\pi$
$620$		0			0
$621$	13.1372	−	5.44161i	0.527178	−	0.218364i
$622$		0			0
$623$		−	15.1403i		−	0.606582i
$624$		0			0
$625$	15.4287	−	19.6711i	0.617149	−	0.786846i
$626$		0			0
$627$	−4.86134	−	11.7363i	−0.194143	−	0.468703i
$628$		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
$635$	24.7075	−	39.4988i	0.980489	−	1.56746i
$636$		0			0
$637$	−54.5185	−	22.5823i	−2.16010	−	0.894743i
$638$		0			0
$639$	−15.2129	+	6.30139i	−0.601813	+	0.249279i
$640$		0			0
$641$	10.3487	−	4.28659i	0.408751	−	0.169310i	−0.168827	−	0.985646i	$-0.553998\pi$
$641$	10.3487	−	4.28659i	0.408751	−	0.169310i	0.577578	+	0.816336i	$0.303998\pi$
$642$		0			0
$643$	32.3743	−	13.4099i	1.27672	−	0.528834i	0.361717	−	0.932288i	$-0.382191\pi$
$643$	32.3743	−	13.4099i	1.27672	−	0.528834i	0.915000	+	0.403454i	$0.132191\pi$
$644$		0			0
$645$	−7.84354	+	5.58915i	−0.308839	+	0.220073i
$646$		0			0
$647$		−	31.5710i		−	1.24118i	−0.784133	−	0.620592i	$-0.786892\pi$
$647$		−	31.5710i		−	1.24118i	0.784133	−	0.620592i	$-0.213108\pi$
$648$		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
$653$	22.3575	−	9.26076i	0.874915	−	0.362402i	0.100392	−	0.994948i	$-0.467990\pi$
$653$	22.3575	−	9.26076i	0.874915	−	0.362402i	0.774522	+	0.632546i	$0.217990\pi$
$654$		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	0.449946	+	0.893056i	$0.351443\pi$
$659$	−12.8278	+	30.9690i	−0.499699	+	1.20638i	−0.949646	+	0.313325i	$0.898557\pi$
$660$		0			0
$661$	18.1588	+	18.1588i	0.706294	+	0.706294i	0.965754	−	0.259460i	$-0.0835447\pi$
$661$	18.1588	+	18.1588i	0.706294	+	0.706294i	−0.259460	+	0.965754i	$0.583545\pi$
$662$		0			0
$663$	−12.3814	−	29.8913i	−0.480854	−	1.16088i
$664$		0			0
$665$	−33.4246	+	53.4343i	−1.29615	+	2.07209i
$666$		0			0
$667$	9.40429	+	22.7040i	0.364136	+	0.879101i
$668$		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
$673$	12.4817	+	5.17009i	0.481134	+	0.199292i	0.610049	−	0.792363i	$-0.291150\pi$
$673$	12.4817	+	5.17009i	0.481134	+	0.199292i	−0.128915	+	0.991656i	$0.541150\pi$
$674$		0			0
$675$	21.4570	−	1.29202i	0.825879	−	0.0497298i
$676$		0			0
$677$	24.9353			0.958341			0.479171	−	0.877722i	$-0.340937\pi$
$677$	24.9353			0.958341			0.479171	+	0.877722i	$0.340937\pi$
$678$		0			0
$679$	12.1548			0.466460
$680$		0			0
$681$			8.71152i			0.333826i
$682$		0			0
$683$	−4.56544	+	11.0219i	−0.174692	+	0.421743i	−0.986838	−	0.161710i	$-0.948299\pi$
$683$	−4.56544	+	11.0219i	−0.174692	+	0.421743i	0.812147	+	0.583453i	$0.198299\pi$
$684$		0			0
$685$	−7.43141	−	1.24720i	−0.283939	−	0.0476531i
$686$		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	−0.999391	−	0.0348894i	$-0.988892\pi$
$691$	−8.34307	−	20.1420i	−0.317385	−	0.766236i	0.682006	−	0.731347i	$-0.261108\pi$
$692$		0			0
$693$	−15.2936	−	15.2936i	−0.580956	−	0.580956i
$694$		0			0
$695$	−16.4045	+	3.77912i	−0.622259	+	0.143350i
$696$		0			0
$697$	8.82929	−	39.9447i	0.334433	−	1.51301i
$698$		0			0
$699$	10.5868	+	10.5868i	0.400430	+	0.400430i
$700$		0			0
$701$			51.4034i			1.94148i	0.240137	+	0.970739i	$0.422808\pi$
$701$			51.4034i			1.94148i	−0.240137	+	0.970739i	$0.577192\pi$
$702$		0			0
$703$	−41.5888	−	17.2266i	−1.56855	−	0.649715i
$704$		0			0
$705$	2.19631	+	9.53381i	0.0827178	+	0.359064i
$706$		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	$-0.665042\pi$
$709$	−38.8799	−	16.1046i	−1.46017	−	0.604821i	−0.964592	+	0.263745i	$0.915042\pi$
$710$		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
$717$		−	3.12877i		−	0.116846i
$718$		0			0
$719$	19.2440	−	7.97113i	0.717680	−	0.297273i	0.00620185	−	0.999981i	$-0.498026\pi$
$719$	19.2440	−	7.97113i	0.717680	−	0.297273i	0.711479	+	0.702708i	$0.248026\pi$
$720$		0			0
$721$	−7.19523	−	17.3708i	−0.267964	−	0.646923i
$722$		0			0
$723$	5.52678	+	2.28927i	0.205543	+	0.0851388i
$724$		0			0
$725$	2.23289	+	37.0823i	0.0829274	+	1.37720i
$726$		0			0
$727$	22.9846	−	9.52055i	0.852453	−	0.353098i	0.0867019	−	0.996234i	$-0.472367\pi$
$727$	22.9846	−	9.52055i	0.852453	−	0.353098i	0.765751	+	0.643137i	$0.222367\pi$
$728$		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
$733$	−29.8571			−1.10280			−0.551399	−	0.834241i	$-0.685906\pi$
$733$	−29.8571			−1.10280			−0.551399	+	0.834241i	$0.685906\pi$
$734$		0			0
$735$	2.77903	−	16.5588i	0.102506	−	0.610780i
$736$		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
$743$		−	41.0683i		−	1.50665i	−0.657648	−	0.753325i	$-0.728449\pi$
$743$		−	41.0683i		−	1.50665i	0.657648	−	0.753325i	$-0.271551\pi$
$744$		0			0
$745$	16.6404	−	11.8576i	0.609656	−	0.434429i
$746$		0			0
$747$	−6.92902			−0.253520
$748$		0			0
$749$	−39.1112	−	16.2004i	−1.42909	−	0.591949i
$750$		0			0
$751$	12.5950	+	5.21703i	0.459599	+	0.190372i	0.600456	−	0.799658i	$-0.294986\pi$
$751$	12.5950	+	5.21703i	0.459599	+	0.190372i	−0.140857	+	0.990030i	$0.544986\pi$
$752$		0			0
$753$	6.55695	−	15.8299i	0.238949	−	0.576873i
$754$		0			0
$755$	10.9040	+	1.83000i	0.396838	+	0.0666006i
$756$		0			0
$757$	−11.9098	+	28.7528i	−0.432869	+	1.04504i	0.545489	+	0.838118i	$0.316344\pi$
$757$	−11.9098	+	28.7528i	−0.432869	+	1.04504i	−0.978358	+	0.206920i	$0.933656\pi$
$758$		0			0
$759$	−4.26260	+	4.26260i	−0.154722	+	0.154722i
$760$		0			0
$761$		−	15.0665i		−	0.546161i	−0.961991	−	0.273081i	$-0.911957\pi$
$761$		−	15.0665i		−	0.546161i	0.961991	−	0.273081i	$-0.0880426\pi$
$762$		0			0
$763$	−30.8749	+	30.8749i	−1.11775	+	1.11775i
$764$		0			0
$765$	−27.4060	+	19.5290i	−0.990865	+	0.706071i
$766$		0			0
$767$	62.1362	−	25.7376i	2.24361	−	0.929333i
$768$		0			0
$769$	4.54226			0.163798			0.0818991	−	0.996641i	$-0.473901\pi$
$769$	4.54226			0.163798			0.0818991	+	0.996641i	$0.473901\pi$
$770$		0			0
$771$	−8.45939	+	8.45939i	−0.304657	+	0.304657i
$772$		0			0
$773$	17.1089	−	41.3044i	0.615363	−	1.48562i	−0.241671	−	0.970358i	$-0.577696\pi$
$773$	17.1089	−	41.3044i	0.615363	−	1.48562i	0.857034	−	0.515260i	$-0.172304\pi$
$774$		0			0
$775$	12.6880	+	26.0768i	0.455767	+	0.936706i
$776$		0			0
$777$	20.9661			0.752156
$778$		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
$785$	−25.9734	+	18.5081i	−0.927029	+	0.660583i
$786$		0			0
$787$	31.4406			1.12074			0.560368	−	0.828243i	$-0.310660\pi$
$787$	31.4406			1.12074			0.560368	+	0.828243i	$0.310660\pi$
$788$		0			0
$789$			0.164514i			0.00585685i
$790$		0			0
$791$	−7.56338	+	18.2596i	−0.268923	+	0.649238i
$792$		0			0
$793$	60.1321	+	24.9076i	2.13536	+	0.884493i
$794$		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
$803$	−10.1337	+	24.4648i	−0.357609	+	0.863345i
$804$		0			0
$805$	29.4964	+	4.95034i	1.03961	+	0.174476i
$806$		0			0
$807$	−1.04881	−	2.53205i	−0.0369199	−	0.0891325i
$808$		0			0
$809$	3.52212	−	8.50315i	0.123831	−	0.298955i	−0.849792	−	0.527119i	$-0.823272\pi$
$809$	3.52212	−	8.50315i	0.123831	−	0.298955i	0.973623	+	0.228164i	$0.0732723\pi$
$810$		0			0
$811$	16.4192	−	16.4192i	0.576557	−	0.576557i	−0.357396	−	0.933953i	$-0.616335\pi$
$811$	16.4192	−	16.4192i	0.576557	−	0.576557i	0.933953	+	0.357396i	$0.116335\pi$
$812$		0			0
$813$	11.7454	−	4.86509i	0.411928	−	0.170626i
$814$		0			0
$815$	30.6916	+	19.1984i	1.07508	+	0.672490i
$816$		0			0
$817$	14.3116	+	34.5513i	0.500701	+	1.20880i
$818$		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
$823$	4.45835	+	10.7634i	0.155408	+	0.375189i	0.982338	−	0.187117i	$-0.0599144\pi$
$823$	4.45835	+	10.7634i	0.155408	+	0.375189i	−0.826929	+	0.562306i	$0.809914\pi$
$824$		0			0
$825$	−8.19437	+	3.98708i	−0.285291	+	0.138812i
$826$		0			0
$827$	−41.9838	+	17.3903i	−1.45992	+	0.604718i	−0.964535	−	0.263956i	$-0.914973\pi$
$827$	−41.9838	+	17.3903i	−1.45992	+	0.604718i	−0.495384	+	0.868674i	$0.664973\pi$
$828$		0			0
$829$	6.78221	−	6.78221i	0.235556	−	0.235556i	−0.579451	−	0.815007i	$-0.696733\pi$
$829$	6.78221	−	6.78221i	0.235556	−	0.235556i	0.815007	+	0.579451i	$0.196733\pi$
$830$		0			0
$831$	−5.50795	+	13.2974i	−0.191069	+	0.461281i
$832$		0			0
$833$	22.8699	+	55.2128i	0.792395	+	1.91301i
$834$		0			0
$835$	13.2837	+	18.6417i	0.459703	+	0.645124i
$836$		0			0
$837$	−9.54219	+	23.0369i	−0.329826	+	0.796272i
$838$		0			0
$839$	2.79958	+	6.75879i	0.0966523	+	0.233339i	0.964809	−	0.262950i	$-0.0846955\pi$
$839$	2.79958	+	6.75879i	0.0966523	+	0.233339i	−0.868157	+	0.496289i	$0.834695\pi$
$840$		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
$847$	−21.8384	−	9.04575i	−0.750375	−	0.310816i
$848$		0			0
$849$	−6.81375	+	16.4499i	−0.233847	+	0.564558i
$850$		0			0
$851$			21.3616i			0.732267i
$852$		0			0
$853$	−16.0968			−0.551145			−0.275572	−	0.961280i	$-0.588867\pi$
$853$	−16.0968			−0.551145			−0.275572	+	0.961280i	$0.588867\pi$
$854$		0			0
$855$	6.07647	−	36.2065i	0.207811	−	1.23824i
$856$		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	$-0.824264\pi$
$859$	−9.58283	+	9.58283i	−0.326962	+	0.326962i	0.524468	+	0.851430i	$0.324264\pi$
$860$		0			0
$861$	−17.0347	−	11.9120i	−0.580542	−	0.405958i
$862$		0			0
$863$	−8.23461			−0.280309			−0.140155	−	0.990130i	$-0.544760\pi$
$863$	−8.23461			−0.280309			−0.140155	+	0.990130i	$0.544760\pi$
$864$		0			0
$865$	−29.0054	+	6.68198i	−0.986212	+	0.227194i
$866$		0			0
$867$	−7.31676	+	17.6642i	−0.248490	+	0.599908i
$868$		0			0
$869$	13.6545	−	13.6545i	0.463198	−	0.463198i
$870$		0			0
$871$	31.5018			1.06740
$872$		0			0
$873$	−6.54116	+	2.70944i	−0.221385	+	0.0917006i
$874$		0			0
$875$	39.7037	+	21.6303i	1.34223	+	0.731237i
$876$		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	0.574213	−	0.818706i	$-0.305308\pi$
$881$	41.3441	−	41.3441i	1.39292	−	1.39292i	0.818706	−	0.574213i	$-0.194692\pi$
$882$		0			0
$883$	10.4083	−	25.1279i	0.350268	−	0.845622i	−0.646318	−	0.763068i	$-0.723692\pi$
$883$	10.4083	−	25.1279i	0.350268	−	0.845622i	0.996587	−	0.0825543i	$-0.0263078\pi$
$884$		0			0
$885$	11.1052	+	15.5845i	0.373298	+	0.523868i
$886$		0			0
$887$	16.5714	−	40.0070i	0.556414	−	1.34330i	−0.356173	−	0.934420i	$-0.615919\pi$
$887$	16.5714	−	40.0070i	0.556414	−	1.34330i	0.912587	−	0.408882i	$-0.134081\pi$
$888$		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
$893$	37.9896			1.27127
$894$		0			0
$895$	16.1713	+	22.6940i	0.540547	+	0.758577i
$896$		0			0
$897$		−	16.7498i		−	0.559258i
$898$		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
$905$	4.92221	+	6.90758i	0.163620	+	0.229616i
$906$		0			0
$907$	39.8764			1.32407			0.662037	−	0.749471i	$-0.269692\pi$
$907$	39.8764			1.32407			0.662037	+	0.749471i	$0.269692\pi$
$908$		0			0
$909$	2.02999	−	4.90083i	0.0673306	−	0.162550i
$910$		0			0
$911$	14.8501	+	14.8501i	0.492005	+	0.492005i	0.908938	−	0.416932i	$-0.136895\pi$
$911$	14.8501	+	14.8501i	0.492005	+	0.492005i	−0.416932	+	0.908938i	$0.636895\pi$
$912$		0			0
$913$	6.17013	−	2.55575i	0.204202	−	0.0845831i
$914$		0			0
$915$	−3.06518	+	18.2638i	−0.101332	+	0.603783i
$916$		0			0
$917$	−9.02424	−	3.73796i	−0.298007	−	0.123438i
$918$		0			0
$919$	−2.09210	−	5.05077i	−0.0690119	−	0.166609i	0.885610	−	0.464429i	$-0.153741\pi$
$919$	−2.09210	−	5.05077i	−0.0690119	−	0.166609i	−0.954622	+	0.297820i	$0.903741\pi$
$920$		0			0
$921$	1.80248	−	0.746613i	0.0593939	−	0.0246017i
$922$		0			0
$923$			44.0984i			1.45152i
$924$		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	$-0.824970\pi$
$929$	−33.0991	+	13.7101i	−1.08594	+	0.449813i	−0.233354	+	0.972392i	$0.574970\pi$
$930$		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
$935$	17.2012	−	27.4987i	0.562539	−	0.899304i
$936$		0			0
$937$	−45.0518	−	18.6611i	−1.47178	−	0.609631i	−0.504515	−	0.863403i	$-0.668329\pi$
$937$	−45.0518	−	18.6611i	−1.47178	−	0.609631i	−0.967264	+	0.253772i	$0.918329\pi$
$938$		0			0
$939$		−	24.1333i		−	0.787559i
$940$		0			0
$941$	−34.5386	−	34.5386i	−1.12593	−	1.12593i	−0.990833	−	0.135094i	$-0.956866\pi$
$941$	−34.5386	−	34.5386i	−1.12593	−	1.12593i	−0.135094	−	0.990833i	$-0.543134\pi$
$942$		0			0
$943$	12.1366	−	17.3560i	0.395223	−	0.565190i
$944$		0			0
$945$	8.72731	+	37.8838i	0.283899	+	1.23236i
$946$		0			0
$947$	13.9238	+	13.9238i	0.452464	+	0.452464i	0.896172	−	0.443707i	$-0.146337\pi$
$947$	13.9238	+	13.9238i	0.452464	+	0.452464i	−0.443707	+	0.896172i	$0.646337\pi$
$948$		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
$955$	−18.3809	+	13.0978i	−0.594791	+	0.423836i
$956$		0			0
$957$	5.18213	−	12.5108i	0.167514	−	0.404415i
$958$		0			0
$959$		−	13.6279i		−	0.440069i
$960$		0			0
$961$	−2.63943			−0.0851429
$962$		0			0
$963$	24.6590			0.794625
$964$		0			0
$965$	15.2122	−	10.8399i	0.489698	−	0.348949i
$966$		0			0
$967$	−9.95408	−	4.12311i	−0.320102	−	0.132590i	0.216846	−	0.976206i	$-0.430423\pi$
$967$	−9.95408	−	4.12311i	−0.320102	−	0.132590i	−0.536948	+	0.843615i	$0.680423\pi$
$968$		0			0
$969$	−13.6795	−	33.0253i	−0.439450	−	1.06093i
$970$		0			0
$971$	−17.7917	+	42.9529i	−0.570962	+	1.37842i	0.329775	+	0.944059i	$0.393027\pi$
$971$	−17.7917	+	42.9529i	−0.570962	+	1.37842i	−0.900737	+	0.434365i	$0.856973\pi$
$972$		0			0
$973$	−11.6509	−	28.1278i	−0.373511	−	0.901734i
$974$		0			0
$975$	8.26621	−	23.9333i	0.264731	−	0.766480i
$976$		0			0
$977$	11.9285	+	28.7981i	0.381628	+	0.921332i	0.991651	+	0.128948i	$0.0411601\pi$
$977$	11.9285	+	28.7981i	0.381628	+	0.921332i	−0.610023	+	0.792384i	$0.708840\pi$
$978$		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	−0.519681	−	0.854360i	$-0.673949\pi$
$983$	10.4931	−	10.4931i	0.334679	−	0.334679i	0.854360	+	0.519681i	$0.173949\pi$
$984$		0			0
$985$	−3.21943	+	0.741661i	−0.102579	+	0.0236313i
$986$		0			0
$987$	−16.3470	+	6.77115i	−0.520331	+	0.215528i
$988$		0			0
$989$	12.5490	−	12.5490i	0.399034	−	0.399034i
$990$		0			0
$991$	33.7166	+	13.9659i	1.07104	+	0.443641i	0.847359	−	0.531020i	$-0.178191\pi$
$991$	33.7166	+	13.9659i	1.07104	+	0.443641i	0.223685	+	0.974661i	$0.428191\pi$
$992$		0			0
$993$		−	20.4230i		−	0.648105i
$994$		0			0
$995$	−10.0060	−	14.0419i	−0.317212	−	0.445160i
$996$		0			0
$997$	37.3330	−	15.4638i	1.18235	−	0.489744i	0.297091	−	0.954849i	$-0.403983\pi$
$997$	37.3330	−	15.4638i	1.18235	−	0.489744i	0.885255	+	0.465105i	$0.153983\pi$
$998$		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.y.a.653.9	yes	84
5.2	odd	4		820.2.x.a.817.9	yes	84
41.27	odd	8		820.2.x.a.273.9	✓	84
205.27	even	8	inner	820.2.y.a.437.9	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.x.a.273.9	✓	84	41.27	odd	8
820.2.x.a.817.9	yes	84	5.2	odd	4
820.2.y.a.437.9	yes	84	205.27	even	8	inner
820.2.y.a.653.9	yes	84	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.y (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.307196 - 0.741636i) q^{3} +(0.501977 + 2.17900i) q^{5} +(-3.73618 + 1.54758i) q^{7} +(1.66567 - 1.66567i) q^{9} +(-0.868860 + 2.09761i) q^{11} +(-2.41417 - 5.82833i) q^{13} +(1.46182 - 1.04166i) q^{15} +(-2.44492 + 5.90256i) q^{17} +(-2.66729 - 6.43941i) q^{19} +(2.29548 + 2.29548i) q^{21} +(-2.33878 + 2.33878i) q^{23} +(-4.49604 + 2.18761i) q^{25} +(-3.97191 - 1.64522i) q^{27} +(2.84330 - 6.86433i) q^{29} -5.79995i q^{31} +1.82258 q^{33} +(-5.24764 - 7.36427i) q^{35} +(4.56684 - 4.56684i) q^{37} +(-3.58088 + 3.58088i) q^{39} +(-6.30515 + 1.11584i) q^{41} -5.36561 q^{43} +(4.46560 + 2.79335i) q^{45} +(-2.08581 + 5.03559i) q^{47} +(6.61431 - 6.61431i) q^{49} +5.12863 q^{51} +(-4.52660 + 1.87498i) q^{53} +(-5.00683 - 0.840288i) q^{55} +(-3.95632 + 3.95632i) q^{57} +10.6611i q^{59} +(-7.29537 + 7.29537i) q^{61} +(-3.64548 + 8.80097i) q^{63} +(11.4880 - 8.18616i) q^{65} +(-1.91094 + 4.61341i) q^{67} +(2.45298 + 1.01606i) q^{69} +(-6.45817 - 2.67506i) q^{71} +11.6632 q^{73} +(3.00357 + 2.66240i) q^{75} -9.18169i q^{77} +(-7.85772 - 3.25478i) q^{79} -3.61570i q^{81} +(-2.07996 - 2.07996i) q^{83} +(-14.0890 - 2.36452i) q^{85} -5.96429 q^{87} +(-1.43272 + 3.45889i) q^{89} +(18.0396 + 18.0396i) q^{91} +(-4.30145 + 1.78172i) q^{93} +(12.6925 - 9.04444i) q^{95} +(-2.77685 - 1.15021i) q^{97} +(2.04669 + 4.94115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + 8 q^{9} + 4 q^{13} + 4 q^{15} - 16 q^{17} - 8 q^{21} - 12 q^{27} + 28 q^{29} + 40 q^{33} - 20 q^{35} + 24 q^{37} - 16 q^{39} - 20 q^{45} + 28 q^{47} - 24 q^{49} - 32 q^{53} + 16 q^{55} - 8 q^{57}+ \cdots + 48 q^{99}+O(q^{100}) \) 84 * q + 8 * q^9 + 4 * q^13 + 4 * q^15 - 16 * q^17 - 8 * q^21 - 12 * q^27 + 28 * q^29 + 40 * q^33 - 20 * q^35 + 24 * q^37 - 16 * q^39 - 20 * q^45 + 28 * q^47 - 24 * q^49 - 32 * q^53 + 16 * q^55 - 8 * q^57 + 4 * q^61 + 72 * q^63 + 12 * q^65 - 48 * q^67 + 16 * q^69 + 8 * q^71 - 20 * q^75 - 80 * q^83 - 40 * q^85 - 24 * q^87 + 16 * q^89 - 40 * q^91 - 28 * q^93 + 12 * q^95 + 20 * q^97 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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