LMFDB - Embedded newform 352.2.w.a.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [352,2,Mod(49,352)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(352, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 4]))

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

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

chi := DirichletCharacter("352.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 352 = 2^{5} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	352.w (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.81073415115$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 88)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	352.113
Dual form			352.2.w.a.81.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.826127 + 0.268425i) q^{3} +(2.15963 - 2.97247i) q^{5} +(0.369362 - 1.13678i) q^{7} +(-1.81662 + 1.31985i) q^{9} +(-2.03213 - 2.62115i) q^{11} +(-2.33969 - 3.22030i) q^{13} +(-0.986240 + 3.03533i) q^{15} +(2.57254 + 1.86906i) q^{17} +(4.09534 - 1.33066i) q^{19} +1.03827i q^{21} -2.46096 q^{23} +(-2.62651 - 8.08357i) q^{25} +(2.67820 - 3.68622i) q^{27} +(-3.65234 - 1.18672i) q^{29} +(7.40138 - 5.37742i) q^{31} +(2.38238 + 1.61993i) q^{33} +(-2.58136 - 3.55294i) q^{35} +(5.06948 + 1.64717i) q^{37} +(2.79729 + 2.03235i) q^{39} +(0.164715 + 0.506940i) q^{41} +6.51729i q^{43} +8.25022i q^{45} +(-0.110898 - 0.341309i) q^{47} +(4.50728 + 3.27473i) q^{49} +(-2.62694 - 0.853546i) q^{51} +(-1.42471 - 1.96095i) q^{53} +(-12.1799 + 0.379753i) q^{55} +(-3.02609 + 2.19858i) q^{57} +(0.566526 + 0.184075i) q^{59} +(-4.28455 + 5.89718i) q^{61} +(0.829389 + 2.55260i) q^{63} -14.6251 q^{65} +11.2692i q^{67} +(2.03306 - 0.660583i) q^{69} +(4.52005 + 3.28401i) q^{71} +(-0.825597 + 2.54093i) q^{73} +(4.33966 + 5.97303i) q^{75} +(-3.73026 + 1.34194i) q^{77} +(-9.30369 + 6.75953i) q^{79} +(0.858601 - 2.64250i) q^{81} +(-0.589450 + 0.811308i) q^{83} +(11.1114 - 3.61033i) q^{85} +3.33584 q^{87} +13.6469 q^{89} +(-4.52497 + 1.47025i) q^{91} +(-4.67105 + 6.42914i) q^{93} +(4.88906 - 15.0470i) q^{95} +(4.81420 - 3.49772i) q^{97} +(7.15114 + 2.07952i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10 q^{7} + 18 q^{15} - 6 q^{17} + 8 q^{23} - 4 q^{25} + 6 q^{31} - 10 q^{33} + 34 q^{39} - 14 q^{41} + 6 q^{47} - 4 q^{49} + 2 q^{55} - 26 q^{57} - 60 q^{63} - 36 q^{65} - 22 q^{71} - 6 q^{73} - 74 q^{79}+ \cdots + 10 q^{97}+O(q^{100}) $ 40 * q + 10 * q^7 + 18 * q^15 - 6 * q^17 + 8 * q^23 - 4 * q^25 + 6 * q^31 - 10 * q^33 + 34 * q^39 - 14 * q^41 + 6 * q^47 - 4 * q^49 + 2 * q^55 - 26 * q^57 - 60 * q^63 - 36 * q^65 - 22 * q^71 - 6 * q^73 - 74 * q^79 - 4 * q^81 - 68 * q^87 - 16 * q^89 - 66 * q^95 + 10 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/352\mathbb{Z}\right)^\times$.

$n$	$133$	$287$	$321$
$\chi(n)$	$-1$	$1$	$e\left(\frac{4}{5}\right)$

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
$3$	−0.826127	+	0.268425i	−0.476965	+	0.154975i	−0.537626	−	0.843183i	$-0.680679\pi$
$3$	−0.826127	+	0.268425i	−0.476965	+	0.154975i	0.0606618	+	0.998158i	$0.480679\pi$
$4$		0			0
$5$	2.15963	−	2.97247i	0.965814	−	1.32933i	0.0216810	−	0.999765i	$-0.493098\pi$
$5$	2.15963	−	2.97247i	0.965814	−	1.32933i	0.944133	−	0.329564i	$-0.106902\pi$
$6$		0			0
$7$	0.369362	−	1.13678i	0.139606	−	0.429662i	−0.856672	−	0.515861i	$-0.827472\pi$
$7$	0.369362	−	1.13678i	0.139606	−	0.429662i	0.996278	+	0.0861988i	$0.0274720\pi$
$8$		0			0
$9$	−1.81662	+	1.31985i	−0.605539	+	0.439950i
$10$		0			0
$11$	−2.03213	−	2.62115i	−0.612711	−	0.790307i
$11$	−2.03213	−	2.62115i	−0.612711	−	0.790307i
$12$		0			0
$13$	−2.33969	−	3.22030i	−0.648913	−	0.893152i	0.350139	−	0.936698i	$-0.386134\pi$
$13$	−2.33969	−	3.22030i	−0.648913	−	0.893152i	−0.999051	+	0.0435462i	$0.986134\pi$
$14$		0			0
$15$	−0.986240	+	3.03533i	−0.254646	+	0.783720i
$16$		0			0
$17$	2.57254	+	1.86906i	0.623932	+	0.453313i	0.854293	−	0.519792i	$-0.173991\pi$
$17$	2.57254	+	1.86906i	0.623932	+	0.453313i	−0.230361	+	0.973105i	$0.573991\pi$
$18$		0			0
$19$	4.09534	−	1.33066i	0.939535	−	0.305273i	0.201079	−	0.979575i	$-0.435555\pi$
$19$	4.09534	−	1.33066i	0.939535	−	0.305273i	0.738456	+	0.674302i	$0.235555\pi$
$20$		0			0
$21$			1.03827i			0.226569i
$22$		0			0
$23$	−2.46096			−0.513145			−0.256573	−	0.966525i	$-0.582593\pi$
$23$	−2.46096			−0.513145			−0.256573	+	0.966525i	$0.582593\pi$
$24$		0			0
$25$	−2.62651	−	8.08357i	−0.525302	−	1.61671i
$26$		0			0
$27$	2.67820	−	3.68622i	0.515420	−	0.709414i
$28$		0			0
$29$	−3.65234	−	1.18672i	−0.678223	−	0.220368i	−0.0504057	−	0.998729i	$-0.516051\pi$
$29$	−3.65234	−	1.18672i	−0.678223	−	0.220368i	−0.627817	+	0.778361i	$0.716051\pi$
$30$		0			0
$31$	7.40138	−	5.37742i	1.32933	−	0.965813i	0.329563	−	0.944134i	$-0.393099\pi$
$31$	7.40138	−	5.37742i	1.32933	−	0.965813i	0.999765	−	0.0216793i	$-0.00690127\pi$
$32$		0			0
$33$	2.38238	+	1.61993i	0.414720	+	0.281993i
$34$		0			0
$35$	−2.58136	−	3.55294i	−0.436329	−	0.600556i
$36$		0			0
$37$	5.06948	+	1.64717i	0.833417	+	0.270794i	0.694484	−	0.719508i	$-0.255633\pi$
$37$	5.06948	+	1.64717i	0.833417	+	0.270794i	0.138933	+	0.990302i	$0.455633\pi$
$38$		0			0
$39$	2.79729	+	2.03235i	0.447925	+	0.325436i
$40$		0			0
$41$	0.164715	+	0.506940i	0.0257241	+	0.0791707i	0.963094	−	0.269164i	$-0.0867473\pi$
$41$	0.164715	+	0.506940i	0.0257241	+	0.0791707i	−0.937370	+	0.348335i	$0.886747\pi$
$42$		0			0
$43$			6.51729i			0.993878i	0.867785	+	0.496939i	$0.165543\pi$
$43$			6.51729i			0.993878i	−0.867785	+	0.496939i	$0.834457\pi$
$44$		0			0
$45$			8.25022i			1.22987i
$46$		0			0
$47$	−0.110898	−	0.341309i	−0.0161761	−	0.0497850i	0.942643	−	0.333804i	$-0.108332\pi$
$47$	−0.110898	−	0.341309i	−0.0161761	−	0.0497850i	−0.958819	+	0.284019i	$0.908332\pi$
$48$		0			0
$49$	4.50728	+	3.27473i	0.643897	+	0.467819i
$50$		0			0
$51$	−2.62694	−	0.853546i	−0.367846	−	0.119520i
$52$		0			0
$53$	−1.42471	−	1.96095i	−0.195700	−	0.269357i	0.699878	−	0.714262i	$-0.253238\pi$
$53$	−1.42471	−	1.96095i	−0.195700	−	0.269357i	−0.895578	+	0.444905i	$0.853238\pi$
$54$		0			0
$55$	−12.1799	+	0.379753i	−1.64234	+	0.0512059i
$56$		0			0
$57$	−3.02609	+	2.19858i	−0.400815	+	0.291209i
$58$		0			0
$59$	0.566526	+	0.184075i	0.0737554	+	0.0239646i	0.345662	−	0.938359i	$-0.387654\pi$
$59$	0.566526	+	0.184075i	0.0737554	+	0.0239646i	−0.271907	+	0.962324i	$0.587654\pi$
$60$		0			0
$61$	−4.28455	+	5.89718i	−0.548580	+	0.755056i	−0.989819	−	0.142334i	$-0.954539\pi$
$61$	−4.28455	+	5.89718i	−0.548580	+	0.755056i	0.441238	+	0.897390i	$0.354539\pi$
$62$		0			0
$63$	0.829389	+	2.55260i	0.104493	+	0.321597i
$64$		0			0
$65$	−14.6251			−1.81402
$66$		0			0
$67$			11.2692i			1.37675i	0.725353	+	0.688377i	$0.241677\pi$
$67$			11.2692i			1.37675i	−0.725353	+	0.688377i	$0.758323\pi$
$68$		0			0
$69$	2.03306	−	0.660583i	0.244752	−	0.0795248i
$70$		0			0
$71$	4.52005	+	3.28401i	0.536432	+	0.389740i	0.822758	−	0.568392i	$-0.192434\pi$
$71$	4.52005	+	3.28401i	0.536432	+	0.389740i	−0.286326	+	0.958132i	$0.592434\pi$
$72$		0			0
$73$	−0.825597	+	2.54093i	−0.0966288	+	0.297393i	−0.987675	−	0.156520i	$-0.949972\pi$
$73$	−0.825597	+	2.54093i	−0.0966288	+	0.297393i	0.891046	+	0.453913i	$0.149972\pi$
$74$		0			0
$75$	4.33966	+	5.97303i	0.501101	+	0.689706i
$76$		0			0
$77$	−3.73026	+	1.34194i	−0.425103	+	0.152928i
$78$		0			0
$79$	−9.30369	+	6.75953i	−1.04675	+	0.760506i	−0.971591	−	0.236665i	$-0.923945\pi$
$79$	−9.30369	+	6.75953i	−1.04675	+	0.760506i	−0.0751561	+	0.997172i	$0.523945\pi$
$80$		0			0
$81$	0.858601	−	2.64250i	0.0954001	−	0.293611i
$82$		0			0
$83$	−0.589450	+	0.811308i	−0.0647006	+	0.0890527i	−0.840141	−	0.542368i	$-0.817528\pi$
$83$	−0.589450	+	0.811308i	−0.0647006	+	0.0890527i	0.775440	+	0.631421i	$0.217528\pi$
$84$		0			0
$85$	11.1114	−	3.61033i	1.20521	−	0.391595i
$86$		0			0
$87$	3.33584			0.357640
$88$		0			0
$89$	13.6469			1.44657			0.723283	−	0.690551i	$-0.242632\pi$
$89$	13.6469			1.44657			0.723283	+	0.690551i	$0.242632\pi$
$90$		0			0
$91$	−4.52497	+	1.47025i	−0.474346	+	0.154124i
$92$		0			0
$93$	−4.67105	+	6.42914i	−0.484365	+	0.666671i
$94$		0			0
$95$	4.88906	−	15.0470i	0.501607	−	1.54379i
$96$		0			0
$97$	4.81420	−	3.49772i	0.488808	−	0.355140i	−0.315918	−	0.948787i	$-0.602312\pi$
$97$	4.81420	−	3.49772i	0.488808	−	0.355140i	0.804726	+	0.593647i	$0.202312\pi$
$98$		0			0
$99$	7.15114	+	2.07952i	0.718716	+	0.208999i
$100$		0			0
$101$	3.51209	+	4.83398i	0.349466	+	0.480998i	0.947176	−	0.320714i	$-0.103923\pi$
$101$	3.51209	+	4.83398i	0.349466	+	0.480998i	−0.597710	+	0.801712i	$0.703923\pi$
$102$		0			0
$103$	1.21309	−	3.73350i	0.119529	−	0.367873i	−0.873336	−	0.487119i	$-0.838048\pi$
$103$	1.21309	−	3.73350i	0.119529	−	0.367873i	0.992865	+	0.119246i	$0.0380477\pi$
$104$		0			0
$105$	3.08623	+	2.24228i	0.301185	+	0.218824i
$106$		0			0
$107$	−12.1838	+	3.95877i	−1.17786	+	0.382709i	−0.831570	−	0.555420i	$-0.812558\pi$
$107$	−12.1838	+	3.95877i	−1.17786	+	0.382709i	−0.346287	+	0.938129i	$0.612558\pi$
$108$		0			0
$109$		−	5.65346i		−	0.541504i	−0.962649	−	0.270752i	$-0.912728\pi$
$109$		−	5.65346i		−	0.541504i	0.962649	−	0.270752i	$-0.0872723\pi$
$110$		0			0
$111$	−4.63018			−0.439477
$112$		0			0
$113$	−4.94390	−	15.2158i	−0.465083	−	1.43138i	−0.858878	−	0.512180i	$-0.828838\pi$
$113$	−4.94390	−	15.2158i	−0.465083	−	1.43138i	0.393796	−	0.919198i	$-0.371162\pi$
$114$		0			0
$115$	−5.31475	+	7.31513i	−0.495603	+	0.682139i
$116$		0			0
$117$	8.50064	+	2.76202i	0.785884	+	0.255349i
$118$		0			0
$119$	3.07491	−	2.23405i	0.281876	−	0.204795i
$120$		0			0
$121$	−2.74086	+	10.6531i	−0.249169	+	0.968460i
$122$		0			0
$123$	−0.272150	−	0.374583i	−0.0245390	−	0.0337750i
$124$		0			0
$125$	−12.2287	−	3.97334i	−1.09377	−	0.355387i
$126$		0			0
$127$	7.48900	+	5.44108i	0.664541	+	0.482817i	0.868193	−	0.496226i	$-0.165281\pi$
$127$	7.48900	+	5.44108i	0.664541	+	0.482817i	−0.203652	+	0.979043i	$0.565281\pi$
$128$		0			0
$129$	−1.74940	−	5.38411i	−0.154026	−	0.474045i
$130$		0			0
$131$		−	13.3281i		−	1.16448i	−0.813016	−	0.582241i	$-0.802176\pi$
$131$		−	13.3281i		−	1.16448i	0.813016	−	0.582241i	$-0.197824\pi$
$132$		0			0
$133$		−	5.14699i		−	0.446301i
$134$		0			0
$135$	−5.17328	−	15.9217i	−0.445245	−	1.37032i
$136$		0			0
$137$	7.85466	+	5.70674i	0.671069	+	0.487560i	0.870383	−	0.492376i	$-0.163871\pi$
$137$	7.85466	+	5.70674i	0.671069	+	0.487560i	−0.199314	+	0.979936i	$0.563871\pi$
$138$		0			0
$139$	21.1657	+	6.87716i	1.79525	+	0.583313i	0.999744	−	0.0226274i	$-0.00720315\pi$
$139$	21.1657	+	6.87716i	1.79525	+	0.583313i	0.795510	+	0.605941i	$0.207203\pi$
$140$		0			0
$141$	0.183232	+	0.252197i	0.0154309	+	0.0212388i
$142$		0			0
$143$	−3.68634	+	12.6768i	−0.308267	+	1.06008i
$144$		0			0
$145$	−11.4152	+	8.29361i	−0.947979	+	0.688747i
$146$		0			0
$147$	−4.60260	−	1.49548i	−0.379616	−	0.123345i
$148$		0			0
$149$	7.40685	−	10.1947i	0.606793	−	0.835179i	−0.389516	−	0.921020i	$-0.627358\pi$
$149$	7.40685	−	10.1947i	0.606793	−	0.835179i	0.996309	+	0.0858410i	$0.0273577\pi$
$150$		0			0
$151$	4.68668	+	14.4241i	0.381397	+	1.17382i	0.939061	+	0.343751i	$0.111698\pi$
$151$	4.68668	+	14.4241i	0.381397	+	1.17382i	−0.557664	+	0.830067i	$0.688302\pi$
$152$		0			0
$153$	−7.14020			−0.577251
$154$		0			0
$155$		−	33.6136i		−	2.69991i
$156$		0			0
$157$	−1.45191	+	0.471754i	−0.115875	+	0.0376501i	−0.366381	−	0.930465i	$-0.619403\pi$
$157$	−1.45191	+	0.471754i	−0.115875	+	0.0376501i	0.250506	+	0.968115i	$0.419403\pi$
$158$		0			0
$159$	1.70336	+	1.23757i	0.135085	+	0.0981453i
$160$		0			0
$161$	−0.908985	+	2.79757i	−0.0716381	+	0.220479i
$162$		0			0
$163$	−9.13195	−	12.5690i	−0.715269	−	0.984484i	−0.999668	−	0.0257776i	$-0.991794\pi$
$163$	−9.13195	−	12.5690i	−0.715269	−	0.984484i	0.284398	−	0.958706i	$-0.408206\pi$
$164$		0			0
$165$	9.96024	−	3.58312i	0.775404	−	0.278946i
$166$		0			0
$167$	−6.79043	+	4.93353i	−0.525459	+	0.381768i	−0.818656	−	0.574284i	$-0.805281\pi$
$167$	−6.79043	+	4.93353i	−0.525459	+	0.381768i	0.293197	+	0.956052i	$0.405281\pi$
$168$		0			0
$169$	−0.878998	+	2.70528i	−0.0676152	+	0.208098i
$170$		0			0
$171$	−5.68340	+	7.82252i	−0.434620	+	0.598203i
$172$		0			0
$173$	−23.6455	+	7.68290i	−1.79774	+	0.584120i	−0.999826	−	0.0186572i	$-0.994061\pi$
$173$	−23.6455	+	7.68290i	−1.79774	+	0.584120i	−0.797910	+	0.602777i	$0.794061\pi$
$174$		0			0
$175$	−10.1594			−0.767976
$176$		0			0
$177$	−0.517432			−0.0388926
$178$		0			0
$179$	15.6791	−	5.09444i	1.17191	−	0.380777i	0.342555	−	0.939498i	$-0.388708\pi$
$179$	15.6791	−	5.09444i	1.17191	−	0.380777i	0.829356	+	0.558721i	$0.188708\pi$
$180$		0			0
$181$	−5.39531	+	7.42601i	−0.401030	+	0.551971i	−0.961002	−	0.276541i	$-0.910812\pi$
$181$	−5.39531	+	7.42601i	−0.401030	+	0.551971i	0.559972	+	0.828512i	$0.310812\pi$
$182$		0			0
$183$	1.95663	−	6.02189i	0.144638	−	0.445151i
$184$		0			0
$185$	15.8444	−	11.5116i	1.16490	−	0.846350i
$186$		0			0
$187$	−0.328659	−	10.5412i	−0.0240339	−	0.770848i
$188$		0			0
$189$	−3.20120	−	4.40607i	−0.232853	−	0.320495i
$190$		0			0
$191$	0.763217	−	2.34894i	0.0552244	−	0.169963i	−0.919640	−	0.392763i	$-0.871519\pi$
$191$	0.763217	−	2.34894i	0.0552244	−	0.169963i	0.974864	+	0.222799i	$0.0715194\pi$
$192$		0			0
$193$	8.09515	+	5.88147i	0.582702	+	0.423358i	0.839697	−	0.543055i	$-0.182732\pi$
$193$	8.09515	+	5.88147i	0.582702	+	0.423358i	−0.256995	+	0.966413i	$0.582732\pi$
$194$		0			0
$195$	12.0822	−	3.92574i	0.865224	−	0.281128i
$196$		0			0
$197$		−	11.7936i		−	0.840260i	−0.907464	−	0.420130i	$-0.861985\pi$
$197$		−	11.7936i		−	0.840260i	0.907464	−	0.420130i	$-0.138015\pi$
$198$		0			0
$199$	14.7867			1.04820			0.524101	−	0.851656i	$-0.324402\pi$
$199$	14.7867			1.04820			0.524101	+	0.851656i	$0.324402\pi$
$200$		0			0
$201$	−3.02494	−	9.30980i	−0.213363	−	0.656663i
$202$		0			0
$203$	−2.69807	+	3.71358i	−0.189368	+	0.260642i
$204$		0			0
$205$	1.86259	+	0.605191i	0.130089	+	0.0422684i
$206$		0			0
$207$	4.47062	−	3.24810i	0.310730	−	0.225758i
$208$		0			0
$209$	−11.8101	−	8.03043i	−0.816924	−	0.555476i
$210$		0			0
$211$	4.99983	+	6.88168i	0.344203	+	0.473754i	0.945663	−	0.325148i	$-0.105414\pi$
$211$	4.99983	+	6.88168i	0.344203	+	0.473754i	−0.601460	+	0.798903i	$0.705414\pi$
$212$		0			0
$213$	−4.61565	−	1.49971i	−0.316259	−	0.102759i
$214$		0			0
$215$	19.3725	+	14.0749i	1.32119	+	0.959902i
$216$		0			0
$217$	−3.37915	−	10.4000i	−0.229392	−	0.705995i
$218$		0			0
$219$		−	2.32074i		−	0.156821i
$220$		0			0
$221$		−	12.6574i		−	0.851427i
$222$		0			0
$223$	−1.55218	−	4.77711i	−0.103941	−	0.319899i	0.885539	−	0.464565i	$-0.153789\pi$
$223$	−1.55218	−	4.77711i	−0.103941	−	0.319899i	−0.989481	+	0.144666i	$0.953789\pi$
$224$		0			0
$225$	15.4405	+	11.2181i	1.02936	+	0.747877i
$226$		0			0
$227$	−17.1881	−	5.58475i	−1.14081	−	0.370673i	−0.323138	−	0.946352i	$-0.604738\pi$
$227$	−17.1881	−	5.58475i	−1.14081	−	0.370673i	−0.817676	+	0.575679i	$0.804738\pi$
$228$		0			0
$229$	2.34091	+	3.22199i	0.154692	+	0.212915i	0.879328	−	0.476217i	$-0.157992\pi$
$229$	2.34091	+	3.22199i	0.154692	+	0.212915i	−0.724636	+	0.689132i	$0.757992\pi$
$230$		0			0
$231$	2.72146	−	2.10990i	0.179059	−	0.138822i
$232$		0			0
$233$	−9.93905	+	7.22114i	−0.651129	+	0.473073i	−0.863656	−	0.504082i	$-0.831831\pi$
$233$	−9.93905	+	7.22114i	−0.651129	+	0.473073i	0.212527	+	0.977155i	$0.431831\pi$
$234$		0			0
$235$	−1.25403	−	0.407459i	−0.0818038	−	0.0265797i
$236$		0			0
$237$	5.87160	−	8.08157i	0.381402	−	0.524954i
$238$		0			0
$239$	−6.47271	−	19.9210i	−0.418685	−	1.28858i	−0.908913	−	0.416985i	$-0.863087\pi$
$239$	−6.47271	−	19.9210i	−0.418685	−	1.28858i	0.490228	−	0.871594i	$-0.336913\pi$
$240$		0			0
$241$	17.4490			1.12399			0.561996	−	0.827140i	$-0.310034\pi$
$241$	17.4490			1.12399			0.561996	+	0.827140i	$0.310034\pi$
$242$		0			0
$243$			16.0828i			1.03171i
$244$		0			0
$245$	19.4681	−	6.32556i	1.24377	−	0.404125i
$246$		0			0
$247$	−13.8669	−	10.0749i	−0.882332	−	0.641051i
$248$		0			0
$249$	0.269185	−	0.828467i	0.0170589	−	0.0525019i
$250$		0			0
$251$	3.50218	+	4.82034i	0.221056	+	0.304257i	0.905113	−	0.425171i	$-0.139786\pi$
$251$	3.50218	+	4.82034i	0.221056	+	0.304257i	−0.684057	+	0.729428i	$0.739786\pi$
$252$		0			0
$253$	5.00100	+	6.45054i	0.314410	+	0.405542i
$254$		0			0
$255$	−8.21036	+	5.96517i	−0.514153	+	0.373554i
$256$		0			0
$257$	−4.37822	+	13.4748i	−0.273106	+	0.840533i	0.716609	+	0.697476i	$0.245693\pi$
$257$	−4.37822	+	13.4748i	−0.273106	+	0.840533i	−0.989714	+	0.143058i	$0.954307\pi$
$258$		0			0
$259$	3.74495	−	5.15448i	0.232700	−	0.320284i
$260$		0			0
$261$	8.20120	−	2.66473i	0.507641	−	0.164943i
$262$		0			0
$263$	−11.0152			−0.679225			−0.339612	−	0.940566i	$-0.610296\pi$
$263$	−11.0152			−0.679225			−0.339612	+	0.940566i	$0.610296\pi$
$264$		0			0
$265$	−8.90572			−0.547074
$266$		0			0
$267$	−11.2741	+	3.66316i	−0.689961	+	0.224182i
$268$		0			0
$269$	1.45964	−	2.00902i	0.0889959	−	0.122492i	−0.762197	−	0.647345i	$-0.775879\pi$
$269$	1.45964	−	2.00902i	0.0889959	−	0.122492i	0.851193	+	0.524852i	$0.175879\pi$
$270$		0			0
$271$	−0.0950935	+	0.292668i	−0.00577652	+	0.0177783i	−0.953903	−	0.300114i	$-0.902975\pi$
$271$	−0.0950935	+	0.292668i	−0.00577652	+	0.0177783i	0.948127	+	0.317893i	$0.102975\pi$
$272$		0			0
$273$	3.34355	−	2.42923i	0.202361	−	0.147024i
$274$		0			0
$275$	−15.8508	+	23.3114i	−0.955841	+	1.40573i
$276$		0			0
$277$	1.46947	+	2.02255i	0.0882919	+	0.121523i	0.850878	−	0.525363i	$-0.176071\pi$
$277$	1.46947	+	2.02255i	0.0882919	+	0.121523i	−0.762586	+	0.646887i	$0.776071\pi$
$278$		0			0
$279$	−6.34809	+	19.5374i	−0.380051	+	1.16968i
$280$		0			0
$281$	1.00572	+	0.730699i	0.0599963	+	0.0435899i	0.617379	−	0.786666i	$-0.288194\pi$
$281$	1.00572	+	0.730699i	0.0599963	+	0.0435899i	−0.557383	+	0.830256i	$0.688194\pi$
$282$		0			0
$283$	−13.1263	+	4.26500i	−0.780279	+	0.253528i	−0.671959	−	0.740588i	$-0.734547\pi$
$283$	−13.1263	+	4.26500i	−0.780279	+	0.253528i	−0.108320	+	0.994116i	$0.534547\pi$
$284$		0			0
$285$			13.7431i			0.814069i
$286$		0			0
$287$	0.637118			0.0376079
$288$		0			0
$289$	−2.12871	−	6.55151i	−0.125219	−	0.385383i
$290$		0			0
$291$	−3.03826	+	4.18181i	−0.178106	+	0.245142i
$292$		0			0
$293$	−14.1561	−	4.59959i	−0.827007	−	0.268711i	−0.135223	−	0.990815i	$-0.543175\pi$
$293$	−14.1561	−	4.59959i	−0.827007	−	0.268711i	−0.691784	+	0.722104i	$0.743175\pi$
$294$		0			0
$295$	1.77064	−	1.28645i	0.103091	−	0.0748998i
$296$		0			0
$297$	−15.1046	+	0.470940i	−0.876458	+	0.0273267i
$298$		0			0
$299$	5.75788	+	7.92504i	0.332987	+	0.458317i
$300$		0			0
$301$	7.40873	+	2.40724i	0.427032	+	0.138751i
$302$		0			0
$303$	−4.19899	−	3.05074i	−0.241226	−	0.175261i
$304$		0			0
$305$	8.27616	+	25.4714i	0.473891	+	1.45849i
$306$		0			0
$307$		−	8.40361i		−	0.479619i	−0.970820	−	0.239810i	$-0.922915\pi$
$307$		−	8.40361i		−	0.479619i	0.970820	−	0.239810i	$-0.0770850\pi$
$308$		0			0
$309$			3.40997i			0.193986i
$310$		0			0
$311$	−7.92512	−	24.3910i	−0.449392	−	1.38309i	−0.877594	−	0.479404i	$-0.840853\pi$
$311$	−7.92512	−	24.3910i	−0.449392	−	1.38309i	0.428202	−	0.903683i	$-0.359147\pi$
$312$		0			0
$313$	−15.2762	−	11.0988i	−0.863460	−	0.627340i	0.0653641	−	0.997861i	$-0.479179\pi$
$313$	−15.2762	−	11.0988i	−0.863460	−	0.627340i	−0.928824	+	0.370521i	$0.879179\pi$
$314$		0			0
$315$	9.37869	+	3.04732i	0.528429	+	0.171697i
$316$		0			0
$317$	11.7338	+	16.1502i	0.659037	+	0.907087i	0.999449	−	0.0331895i	$-0.0105665\pi$
$317$	11.7338	+	16.1502i	0.659037	+	0.907087i	−0.340412	+	0.940276i	$0.610566\pi$
$318$		0			0
$319$	4.31148	+	11.9849i	0.241397	+	0.671026i
$320$		0			0
$321$	9.00277	−	6.54089i	0.502485	−	0.365077i
$322$		0			0
$323$	13.0225	+	4.23126i	0.724591	+	0.235434i
$324$		0			0
$325$	−19.8863	+	27.3712i	−1.10309	+	1.51828i
$326$		0			0
$327$	1.51753	+	4.67048i	0.0839196	+	0.258278i
$328$		0			0
$329$	−0.428955			−0.0236490
$330$		0			0
$331$			18.8624i			1.03677i	0.855147	+	0.518386i	$0.173467\pi$
$331$			18.8624i			1.03677i	−0.855147	+	0.518386i	$0.826533\pi$
$332$		0			0
$333$	−11.3833	+	3.69867i	−0.623803	+	0.202686i
$334$		0			0
$335$	33.4974	+	24.3373i	1.83016	+	1.32969i
$336$		0			0
$337$	6.57702	−	20.2420i	0.358273	−	1.10265i	−0.595814	−	0.803123i	$-0.703170\pi$
$337$	6.57702	−	20.2420i	0.358273	−	1.10265i	0.954087	−	0.299529i	$-0.0968297\pi$
$338$		0			0
$339$	8.16857	+	11.2431i	0.443656	+	0.610640i
$340$		0			0
$341$	−29.1356	−	8.47250i	−1.57778	−	0.458812i
$342$		0			0
$343$	12.1565	−	8.83220i	0.656388	−	0.476894i
$344$		0			0
$345$	2.42710	−	7.46983i	0.130670	−	0.402162i
$346$		0			0
$347$	3.20169	−	4.40674i	0.171876	−	0.236566i	−0.714386	−	0.699752i	$-0.753294\pi$
$347$	3.20169	−	4.40674i	0.171876	−	0.236566i	0.886261	+	0.463186i	$0.153294\pi$
$348$		0			0
$349$	9.70881	−	3.15458i	0.519701	−	0.168861i	−0.0374088	−	0.999300i	$-0.511910\pi$
$349$	9.70881	−	3.15458i	0.519701	−	0.168861i	0.557109	+	0.830439i	$0.311910\pi$
$350$		0			0
$351$	−18.1369			−0.968077
$352$		0			0
$353$	5.11121			0.272042			0.136021	−	0.990706i	$-0.456569\pi$
$353$	5.11121			0.272042			0.136021	+	0.990706i	$0.456569\pi$
$354$		0			0
$355$	19.5233	−	6.34349i	1.03619	−	0.336677i
$356$		0			0
$357$	−1.94059	+	2.67099i	−0.102707	+	0.141364i
$358$		0			0
$359$	−6.48321	+	19.9533i	−0.342171	+	1.05309i	0.620910	+	0.783882i	$0.286763\pi$
$359$	−6.48321	+	19.9533i	−0.342171	+	1.05309i	−0.963081	+	0.269212i	$0.913237\pi$
$360$		0			0
$361$	−0.370174	+	0.268947i	−0.0194828	+	0.0141551i
$362$		0			0
$363$	−0.595247	−	9.53649i	−0.0312423	−	0.500536i
$364$		0			0
$365$	5.76985	+	7.94152i	0.302008	+	0.415678i
$366$		0			0
$367$	9.74300	−	29.9859i	0.508580	−	1.56525i	−0.286086	−	0.958204i	$-0.592354\pi$
$367$	9.74300	−	29.9859i	0.508580	−	1.56525i	0.794667	−	0.607046i	$-0.207646\pi$
$368$		0			0
$369$	−0.968308	−	0.703517i	−0.0504081	−	0.0366236i
$370$		0			0
$371$	−2.75540	+	0.895285i	−0.143053	+	0.0464809i
$372$		0			0
$373$			24.8244i			1.28536i	0.766136	+	0.642678i	$0.222177\pi$
$373$			24.8244i			1.28536i	−0.766136	+	0.642678i	$0.777823\pi$
$374$		0			0
$375$	11.1690			0.576765
$376$		0			0
$377$	4.72375	+	14.5382i	0.243285	+	0.748755i
$378$		0			0
$379$	21.0081	−	28.9152i	1.07911	−	1.48527i	0.218620	−	0.975810i	$-0.429844\pi$
$379$	21.0081	−	28.9152i	1.07911	−	1.48527i	0.860493	−	0.509462i	$-0.170156\pi$
$380$		0			0
$381$	−7.64738	−	2.48479i	−0.391787	−	0.127299i
$382$		0			0
$383$	−15.4018	+	11.1901i	−0.786997	+	0.571787i	−0.907071	−	0.420978i	$-0.861687\pi$
$383$	−15.4018	+	11.1901i	−0.786997	+	0.571787i	0.120073	+	0.992765i	$0.461687\pi$
$384$		0			0
$385$	−4.06711	+	13.9862i	−0.207279	+	0.712802i
$386$		0			0
$387$	−8.60185	−	11.8394i	−0.437257	−	0.601832i
$388$		0			0
$389$	30.9758	+	10.0646i	1.57053	+	0.510297i	0.959596	−	0.281381i	$-0.0907925\pi$
$389$	30.9758	+	10.0646i	1.57053	+	0.510297i	0.610938	+	0.791679i	$0.290793\pi$
$390$		0			0
$391$	−6.33091	−	4.59968i	−0.320168	−	0.232616i
$392$		0			0
$393$	3.57760	+	11.0107i	0.180466	+	0.555417i
$394$		0			0
$395$			42.2530i			2.12598i
$396$		0			0
$397$			13.0143i			0.653167i	0.945168	+	0.326584i	$0.105897\pi$
$397$			13.0143i			0.653167i	−0.945168	+	0.326584i	$0.894103\pi$
$398$		0			0
$399$	1.38158	+	4.25207i	0.0691655	+	0.212870i
$400$		0			0
$401$	−16.6284	−	12.0813i	−0.830384	−	0.603310i	0.0892837	−	0.996006i	$-0.471542\pi$
$401$	−16.6284	−	12.0813i	−0.830384	−	0.603310i	−0.919668	+	0.392697i	$0.871542\pi$
$402$		0			0
$403$	−34.6339	−	11.2532i	−1.72523	−	0.560563i
$404$		0			0
$405$	−6.00050	−	8.25898i	−0.298167	−	0.410392i
$406$		0			0
$407$	−5.98437	−	16.6352i	−0.296634	−	0.824574i
$408$		0			0
$409$	−7.97764	+	5.79610i	−0.394469	+	0.286598i	−0.767284	−	0.641307i	$-0.778392\pi$
$409$	−7.97764	+	5.79610i	−0.394469	+	0.286598i	0.372815	+	0.927906i	$0.378392\pi$
$410$		0			0
$411$	−8.02078	−	2.60611i	−0.395636	−	0.128550i
$412$		0			0
$413$	0.418506	−	0.576025i	0.0205934	−	0.0283443i
$414$		0			0
$415$	1.13860	+	3.50425i	0.0558916	+	0.172017i
$416$		0			0
$417$	−19.3316			−0.946671
$418$		0			0
$419$		−	0.169087i		−	0.00826046i	−0.999991	−	0.00413023i	$-0.998685\pi$
$419$		−	0.169087i		−	0.00826046i	0.999991	−	0.00413023i	$-0.00131470\pi$
$420$		0			0
$421$	−22.3620	+	7.26586i	−1.08986	+	0.354116i	−0.798192	−	0.602404i	$-0.794210\pi$
$421$	−22.3620	+	7.26586i	−1.08986	+	0.354116i	−0.291666	+	0.956520i	$0.594210\pi$
$422$		0			0
$423$	0.651936	+	0.473659i	0.0316982	+	0.0230301i
$424$		0			0
$425$	8.35186	−	25.7044i	0.405125	−	1.24685i
$426$		0			0
$427$	5.12124	+	7.04878i	0.247834	+	0.341114i
$428$		0			0
$429$	−0.357372	−	11.4621i	−0.0172541	−	0.553396i
$430$		0			0
$431$	−5.89994	+	4.28656i	−0.284190	+	0.206476i	−0.720743	−	0.693202i	$-0.756199\pi$
$431$	−5.89994	+	4.28656i	−0.284190	+	0.206476i	0.436553	+	0.899679i	$0.356199\pi$
$432$		0			0
$433$	0.722575	−	2.22386i	0.0347247	−	0.106872i	−0.932192	−	0.361965i	$-0.882106\pi$
$433$	0.722575	−	2.22386i	0.0347247	−	0.106872i	0.966917	+	0.255093i	$0.0821061\pi$
$434$		0			0
$435$	7.20417	−	9.91569i	0.345414	−	0.475421i
$436$		0			0
$437$	−10.0785	+	3.27469i	−0.482118	+	0.156650i
$438$		0			0
$439$	1.21401			0.0579413			0.0289707	−	0.999580i	$-0.490777\pi$
$439$	1.21401			0.0579413			0.0289707	+	0.999580i	$0.490777\pi$
$440$		0			0
$441$	−12.5102			−0.595722
$442$		0			0
$443$	−4.39270	+	1.42728i	−0.208704	+	0.0678119i	−0.411503	−	0.911408i	$-0.634996\pi$
$443$	−4.39270	+	1.42728i	−0.208704	+	0.0678119i	0.202799	+	0.979220i	$0.434996\pi$
$444$		0			0
$445$	29.4722	−	40.5650i	1.39711	−	1.92296i
$446$		0			0
$447$	−3.38250	+	10.4103i	−0.159987	+	0.492388i
$448$		0			0
$449$	−4.74796	+	3.44960i	−0.224070	+	0.162797i	−0.694157	−	0.719824i	$-0.744223\pi$
$449$	−4.74796	+	3.44960i	−0.224070	+	0.162797i	0.470087	+	0.882620i	$0.344223\pi$
$450$		0			0
$451$	0.994043	−	1.46191i	0.0468077	−	0.0688387i
$452$		0			0
$453$	−7.74358	−	10.6581i	−0.363825	−	0.500762i
$454$		0			0
$455$	−5.40196	+	16.6255i	−0.253248	+	0.779417i
$456$		0			0
$457$	19.8188	+	14.3992i	0.927084	+	0.673566i	0.945277	−	0.326269i	$-0.105791\pi$
$457$	19.8188	+	14.3992i	0.927084	+	0.673566i	−0.0181932	+	0.999834i	$0.505791\pi$
$458$		0			0
$459$	13.7795	−	4.47724i	0.643174	−	0.208980i
$460$		0			0
$461$		−	6.59878i		−	0.307336i	−0.988123	−	0.153668i	$-0.950891\pi$
$461$		−	6.59878i		−	0.307336i	0.988123	−	0.153668i	$-0.0491086\pi$
$462$		0			0
$463$	14.4202			0.670163			0.335081	−	0.942189i	$-0.391236\pi$
$463$	14.4202			0.670163			0.335081	+	0.942189i	$0.391236\pi$
$464$		0			0
$465$	9.02273	+	27.7691i	0.418419	+	1.28776i
$466$		0			0
$467$	−3.22623	+	4.44053i	−0.149292	+	0.205483i	−0.877113	−	0.480285i	$-0.840533\pi$
$467$	−3.22623	+	4.44053i	−0.149292	+	0.205483i	0.727821	+	0.685768i	$0.240533\pi$
$468$		0			0
$469$	12.8106	+	4.16242i	0.591540	+	0.192203i
$470$		0			0
$471$	1.07283	−	0.779457i	0.0494334	−	0.0359155i
$472$		0			0
$473$	17.0828	−	13.2440i	0.785469	−	0.608961i
$474$		0			0
$475$	−21.5129	−	29.6100i	−0.987079	−	1.35860i
$476$		0			0
$477$	5.17632	+	1.68189i	0.237007	+	0.0770084i
$478$		0			0
$479$	−24.1603	−	17.5535i	−1.10391	−	0.802039i	−0.122217	−	0.992503i	$-0.539001\pi$
$479$	−24.1603	−	17.5535i	−1.10391	−	0.802039i	−0.981694	+	0.190465i	$0.939001\pi$
$480$		0			0
$481$	−6.55660	−	20.1791i	−0.298955	−	0.920090i
$482$		0			0
$483$		−	2.55514i		−	0.116263i
$484$		0			0
$485$		−	21.8638i		−	0.992786i
$486$		0			0
$487$	0.920108	+	2.83180i	0.0416941	+	0.128321i	0.969737	−	0.244152i	$-0.0785097\pi$
$487$	0.920108	+	2.83180i	0.0416941	+	0.128321i	−0.928043	+	0.372474i	$0.878510\pi$
$488$		0			0
$489$	10.9180	+	7.93238i	0.493729	+	0.358715i
$490$		0			0
$491$	2.83468	+	0.921042i	0.127927	+	0.0415661i	0.372281	−	0.928120i	$-0.378576\pi$
$491$	2.83468	+	0.921042i	0.127927	+	0.0415661i	−0.244354	+	0.969686i	$0.578576\pi$
$492$		0			0
$493$	−7.17774	−	9.87932i	−0.323269	−	0.444942i
$494$		0			0
$495$	21.6251	−	16.7656i	0.971975	−	0.753556i
$496$		0			0
$497$	5.40273	−	3.92532i	0.242346	−	0.176075i
$498$		0			0
$499$	14.4506	+	4.69530i	0.646900	+	0.210190i	0.614047	−	0.789270i	$-0.289541\pi$
$499$	14.4506	+	4.69530i	0.646900	+	0.210190i	0.0328530	+	0.999460i	$0.489541\pi$
$500$		0			0
$501$	4.28547	−	5.89844i	0.191461	−	0.263523i
$502$		0			0
$503$	−10.1733	−	31.3103i	−0.453607	−	1.39606i	−0.872763	−	0.488144i	$-0.837674\pi$
$503$	−10.1733	−	31.3103i	−0.453607	−	1.39606i	0.419156	−	0.907914i	$-0.362326\pi$
$504$		0			0
$505$	21.9536			0.976924
$506$		0			0
$507$		−	2.47085i		−	0.109734i
$508$		0			0
$509$	12.8194	−	4.16527i	0.568209	−	0.184622i	−0.0108026	−	0.999942i	$-0.503439\pi$
$509$	12.8194	−	4.16527i	0.568209	−	0.184622i	0.579011	+	0.815319i	$0.303439\pi$
$510$		0			0
$511$	2.58353	+	1.87704i	0.114289	+	0.0830356i
$512$		0			0
$513$	6.06303	−	18.6601i	0.267689	−	0.823863i
$514$		0			0
$515$	−8.47791	−	11.6688i	−0.373581	−	0.514191i
$516$		0			0
$517$	−0.669262	+	0.984266i	−0.0294341	+	0.0432880i
$518$		0			0
$519$	17.4719	−	12.6941i	0.766932	−	0.557209i
$520$		0			0
$521$	2.87587	−	8.85103i	0.125994	−	0.387771i	−0.868087	−	0.496413i	$-0.834650\pi$
$521$	2.87587	−	8.85103i	0.125994	−	0.387771i	0.994081	+	0.108642i	$0.0346503\pi$
$522$		0			0
$523$	−8.42368	+	11.5942i	−0.368342	+	0.506979i	−0.952449	−	0.304697i	$-0.901445\pi$
$523$	−8.42368	+	11.5942i	−0.368342	+	0.506979i	0.584107	+	0.811676i	$0.301445\pi$
$524$		0			0
$525$	8.39293	−	2.72703i	0.366297	−	0.119017i
$526$		0			0
$527$	29.0911			1.26723
$528$		0			0
$529$	−16.9437			−0.736682
$530$		0			0
$531$	−1.27211	+	0.413334i	−0.0552050	+	0.0179372i
$532$		0			0
$533$	1.24712	−	1.71651i	0.0540187	−	0.0743504i
$534$		0			0
$535$	−14.5452	+	44.7656i	−0.628845	+	1.93538i
$536$		0			0
$537$	−11.5854	+	8.41731i	−0.499949	+	0.363234i
$538$		0			0
$539$	−0.575835	−	18.4689i	−0.0248030	−	0.795514i
$540$		0			0
$541$	−13.5920	−	18.7077i	−0.584364	−	0.804308i	0.409801	−	0.912175i	$-0.365598\pi$
$541$	−13.5920	−	18.7077i	−0.584364	−	0.804308i	−0.994165	+	0.107867i	$0.965598\pi$
$542$		0			0
$543$	2.46389	−	7.58306i	0.105735	−	0.325420i
$544$		0			0
$545$	−16.8048	−	12.2094i	−0.719836	−	0.522992i
$546$		0			0
$547$	8.59894	−	2.79397i	0.367664	−	0.119461i	−0.119357	−	0.992851i	$-0.538083\pi$
$547$	8.59894	−	2.79397i	0.367664	−	0.119461i	0.487021	+	0.873390i	$0.338083\pi$
$548$		0			0
$549$		−	16.3679i		−	0.698564i
$550$		0			0
$551$	−16.5367			−0.704487
$552$		0			0
$553$	4.24766	+	13.0730i	0.180629	+	0.555919i
$554$		0			0
$555$	−9.99945	+	13.7631i	−0.424453	+	0.584209i
$556$		0			0
$557$	26.4461	+	8.59286i	1.12056	+	0.364091i	0.809980	−	0.586457i	$-0.199478\pi$
$557$	26.4461	+	8.59286i	1.12056	+	0.364091i	0.310577	+	0.950548i	$0.399478\pi$
$558$		0			0
$559$	20.9877	−	15.2484i	0.887684	−	0.644940i
$560$		0			0
$561$	3.10103	+	8.62014i	0.130926	+	0.363943i
$562$		0			0
$563$	20.7692	+	28.5863i	0.875316	+	1.20477i	0.977696	+	0.210024i	$0.0673542\pi$
$563$	20.7692	+	28.5863i	0.875316	+	1.20477i	−0.102380	+	0.994745i	$0.532646\pi$
$564$		0			0
$565$	−55.9053	−	18.1647i	−2.35196	−	0.764197i
$566$		0			0
$567$	−2.68681	−	1.95208i	−0.112835	−	0.0819797i
$568$		0			0
$569$	10.1065	+	31.1047i	0.423687	+	1.30398i	0.904246	+	0.427013i	$0.140434\pi$
$569$	10.1065	+	31.1047i	0.423687	+	1.30398i	−0.480558	+	0.876963i	$0.659566\pi$
$570$		0			0
$571$		−	32.0987i		−	1.34329i	−0.740874	−	0.671644i	$-0.765588\pi$
$571$		−	32.0987i		−	1.34329i	0.740874	−	0.671644i	$-0.234412\pi$
$572$		0			0
$573$			2.14539i			0.0896249i
$574$		0			0
$575$	6.46373	+	19.8933i	0.269556	+	0.829609i
$576$		0			0
$577$	−17.1459	−	12.4572i	−0.713794	−	0.518602i	0.170601	−	0.985340i	$-0.445429\pi$
$577$	−17.1459	−	12.4572i	−0.713794	−	0.518602i	−0.884396	+	0.466738i	$0.845429\pi$
$578$		0			0
$579$	−8.26636	−	2.68590i	−0.343538	−	0.111622i
$580$		0			0
$581$	0.704558	+	0.969742i	0.0292300	+	0.0402317i
$582$		0			0
$583$	−2.24474	+	7.71931i	−0.0929675	+	0.319701i
$584$		0			0
$585$	26.5682	−	19.3029i	1.09846	−	0.798079i
$586$		0			0
$587$	6.43150	+	2.08972i	0.265457	+	0.0862521i	0.438721	−	0.898623i	$-0.355432\pi$
$587$	6.43150	+	2.08972i	0.265457	+	0.0862521i	−0.173265	+	0.984875i	$0.555432\pi$
$588$		0			0
$589$	23.1557	−	31.8710i	0.954113	−	1.31322i
$590$		0			0
$591$	3.16570	+	9.74301i	0.130219	+	0.400774i
$592$		0			0
$593$	8.93648			0.366977			0.183489	−	0.983022i	$-0.441261\pi$
$593$	8.93648			0.366977			0.183489	+	0.983022i	$0.441261\pi$
$594$		0			0
$595$		−	13.9648i		−	0.572500i
$596$		0			0
$597$	−12.2157	+	3.96912i	−0.499955	+	0.162445i
$598$		0			0
$599$	−4.58215	−	3.32913i	−0.187222	−	0.136025i	0.490226	−	0.871595i	$-0.336914\pi$
$599$	−4.58215	−	3.32913i	−0.187222	−	0.136025i	−0.677448	+	0.735571i	$0.736914\pi$
$600$		0			0
$601$	−10.6085	+	32.6495i	−0.432729	+	1.33180i	0.462668	+	0.886532i	$0.346892\pi$
$601$	−10.6085	+	32.6495i	−0.432729	+	1.33180i	−0.895396	+	0.445270i	$0.853108\pi$
$602$		0			0
$603$	−14.8737	−	20.4719i	−0.605703	−	0.833679i
$604$		0			0
$605$	25.7467	+	31.1538i	1.04675	+	1.26658i
$606$		0			0
$607$	−32.7211	+	23.7733i	−1.32811	+	0.964929i	−0.328318	+	0.944567i	$0.606482\pi$
$607$	−32.7211	+	23.7733i	−1.32811	+	0.964929i	−0.999793	+	0.0203611i	$0.993518\pi$
$608$		0			0
$609$	1.23213	−	3.79212i	0.0499286	−	0.153664i
$610$		0			0
$611$	−0.839652	+	1.15568i	−0.0339687	+	0.0467539i
$612$		0			0
$613$	−13.7906	+	4.48085i	−0.556998	+	0.180980i	−0.573970	−	0.818876i	$-0.694597\pi$
$613$	−13.7906	+	4.48085i	−0.556998	+	0.180980i	0.0169719	+	0.999856i	$0.494597\pi$
$614$		0			0
$615$	−1.70118			−0.0685982
$616$		0			0
$617$	−17.5018			−0.704595			−0.352297	−	0.935888i	$-0.614599\pi$
$617$	−17.5018			−0.704595			−0.352297	+	0.935888i	$0.614599\pi$
$618$		0			0
$619$	−26.6998	+	8.67528i	−1.07315	+	0.348689i	−0.791715	−	0.610890i	$-0.790812\pi$
$619$	−26.6998	+	8.67528i	−1.07315	+	0.348689i	−0.281439	+	0.959579i	$0.590812\pi$
$620$		0			0
$621$	−6.59094	+	9.07165i	−0.264485	+	0.364033i
$622$		0			0
$623$	5.04064	−	15.5135i	0.201949	−	0.621535i
$624$		0			0
$625$	−3.83860	+	2.78891i	−0.153544	+	0.111556i
$626$		0			0
$627$	11.9122	+	3.46402i	0.475729	+	0.138340i
$628$		0			0
$629$	9.96277	+	13.7126i	0.397242	+	0.546756i
$630$		0			0
$631$	−5.53882	+	17.0467i	−0.220497	+	0.678620i	0.778221	+	0.627991i	$0.216123\pi$
$631$	−5.53882	+	17.0467i	−0.220497	+	0.678620i	−0.998718	+	0.0506287i	$0.983877\pi$
$632$		0			0
$633$	−5.97771	−	4.34306i	−0.237593	−	0.172621i
$634$		0			0
$635$	32.3469	−	10.5101i	1.28365	−	0.417082i
$636$		0			0
$637$		−	22.1767i		−	0.878671i
$638$		0			0
$639$	−12.5456			−0.496297
$640$		0			0
$641$	1.09534	+	3.37112i	0.0432634	+	0.133151i	0.970355	−	0.241683i	$-0.0776995\pi$
$641$	1.09534	+	3.37112i	0.0432634	+	0.133151i	−0.927092	+	0.374835i	$0.877700\pi$
$642$		0			0
$643$	−9.19302	+	12.6531i	−0.362537	+	0.498990i	−0.950854	−	0.309641i	$-0.899791\pi$
$643$	−9.19302	+	12.6531i	−0.362537	+	0.498990i	0.588316	+	0.808631i	$0.299791\pi$
$644$		0			0
$645$	−19.7822	−	6.42762i	−0.778922	−	0.253087i
$646$		0			0
$647$	−22.4391	+	16.3030i	−0.882174	+	0.640937i	−0.933826	−	0.357728i	$-0.883551\pi$
$647$	−22.4391	+	16.3030i	−0.882174	+	0.640937i	0.0516518	+	0.998665i	$0.483551\pi$
$648$		0			0
$649$	−0.668767	−	1.85902i	−0.0262514	−	0.0729727i
$650$		0			0
$651$	5.58321	+	7.68464i	0.218823	+	0.301185i
$652$		0			0
$653$	4.21888	+	1.37080i	0.165098	+	0.0536434i	0.390400	−	0.920646i	$-0.372337\pi$
$653$	4.21888	+	1.37080i	0.165098	+	0.0536434i	−0.225302	+	0.974289i	$0.572337\pi$
$654$		0			0
$655$	−39.6174	−	28.7837i	−1.54798	−	1.12467i
$656$		0			0
$657$	−1.85385	−	5.70556i	−0.0723255	−	0.222595i
$658$		0			0
$659$		−	14.0037i		−	0.545506i	−0.962084	−	0.272753i	$-0.912066\pi$
$659$		−	14.0037i		−	0.545506i	0.962084	−	0.272753i	$-0.0879341\pi$
$660$		0			0
$661$			33.4719i			1.30191i	0.759118	+	0.650953i	$0.225631\pi$
$661$			33.4719i			1.30191i	−0.759118	+	0.650953i	$0.774369\pi$
$662$		0			0
$663$	3.39755	+	10.4566i	0.131950	+	0.406100i
$664$		0			0
$665$	−15.2993	−	11.1156i	−0.593281	−	0.431044i
$666$		0			0
$667$	8.98826	+	2.92046i	0.348027	+	0.113081i
$668$		0			0
$669$	2.56459	+	3.52985i	0.0991527	+	0.136472i
$670$		0			0
$671$	24.1642	−	0.753404i	0.932847	−	0.0290848i
$672$		0			0
$673$	0.817162	−	0.593703i	0.0314993	−	0.0228856i	−0.571924	−	0.820306i	$-0.693803\pi$
$673$	0.817162	−	0.593703i	0.0314993	−	0.0228856i	0.603423	+	0.797421i	$0.293803\pi$
$674$		0			0
$675$	−36.8322	−	11.9675i	−1.41767	−	0.460629i
$676$		0			0
$677$	−18.3934	+	25.3163i	−0.706915	+	0.972985i	0.292943	+	0.956130i	$0.405365\pi$
$677$	−18.3934	+	25.3163i	−0.706915	+	0.972985i	−0.999858	+	0.0168552i	$0.994635\pi$
$678$		0			0
$679$	−2.19796	−	6.76461i	−0.0843498	−	0.259602i
$680$		0			0
$681$	15.6986			0.601573
$682$		0			0
$683$			12.2698i			0.469491i	0.972057	+	0.234745i	$0.0754256\pi$
$683$			12.2698i			0.469491i	−0.972057	+	0.234745i	$0.924574\pi$
$684$		0			0
$685$	33.9263	−	11.0233i	1.29626	−	0.421179i
$686$		0			0
$687$	−2.79875	−	2.03341i	−0.106779	−	0.0775794i
$688$		0			0
$689$	−2.98147	+	9.17603i	−0.113585	+	0.349579i
$690$		0			0
$691$	6.17353	+	8.49714i	0.234852	+	0.323246i	0.910134	−	0.414313i	$-0.135978\pi$
$691$	6.17353	+	8.49714i	0.234852	+	0.323246i	−0.675282	+	0.737559i	$0.735978\pi$
$692$		0			0
$693$	5.00531	−	7.36117i	0.190136	−	0.279628i
$694$		0			0
$695$	66.1522	−	48.0624i	2.50930	−	1.82311i
$696$		0			0
$697$	−0.523765	+	1.61198i	−0.0198390	+	0.0610582i
$698$		0			0
$699$	6.27258	−	8.63347i	0.237251	−	0.326548i
$700$		0			0
$701$	−5.50999	+	1.79030i	−0.208109	+	0.0676188i	−0.411217	−	0.911538i	$-0.634896\pi$
$701$	−5.50999	+	1.79030i	−0.208109	+	0.0676188i	0.203107	+	0.979157i	$0.434896\pi$
$702$		0			0
$703$	22.9531			0.865691
$704$		0			0
$705$	1.14536			0.0431367
$706$		0			0
$707$	6.79240	−	2.20698i	0.255454	−	0.0830022i
$708$		0			0
$709$	−26.7781	+	36.8569i	−1.00567	+	1.38419i	−0.0838916	+	0.996475i	$0.526735\pi$
$709$	−26.7781	+	36.8569i	−1.00567	+	1.38419i	−0.921780	+	0.387713i	$0.873265\pi$
$710$		0			0
$711$	7.97969	−	24.5590i	0.299262	−	0.921033i
$712$		0			0
$713$	−18.2145	+	13.2336i	−0.682138	+	0.495603i
$714$		0			0
$715$	29.7202	+	38.3346i	1.11147	+	1.43363i
$716$		0			0
$717$	10.6946	+	14.7198i	0.399396	+	0.549721i
$718$		0			0
$719$	−0.905713	+	2.78750i	−0.0337774	+	0.103956i	−0.966524	−	0.256577i	$-0.917405\pi$
$719$	−0.905713	+	2.78750i	−0.0337774	+	0.103956i	0.932746	+	0.360533i	$0.117405\pi$
$720$		0			0
$721$	−3.79610	−	2.75803i	−0.141374	−	0.102714i
$722$		0			0
$723$	−14.4151	+	4.68376i	−0.536104	+	0.174191i
$724$		0			0
$725$			32.6409i			1.21225i
$726$		0			0
$727$	24.5751			0.911438			0.455719	−	0.890124i	$-0.349382\pi$
$727$	24.5751			0.911438			0.455719	+	0.890124i	$0.349382\pi$
$728$		0			0
$729$	−1.74122	−	5.35891i	−0.0644895	−	0.198478i
$730$		0			0
$731$	−12.1812	+	16.7660i	−0.450538	+	0.620113i
$732$		0			0
$733$	19.7862	+	6.42893i	0.730820	+	0.237458i	0.650708	−	0.759328i	$-0.274472\pi$
$733$	19.7862	+	6.42893i	0.730820	+	0.237458i	0.0801122	+	0.996786i	$0.474472\pi$
$734$		0			0
$735$	−14.3852	+	10.4514i	−0.530605	+	0.385507i
$736$		0			0
$737$	29.5383	−	22.9006i	1.08806	−	0.843553i
$738$		0			0
$739$	1.61711	+	2.22575i	0.0594862	+	0.0818757i	0.837724	−	0.546094i	$-0.183886\pi$
$739$	1.61711	+	2.22575i	0.0594862	+	0.0818757i	−0.778237	+	0.627970i	$0.783886\pi$
$740$		0			0
$741$	14.1602	+	4.60093i	0.520188	+	0.169019i
$742$		0			0
$743$	36.3879	+	26.4374i	1.33494	+	0.969894i	0.999614	+	0.0277933i	$0.00884801\pi$
$743$	36.3879	+	26.4374i	1.33494	+	0.969894i	0.335331	+	0.942101i	$0.391152\pi$
$744$		0			0
$745$	−14.3073	−	44.0333i	−0.524178	−	1.61325i
$746$		0			0
$747$		−	2.25182i		−	0.0823899i
$748$		0			0
$749$			15.3126i			0.559509i
$750$		0			0
$751$	10.9010	+	33.5497i	0.397782	+	1.22425i	0.926774	+	0.375619i	$0.122570\pi$
$751$	10.9010	+	33.5497i	0.397782	+	1.22425i	−0.528992	+	0.848627i	$0.677430\pi$
$752$		0			0
$753$	−4.18715	−	3.04214i	−0.152588	−	0.110862i
$754$		0			0
$755$	52.9967	+	17.2197i	1.92875	+	0.626688i
$756$		0			0
$757$	−27.5638	−	37.9383i	−1.00182	−	1.37889i	−0.924201	−	0.381906i	$-0.875268\pi$
$757$	−27.5638	−	37.9383i	−1.00182	−	1.37889i	−0.0776206	−	0.996983i	$-0.524732\pi$
$758$		0			0
$759$	−5.86295	−	3.98658i	−0.212811	−	0.144704i
$760$		0			0
$761$	−3.57793	+	2.59952i	−0.129700	+	0.0942324i	−0.650744	−	0.759297i	$-0.725543\pi$
$761$	−3.57793	+	2.59952i	−0.129700	+	0.0942324i	0.521044	+	0.853530i	$0.325543\pi$
$762$		0			0
$763$	−6.42674	−	2.08818i	−0.232664	−	0.0755970i
$764$		0			0
$765$	−15.4202	+	21.2240i	−0.557517	+	0.767356i
$766$		0			0
$767$	−0.732715	−	2.25506i	−0.0264568	−	0.0814256i
$768$		0			0
$769$	53.6158			1.93344			0.966718	−	0.255844i	$-0.0823534\pi$
$769$	53.6158			1.93344			0.966718	+	0.255844i	$0.0823534\pi$
$770$		0			0
$771$		−	12.3071i		−	0.443229i
$772$		0			0
$773$	−40.8810	+	13.2830i	−1.47039	+	0.477758i	−0.931225	−	0.364445i	$-0.881259\pi$
$773$	−40.8810	+	13.2830i	−1.47039	+	0.477758i	−0.539161	+	0.842202i	$0.681259\pi$
$774$		0			0
$775$	−62.9085	−	45.7057i	−2.25974	−	1.64180i
$776$		0			0
$777$	−1.71021	+	5.26349i	−0.0613535	+	0.188827i
$778$		0			0
$779$	1.34912	+	1.85691i	0.0483374	+	0.0665307i
$780$		0			0
$781$	−0.577467	−	18.5213i	−0.0206634	−	0.662744i
$782$		0			0
$783$	−14.1562	+	10.2851i	−0.505901	+	0.367559i
$784$		0			0
$785$	−1.73331	+	5.33457i	−0.0618644	+	0.190399i
$786$		0			0
$787$	−8.95616	+	12.3271i	−0.319253	+	0.439414i	−0.938239	−	0.345988i	$-0.887544\pi$
$787$	−8.95616	+	12.3271i	−0.319253	+	0.439414i	0.618986	+	0.785402i	$0.287544\pi$
$788$		0			0
$789$	9.09993	−	2.95675i	0.323966	−	0.105263i
$790$		0			0
$791$	−19.1230			−0.679937
$792$		0			0
$793$	29.0152			1.03036
$794$		0			0
$795$	7.35725	−	2.39052i	0.260935	−	0.0847829i
$796$		0			0
$797$	−18.9900	+	26.1375i	−0.672660	+	0.925837i	−0.999817	−	0.0191333i	$-0.993909\pi$
$797$	−18.9900	+	26.1375i	−0.672660	+	0.925837i	0.327157	+	0.944970i	$0.393909\pi$
$798$		0			0
$799$	0.352637	−	1.08531i	0.0124754	−	0.0383953i
$800$		0			0
$801$	−24.7912	+	18.0118i	−0.875953	+	0.636417i
$802$		0			0
$803$	8.33788	−	2.99949i	0.294237	−	0.105850i
$804$		0			0
$805$	6.35262	+	8.74363i	0.223901	+	0.308173i
$806$		0			0
$807$	−0.666577	+	2.05151i	−0.0234646	+	0.0722167i
$808$		0			0
$809$	−40.7382	−	29.5981i	−1.43228	−	1.04061i	−0.989587	−	0.143939i	$-0.954023\pi$
$809$	−40.7382	−	29.5981i	−1.43228	−	1.04061i	−0.442693	−	0.896673i	$-0.645977\pi$
$810$		0			0
$811$	−41.5216	+	13.4912i	−1.45802	+	0.473739i	−0.927464	−	0.373911i	$-0.878016\pi$
$811$	−41.5216	+	13.4912i	−1.45802	+	0.473739i	−0.530555	+	0.847650i	$0.678016\pi$
$812$		0			0
$813$		−	0.267306i		−	0.00937483i
$814$		0			0
$815$	−57.0827			−1.99952
$816$		0			0
$817$	8.67228	+	26.6905i	0.303405	+	0.933783i
$818$		0			0
$819$	6.27963	−	8.64316i	0.219428	−	0.302017i
$820$		0			0
$821$	18.0688	+	5.87092i	0.630607	+	0.204897i	0.606844	−	0.794821i	$-0.292435\pi$
$821$	18.0688	+	5.87092i	0.630607	+	0.204897i	0.0237628	+	0.999718i	$0.492435\pi$
$822$		0			0
$823$	−10.6891	+	7.76610i	−0.372599	+	0.270709i	−0.758288	−	0.651920i	$-0.773964\pi$
$823$	−10.6891	+	7.76610i	−0.372599	+	0.270709i	0.385689	+	0.922629i	$0.373964\pi$
$824$		0			0
$825$	6.83744	−	23.5129i	0.238049	−	0.818614i
$826$		0			0
$827$	10.4334	+	14.3603i	0.362804	+	0.499357i	0.950927	−	0.309415i	$-0.100133\pi$
$827$	10.4334	+	14.3603i	0.362804	+	0.499357i	−0.588123	+	0.808771i	$0.700133\pi$
$828$		0			0
$829$	8.14454	+	2.64632i	0.282872	+	0.0919106i	0.447017	−	0.894526i	$-0.352486\pi$
$829$	8.14454	+	2.64632i	0.282872	+	0.0919106i	−0.164145	+	0.986436i	$0.552486\pi$
$830$		0			0
$831$	−1.75687	−	1.27644i	−0.0609452	−	0.0442793i
$832$		0			0
$833$	5.47449	+	16.8487i	0.189680	+	0.583774i
$834$		0			0
$835$			30.8389i			1.06723i
$836$		0			0
$837$		−	41.6850i		−	1.44084i
$838$		0			0
$839$	11.7633	+	36.2037i	0.406114	+	1.24989i	0.919962	+	0.392008i	$0.128220\pi$
$839$	11.7633	+	36.2037i	0.406114	+	1.24989i	−0.513848	+	0.857881i	$0.671780\pi$
$840$		0			0
$841$	−11.5302	−	8.37718i	−0.397593	−	0.288868i
$842$		0			0
$843$	−1.02699	−	0.333690i	−0.0353715	−	0.0114929i
$844$		0			0
$845$	6.14305	+	8.45519i	0.211327	+	0.290867i
$846$		0			0
$847$	11.0978	+	7.05059i	0.381325	+	0.242261i
$848$		0			0
$849$	9.69917	−	7.04686i	0.332875	−	0.241848i
$850$		0			0
$851$	−12.4758	−	4.05363i	−0.427664	−	0.138957i
$852$		0			0
$853$	20.1305	−	27.7072i	0.689254	−	0.948677i	−0.310744	−	0.950493i	$-0.600578\pi$
$853$	20.1305	−	27.7072i	0.689254	−	0.948677i	0.999998	+	0.00181694i	$0.000578350\pi$
$854$		0			0
$855$	10.9782	+	33.7875i	0.375447	+	1.15551i
$856$		0			0
$857$	−52.8215			−1.80435			−0.902174	−	0.431371i	$-0.858030\pi$
$857$	−52.8215			−1.80435			−0.902174	+	0.431371i	$0.858030\pi$
$858$		0			0
$859$			8.91497i			0.304175i	0.988367	+	0.152087i	$0.0485995\pi$
$859$			8.91497i			0.304175i	−0.988367	+	0.152087i	$0.951400\pi$
$860$		0			0
$861$	−0.526340	+	0.171018i	−0.0179376	+	0.00582829i
$862$		0			0
$863$	−0.848339	−	0.616354i	−0.0288778	−	0.0209809i	0.573253	−	0.819379i	$-0.305681\pi$
$863$	−0.848339	−	0.616354i	−0.0288778	−	0.0209809i	−0.602131	+	0.798398i	$0.705681\pi$
$864$		0			0
$865$	−28.2283	+	86.8778i	−0.959791	+	2.95393i
$866$		0			0
$867$	3.51718	+	4.84098i	0.119450	+	0.164408i
$868$		0			0
$869$	36.6241	+	10.6501i	1.24239	+	0.361280i
$870$		0			0
$871$	36.2903	−	26.3665i	1.22965	−	0.893393i
$872$		0			0
$873$	−4.12909	+	12.7080i	−0.139749	+	0.430102i
$874$		0			0
$875$	−9.03364	+	12.4337i	−0.305393	+	0.420337i
$876$		0			0
$877$	11.4920	−	3.73397i	0.388056	−	0.126087i	−0.108490	−	0.994098i	$-0.534601\pi$
$877$	11.4920	−	3.73397i	0.388056	−	0.126087i	0.496546	+	0.868010i	$0.334601\pi$
$878$		0			0
$879$	12.9294			0.436096
$880$		0			0
$881$	11.8356			0.398752			0.199376	−	0.979923i	$-0.436109\pi$
$881$	11.8356			0.398752			0.199376	+	0.979923i	$0.436109\pi$
$882$		0			0
$883$	−48.6275	+	15.8000i	−1.63645	+	0.531713i	−0.975740	−	0.218932i	$-0.929743\pi$
$883$	−48.6275	+	15.8000i	−1.63645	+	0.531713i	−0.660705	+	0.750645i	$0.729743\pi$
$884$		0			0
$885$	−1.11746	+	1.53805i	−0.0375630	+	0.0517011i
$886$		0			0
$887$	−5.24892	+	16.1545i	−0.176242	+	0.542416i	−0.999688	−	0.0249781i	$-0.992048\pi$
$887$	−5.24892	+	16.1545i	−0.176242	+	0.542416i	0.823446	+	0.567394i	$0.192048\pi$
$888$		0			0
$889$	8.95146	−	6.50362i	0.300222	−	0.218124i
$890$		0			0
$891$	−8.67119	+	3.11940i	−0.290496	+	0.104504i
$892$		0			0
$893$	−0.908329	−	1.25021i	−0.0303961	−	0.0418366i
$894$		0			0
$895$	18.7179	−	57.6077i	0.625670	−	1.92561i
$896$		0			0
$897$	−6.88401	−	5.00153i	−0.229850	−	0.166996i
$898$		0			0
$899$	−33.4139	+	10.8568i	−1.11441	+	0.362095i
$900$		0			0
$901$		−	7.70750i		−	0.256774i
$902$		0			0
$903$	−6.76671			−0.225182
$904$		0			0
$905$	10.4217	+	32.0748i	0.346430	+	1.06620i
$906$		0			0
$907$	8.46620	−	11.6527i	0.281116	−	0.386922i	−0.644987	−	0.764193i	$-0.723137\pi$
$907$	8.46620	−	11.6527i	0.281116	−	0.386922i	0.926103	+	0.377271i	$0.123137\pi$
$908$		0			0
$909$	−12.7602	−	4.14605i	−0.423231	−	0.137516i
$910$		0			0
$911$	−32.3517	+	23.5049i	−1.07186	+	0.778751i	−0.976246	−	0.216667i	$-0.930481\pi$
$911$	−32.3517	+	23.5049i	−1.07186	+	0.778751i	−0.0956137	+	0.995419i	$0.530481\pi$
$912$		0			0
$913$	3.32440	−	0.103650i	0.110022	−	0.00343032i
$914$		0			0
$915$	−13.6743	−	18.8211i	−0.452059	−	0.622205i
$916$		0			0
$917$	−15.1511	−	4.92290i	−0.500334	−	0.162568i
$918$		0			0
$919$	−5.72709	−	4.16097i	−0.188919	−	0.137258i	0.489305	−	0.872112i	$-0.337250\pi$
$919$	−5.72709	−	4.16097i	−0.188919	−	0.137258i	−0.678225	+	0.734855i	$0.737250\pi$
$920$		0			0
$921$	2.25574	+	6.94245i	0.0743291	+	0.228761i
$922$		0			0
$923$		−	22.2395i		−	0.732022i
$924$		0			0
$925$		−	45.3058i		−	1.48965i
$926$		0			0
$927$	2.72395	+	8.38345i	0.0894661	+	0.275348i
$928$		0			0
$929$	31.0156	+	22.5341i	1.01759	+	0.739320i	0.965787	−	0.259337i	$-0.0835040\pi$
$929$	31.0156	+	22.5341i	1.01759	+	0.739320i	0.0518005	+	0.998657i	$0.483504\pi$
$930$		0			0
$931$	22.8164	+	7.41349i	0.747776	+	0.242967i
$932$		0			0
$933$	13.0943	+	18.0228i	0.428688	+	0.590039i
$934$		0			0
$935$	−32.0432	−	21.7881i	−1.04792	−	0.712547i
$936$		0			0
$937$	46.9358	−	34.1009i	1.53333	−	1.11403i	0.578973	−	0.815346i	$-0.303454\pi$
$937$	46.9358	−	34.1009i	1.53333	−	1.11403i	0.954353	−	0.298680i	$-0.0965465\pi$
$938$		0			0
$939$	15.5992	+	5.06850i	0.509062	+	0.165404i
$940$		0			0
$941$	6.48795	−	8.92990i	0.211501	−	0.291106i	−0.690065	−	0.723747i	$-0.742418\pi$
$941$	6.48795	−	8.92990i	0.211501	−	0.291106i	0.901566	+	0.432641i	$0.142418\pi$
$942$		0			0
$943$	−0.405356	−	1.24756i	−0.0132002	−	0.0406261i
$944$		0			0
$945$	−20.0103			−0.650936
$946$		0			0
$947$			15.5478i			0.505235i	0.967566	+	0.252617i	$0.0812914\pi$
$947$			15.5478i			0.505235i	−0.967566	+	0.252617i	$0.918709\pi$
$948$		0			0
$949$	10.1142	−	3.28630i	0.328321	−	0.106678i
$950$		0			0
$951$	−14.0287	−	10.1925i	−0.454913	−	0.330514i
$952$		0			0
$953$	2.41825	−	7.44259i	0.0783346	−	0.241089i	−0.904219	−	0.427069i	$-0.859546\pi$
$953$	2.41825	−	7.44259i	0.0783346	−	0.241089i	0.982554	+	0.185980i	$0.0595460\pi$
$954$		0			0
$955$	−5.33389	−	7.34147i	−0.172601	−	0.237564i
$956$		0			0
$957$	−6.77888	−	8.74374i	−0.219130	−	0.282645i
$958$		0			0
$959$	9.38853	−	6.82116i	0.303171	−	0.220267i
$960$		0			0
$961$	16.2843	−	50.1179i	0.525300	−	1.61671i
$962$		0			0
$963$	16.9084	−	23.2724i	0.544866	−	0.749943i
$964$		0			0
$965$	34.9650	−	11.3608i	1.12556	−	0.365718i
$966$		0			0
$967$	47.0564			1.51323			0.756615	−	0.653860i	$-0.226852\pi$
$967$	47.0564			1.51323			0.756615	+	0.653860i	$0.226852\pi$
$968$		0			0
$969$	−11.8940			−0.382090
$970$		0			0
$971$	36.8899	−	11.9863i	1.18385	−	0.384657i	0.350057	−	0.936729i	$-0.386162\pi$
$971$	36.8899	−	11.9863i	1.18385	−	0.384657i	0.833797	+	0.552071i	$0.186162\pi$
$972$		0			0
$973$	15.6356	−	21.5206i	0.501256	−	0.689919i
$974$		0			0
$975$	9.08152	−	27.9500i	0.290841	−	0.895118i
$976$		0			0
$977$	31.5826	−	22.9461i	1.01042	−	0.734111i	0.0461207	−	0.998936i	$-0.485314\pi$
$977$	31.5826	−	22.9461i	1.01042	−	0.734111i	0.964297	+	0.264825i	$0.0853141\pi$
$978$		0			0
$979$	−27.7323	−	35.7705i	−0.886328	−	1.14323i
$980$		0			0
$981$	7.46172	+	10.2702i	0.238234	+	0.327902i
$982$		0			0
$983$	−1.73793	+	5.34880i	−0.0554314	+	0.170600i	−0.974939	−	0.222471i	$-0.928588\pi$
$983$	−1.73793	+	5.34880i	−0.0554314	+	0.170600i	0.919508	+	0.393072i	$0.128588\pi$
$984$		0			0
$985$	−35.0561	−	25.4698i	−1.11698	−	0.811535i
$986$		0			0
$987$	0.354371	−	0.115142i	0.0112797	−	0.00366501i
$988$		0			0
$989$		−	16.0388i		−	0.510004i
$990$		0			0
$991$	−7.34032			−0.233173			−0.116586	−	0.993181i	$-0.537195\pi$
$991$	−7.34032			−0.233173			−0.116586	+	0.993181i	$0.537195\pi$
$992$		0			0
$993$	−5.06314	−	15.5827i	−0.160674	−	0.494503i
$994$		0			0
$995$	31.9337	−	43.9530i	1.01237	−	1.39340i
$996$		0			0
$997$	−54.1523	−	17.5952i	−1.71502	−	0.557244i	−0.723864	−	0.689942i	$-0.757636\pi$
$997$	−54.1523	−	17.5952i	−1.71502	−	0.557244i	−0.991156	+	0.132698i	$0.957636\pi$
$998$		0			0
$999$	19.6489	−	14.2758i	0.621665	−	0.451666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	352.2.w.a.113.4		40
4.3	odd	2		88.2.o.a.69.4	yes	40
8.3	odd	2		88.2.o.a.69.3	yes	40
8.5	even	2	inner	352.2.w.a.113.7		40
11.2	odd	10		3872.2.c.i.1937.14		20
11.4	even	5	inner	352.2.w.a.81.7		40
11.9	even	5		3872.2.c.h.1937.14		20
12.11	even	2		792.2.br.b.685.7		40
24.11	even	2		792.2.br.b.685.8		40
44.3	odd	10		968.2.o.j.269.7		40
44.7	even	10		968.2.o.i.565.8		40
44.15	odd	10		88.2.o.a.37.3	✓	40
44.19	even	10		968.2.o.d.269.4		40
44.27	odd	10		968.2.o.j.493.6		40
44.31	odd	10		968.2.c.h.485.19		20
44.35	even	10		968.2.c.i.485.2		20
44.39	even	10		968.2.o.d.493.5		40
44.43	even	2		968.2.o.i.245.7		40
88.3	odd	10		968.2.o.j.269.6		40
88.13	odd	10		3872.2.c.i.1937.7		20
88.19	even	10		968.2.o.d.269.5		40
88.27	odd	10		968.2.o.j.493.7		40
88.35	even	10		968.2.c.i.485.1		20
88.37	even	10	inner	352.2.w.a.81.4		40
88.43	even	2		968.2.o.i.245.8		40
88.51	even	10		968.2.o.i.565.7		40
88.53	even	10		3872.2.c.h.1937.7		20
88.59	odd	10		88.2.o.a.37.4	yes	40
88.75	odd	10		968.2.c.h.485.20		20
88.83	even	10		968.2.o.d.493.4		40
132.59	even	10		792.2.br.b.37.8		40
264.59	even	10		792.2.br.b.37.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.o.a.37.3	✓	40	44.15	odd	10
88.2.o.a.37.4	yes	40	88.59	odd	10
88.2.o.a.69.3	yes	40	8.3	odd	2
88.2.o.a.69.4	yes	40	4.3	odd	2
352.2.w.a.81.4		40	88.37	even	10	inner
352.2.w.a.81.7		40	11.4	even	5	inner
352.2.w.a.113.4		40	1.1	even	1	trivial
352.2.w.a.113.7		40	8.5	even	2	inner
792.2.br.b.37.7		40	264.59	even	10
792.2.br.b.37.8		40	132.59	even	10
792.2.br.b.685.7		40	12.11	even	2
792.2.br.b.685.8		40	24.11	even	2
968.2.c.h.485.19		20	44.31	odd	10
968.2.c.h.485.20		20	88.75	odd	10
968.2.c.i.485.1		20	88.35	even	10
968.2.c.i.485.2		20	44.35	even	10
968.2.o.d.269.4		40	44.19	even	10
968.2.o.d.269.5		40	88.19	even	10
968.2.o.d.493.4		40	88.83	even	10
968.2.o.d.493.5		40	44.39	even	10
968.2.o.i.245.7		40	44.43	even	2
968.2.o.i.245.8		40	88.43	even	2
968.2.o.i.565.7		40	88.51	even	10
968.2.o.i.565.8		40	44.7	even	10
968.2.o.j.269.6		40	88.3	odd	10
968.2.o.j.269.7		40	44.3	odd	10
968.2.o.j.493.6		40	44.27	odd	10
968.2.o.j.493.7		40	88.27	odd	10
3872.2.c.h.1937.7		20	88.53	even	10
3872.2.c.h.1937.14		20	11.9	even	5
3872.2.c.i.1937.7		20	88.13	odd	10
3872.2.c.i.1937.14		20	11.2	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 352 = 2^{5} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	352.w (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.826127 + 0.268425i) q^{3} +(2.15963 - 2.97247i) q^{5} +(0.369362 - 1.13678i) q^{7} +(-1.81662 + 1.31985i) q^{9} +(-2.03213 - 2.62115i) q^{11} +(-2.33969 - 3.22030i) q^{13} +(-0.986240 + 3.03533i) q^{15} +(2.57254 + 1.86906i) q^{17} +(4.09534 - 1.33066i) q^{19} +1.03827i q^{21} -2.46096 q^{23} +(-2.62651 - 8.08357i) q^{25} +(2.67820 - 3.68622i) q^{27} +(-3.65234 - 1.18672i) q^{29} +(7.40138 - 5.37742i) q^{31} +(2.38238 + 1.61993i) q^{33} +(-2.58136 - 3.55294i) q^{35} +(5.06948 + 1.64717i) q^{37} +(2.79729 + 2.03235i) q^{39} +(0.164715 + 0.506940i) q^{41} +6.51729i q^{43} +8.25022i q^{45} +(-0.110898 - 0.341309i) q^{47} +(4.50728 + 3.27473i) q^{49} +(-2.62694 - 0.853546i) q^{51} +(-1.42471 - 1.96095i) q^{53} +(-12.1799 + 0.379753i) q^{55} +(-3.02609 + 2.19858i) q^{57} +(0.566526 + 0.184075i) q^{59} +(-4.28455 + 5.89718i) q^{61} +(0.829389 + 2.55260i) q^{63} -14.6251 q^{65} +11.2692i q^{67} +(2.03306 - 0.660583i) q^{69} +(4.52005 + 3.28401i) q^{71} +(-0.825597 + 2.54093i) q^{73} +(4.33966 + 5.97303i) q^{75} +(-3.73026 + 1.34194i) q^{77} +(-9.30369 + 6.75953i) q^{79} +(0.858601 - 2.64250i) q^{81} +(-0.589450 + 0.811308i) q^{83} +(11.1114 - 3.61033i) q^{85} +3.33584 q^{87} +13.6469 q^{89} +(-4.52497 + 1.47025i) q^{91} +(-4.67105 + 6.42914i) q^{93} +(4.88906 - 15.0470i) q^{95} +(4.81420 - 3.49772i) q^{97} +(7.15114 + 2.07952i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10 q^{7} + 18 q^{15} - 6 q^{17} + 8 q^{23} - 4 q^{25} + 6 q^{31} - 10 q^{33} + 34 q^{39} - 14 q^{41} + 6 q^{47} - 4 q^{49} + 2 q^{55} - 26 q^{57} - 60 q^{63} - 36 q^{65} - 22 q^{71} - 6 q^{73} - 74 q^{79}+ \cdots + 10 q^{97}+O(q^{100}) \) 40 * q + 10 * q^7 + 18 * q^15 - 6 * q^17 + 8 * q^23 - 4 * q^25 + 6 * q^31 - 10 * q^33 + 34 * q^39 - 14 * q^41 + 6 * q^47 - 4 * q^49 + 2 * q^55 - 26 * q^57 - 60 * q^63 - 36 * q^65 - 22 * q^71 - 6 * q^73 - 74 * q^79 - 4 * q^81 - 68 * q^87 - 16 * q^89 - 66 * q^95 + 10 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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