LMFDB - Embedded newform 800.2.be.a.209.28

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [800,2,Mod(209,800)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("800.209"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(800, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 7])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 800 = 2^{5} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	800.be (of order $10$, degree $4$, not 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:	$6.38803216170$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			209.28
Character	$\chi$	$=$	800.209
Dual form			800.2.be.a.689.28

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.970606 + 2.98722i) q^{3} +(-0.762120 + 2.10218i) q^{5} +1.71800i q^{7} +(-5.55435 + 4.03547i) q^{9} +(-1.35234 + 1.86134i) q^{11} +(4.80828 - 3.49342i) q^{13} +(-7.01940 - 0.236226i) q^{15} +(-2.53693 - 0.824300i) q^{17} +(5.48112 + 1.78092i) q^{19} +(-5.13203 + 1.66750i) q^{21} +(0.393834 - 0.542066i) q^{23} +(-3.83835 - 3.20423i) q^{25} +(-9.82268 - 7.13660i) q^{27} +(-1.22579 + 0.398283i) q^{29} +(-0.362926 + 1.11697i) q^{31} +(-6.87282 - 2.23312i) q^{33} +(-3.61155 - 1.30932i) q^{35} +(2.95345 - 2.14581i) q^{37} +(15.1026 + 10.9726i) q^{39} +(6.21636 - 4.51645i) q^{41} +3.75396 q^{43} +(-4.25022 - 14.7518i) q^{45} +(-8.51974 + 2.76823i) q^{47} +4.04848 q^{49} -8.37845i q^{51} +(1.09116 + 3.35825i) q^{53} +(-2.88223 - 4.26144i) q^{55} +18.1019i q^{57} +(-3.58141 - 4.92938i) q^{59} +(0.542140 - 0.746192i) q^{61} +(-6.93293 - 9.54236i) q^{63} +(3.67932 + 12.7703i) q^{65} +(-4.74089 + 14.5910i) q^{67} +(2.00153 + 0.650336i) q^{69} +(-1.92683 - 5.93017i) q^{71} +(3.14398 - 4.32732i) q^{73} +(5.84621 - 14.5760i) q^{75} +(-3.19778 - 2.32332i) q^{77} +(0.125628 + 0.386644i) q^{79} +(5.41990 - 16.6807i) q^{81} +(0.356893 - 1.09840i) q^{83} +(3.66628 - 4.70489i) q^{85} +(-2.37952 - 3.27513i) q^{87} +(3.34918 + 2.43332i) q^{89} +(6.00168 + 8.26061i) q^{91} -3.68890 q^{93} +(-7.92110 + 10.1650i) q^{95} +(-14.4383 + 4.69127i) q^{97} -15.7959i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) $ 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/800\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$577$
$\chi(n)$	$-1$	$1$	$e\left(\frac{7}{10}\right)$

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
$3$	0.970606	+	2.98722i	0.560380	+	1.72467i	0.681295	+	0.732009i	$0.261417\pi$
$3$	0.970606	+	2.98722i	0.560380	+	1.72467i	−0.120915	+	0.992663i	$0.538583\pi$
$4$		0			0
$5$	−0.762120	+	2.10218i	−0.340830	+	0.940125i
$5$	−0.762120	+	2.10218i	−0.340830	+	0.940125i
$6$		0			0
$7$			1.71800i			0.649342i	0.945827	+	0.324671i	$0.105254\pi$
$7$			1.71800i			0.649342i	−0.945827	+	0.324671i	$0.894746\pi$
$8$		0			0
$9$	−5.55435	+	4.03547i	−1.85145	+	1.34516i
$10$		0			0
$11$	−1.35234	+	1.86134i	−0.407747	+	0.561215i	−0.962667	−	0.270688i	$-0.912749\pi$
$11$	−1.35234	+	1.86134i	−0.407747	+	0.561215i	0.554920	+	0.831903i	$0.312749\pi$
$12$		0			0
$13$	4.80828	−	3.49342i	1.33358	−	0.968900i	0.333922	−	0.942601i	$-0.391628\pi$
$13$	4.80828	−	3.49342i	1.33358	−	0.968900i	0.999654	−	0.0262994i	$-0.00837233\pi$
$14$		0			0
$15$	−7.01940	−	0.236226i	−1.81240	−	0.0609934i
$16$		0			0
$17$	−2.53693	−	0.824300i	−0.615297	−	0.199922i	−0.0152459	−	0.999884i	$-0.504853\pi$
$17$	−2.53693	−	0.824300i	−0.615297	−	0.199922i	−0.600051	+	0.799962i	$0.704853\pi$
$18$		0			0
$19$	5.48112	+	1.78092i	1.25746	+	0.408572i	0.860587	−	0.509304i	$-0.170097\pi$
$19$	5.48112	+	1.78092i	1.25746	+	0.408572i	0.396868	+	0.917876i	$0.370097\pi$
$20$		0			0
$21$	−5.13203	+	1.66750i	−1.11990	+	0.363878i
$22$		0			0
$23$	0.393834	−	0.542066i	0.0821200	−	0.113029i	−0.765981	−	0.642864i	$-0.777746\pi$
$23$	0.393834	−	0.542066i	0.0821200	−	0.113029i	0.848101	+	0.529835i	$0.177746\pi$
$24$		0			0
$25$	−3.83835	−	3.20423i	−0.767669	−	0.640846i
$26$		0			0
$27$	−9.82268	−	7.13660i	−1.89038	−	1.37344i
$28$		0			0
$29$	−1.22579	+	0.398283i	−0.227624	+	0.0739594i	−0.420608	−	0.907242i	$-0.638183\pi$
$29$	−1.22579	+	0.398283i	−0.227624	+	0.0739594i	0.192985	+	0.981202i	$0.438183\pi$
$30$		0			0
$31$	−0.362926	+	1.11697i	−0.0651834	+	0.200614i	−0.978344	−	0.206986i	$-0.933634\pi$
$31$	−0.362926	+	1.11697i	−0.0651834	+	0.200614i	0.913160	+	0.407600i	$0.133634\pi$
$32$		0			0
$33$	−6.87282	−	2.23312i	−1.19640	−	0.388735i
$34$		0			0
$35$	−3.61155	−	1.30932i	−0.610463	−	0.221315i
$36$		0			0
$37$	2.95345	−	2.14581i	0.485545	−	0.352769i	−0.317924	−	0.948116i	$-0.602986\pi$
$37$	2.95345	−	2.14581i	0.485545	−	0.352769i	0.803468	+	0.595347i	$0.202986\pi$
$38$		0			0
$39$	15.1026	+	10.9726i	2.41834	+	1.75703i
$40$		0			0
$41$	6.21636	−	4.51645i	0.970832	−	0.705351i	0.0151912	−	0.999885i	$-0.495164\pi$
$41$	6.21636	−	4.51645i	0.970832	−	0.705351i	0.955641	+	0.294534i	$0.0951643\pi$
$42$		0			0
$43$	3.75396			0.572473			0.286236	−	0.958159i	$-0.407596\pi$
$43$	3.75396			0.572473			0.286236	+	0.958159i	$0.407596\pi$
$44$		0			0
$45$	−4.25022	−	14.7518i	−0.633585	−	2.19906i
$46$		0			0
$47$	−8.51974	+	2.76823i	−1.24273	+	0.403788i	−0.855311	−	0.518115i	$-0.826634\pi$
$47$	−8.51974	+	2.76823i	−1.24273	+	0.403788i	−0.387421	+	0.921903i	$0.626634\pi$
$48$		0			0
$49$	4.04848			0.578355
$50$		0			0
$51$		−	8.37845i		−	1.17322i
$52$		0			0
$53$	1.09116	+	3.35825i	0.149882	+	0.461291i	0.997607	−	0.0691467i	$-0.0220277\pi$
$53$	1.09116	+	3.35825i	0.149882	+	0.461291i	−0.847724	+	0.530438i	$0.822028\pi$
$54$		0			0
$55$	−2.88223	−	4.26144i	−0.388640	−	0.574612i
$56$		0			0
$57$			18.1019i			2.39765i
$58$		0			0
$59$	−3.58141	−	4.92938i	−0.466259	−	0.641751i	0.509533	−	0.860451i	$-0.329818\pi$
$59$	−3.58141	−	4.92938i	−0.466259	−	0.641751i	−0.975792	+	0.218700i	$0.929818\pi$
$60$		0			0
$61$	0.542140	−	0.746192i	0.0694139	−	0.0955401i	−0.772898	−	0.634530i	$-0.781194\pi$
$61$	0.542140	−	0.746192i	0.0694139	−	0.0955401i	0.842312	+	0.538990i	$0.181194\pi$
$62$		0			0
$63$	−6.93293	−	9.54236i	−0.873467	−	1.20222i
$64$		0			0
$65$	3.67932	+	12.7703i	0.456364	+	1.58396i
$66$		0			0
$67$	−4.74089	+	14.5910i	−0.579192	+	1.78257i	0.0422481	+	0.999107i	$0.486548\pi$
$67$	−4.74089	+	14.5910i	−0.579192	+	1.78257i	−0.621440	+	0.783462i	$0.713452\pi$
$68$		0			0
$69$	2.00153	+	0.650336i	0.240956	+	0.0782912i
$70$		0			0
$71$	−1.92683	−	5.93017i	−0.228673	−	0.703782i	−0.997898	−	0.0648044i	$-0.979358\pi$
$71$	−1.92683	−	5.93017i	−0.228673	−	0.703782i	0.769225	−	0.638978i	$-0.220642\pi$
$72$		0			0
$73$	3.14398	−	4.32732i	0.367975	−	0.506475i	−0.584374	−	0.811485i	$-0.698660\pi$
$73$	3.14398	−	4.32732i	0.367975	−	0.506475i	0.952349	+	0.305010i	$0.0986598\pi$
$74$		0			0
$75$	5.84621	−	14.5760i	0.675063	−	1.68309i
$76$		0			0
$77$	−3.19778	−	2.32332i	−0.364421	−	0.264767i
$78$		0			0
$79$	0.125628	+	0.386644i	0.0141343	+	0.0435008i	0.957875	−	0.287186i	$-0.0927197\pi$
$79$	0.125628	+	0.386644i	0.0141343	+	0.0435008i	−0.943741	+	0.330687i	$0.892720\pi$
$80$		0			0
$81$	5.41990	−	16.6807i	0.602211	−	1.85342i
$82$		0			0
$83$	0.356893	−	1.09840i	0.0391741	−	0.120565i	−0.929557	−	0.368678i	$-0.879810\pi$
$83$	0.356893	−	1.09840i	0.0391741	−	0.120565i	0.968731	+	0.248113i	$0.0798104\pi$
$84$		0			0
$85$	3.66628	−	4.70489i	0.397664	−	0.510317i
$86$		0			0
$87$	−2.37952	−	3.27513i	−0.255111	−	0.351131i
$88$		0			0
$89$	3.34918	+	2.43332i	0.355013	+	0.257932i	0.750969	−	0.660338i	$-0.229587\pi$
$89$	3.34918	+	2.43332i	0.355013	+	0.257932i	−0.395956	+	0.918269i	$0.629587\pi$
$90$		0			0
$91$	6.00168	+	8.26061i	0.629148	+	0.865947i
$92$		0			0
$93$	−3.68890			−0.382521
$94$		0			0
$95$	−7.92110	+	10.1650i	−0.812688	+	1.04291i
$96$		0			0
$97$	−14.4383	+	4.69127i	−1.46598	+	0.476327i	−0.929892	−	0.367833i	$-0.880100\pi$
$97$	−14.4383	+	4.69127i	−1.46598	+	0.476327i	−0.536091	+	0.844160i	$0.680100\pi$
$98$		0			0
$99$		−	15.7959i		−	1.58754i
$100$		0			0
$101$			13.7524i			1.36842i	0.729286	+	0.684209i	$0.239852\pi$
$101$			13.7524i			1.36842i	−0.729286	+	0.684209i	$0.760148\pi$
$102$		0			0
$103$	−8.32817	+	2.70599i	−0.820599	+	0.266629i	−0.689081	−	0.724685i	$-0.741985\pi$
$103$	−8.32817	+	2.70599i	−0.820599	+	0.266629i	−0.131519	+	0.991314i	$0.541985\pi$
$104$		0			0
$105$	0.405836	−	12.0593i	0.0396056	−	1.17687i
$106$		0			0
$107$	3.49350			0.337729			0.168865	−	0.985639i	$-0.445990\pi$
$107$	3.49350			0.337729			0.168865	+	0.985639i	$0.445990\pi$
$108$		0			0
$109$	2.56568	+	3.53135i	0.245747	+	0.338242i	0.914016	−	0.405678i	$-0.132964\pi$
$109$	2.56568	+	3.53135i	0.245747	+	0.338242i	−0.668269	+	0.743920i	$0.732964\pi$
$110$		0			0
$111$	9.27664	+	6.73988i	0.880500	+	0.639721i
$112$		0			0
$113$	−0.895884	−	1.23308i	−0.0842776	−	0.115998i	0.764796	−	0.644272i	$-0.222839\pi$
$113$	−0.895884	−	1.23308i	−0.0842776	−	0.115998i	−0.849074	+	0.528274i	$0.822839\pi$
$114$		0			0
$115$	0.839373	+	1.24103i	0.0782719	+	0.115727i
$116$		0			0
$117$	−12.6093	+	38.8073i	−1.16573	+	3.58774i
$118$		0			0
$119$	1.41615	−	4.35845i	0.129818	−	0.399538i
$120$		0			0
$121$	1.76343	+	5.42728i	0.160312	+	0.493389i
$122$		0			0
$123$	19.5253	+	14.1859i	1.76053	+	1.27910i
$124$		0			0
$125$	9.66116	−	5.62690i	0.864120	−	0.503285i
$126$		0			0
$127$	9.99210	−	13.7529i	0.886655	−	1.22038i	−0.0878777	−	0.996131i	$-0.528008\pi$
$127$	9.99210	−	13.7529i	0.886655	−	1.22038i	0.974533	−	0.224245i	$-0.0719915\pi$
$128$		0			0
$129$	3.64361	+	11.2139i	0.320802	+	0.987328i
$130$		0			0
$131$	5.71604	+	1.85725i	0.499413	+	0.162269i	0.547882	−	0.836556i	$-0.315434\pi$
$131$	5.71604	+	1.85725i	0.499413	+	0.162269i	−0.0484693	+	0.998825i	$0.515434\pi$
$132$		0			0
$133$	−3.05962	+	9.41655i	−0.265303	+	0.816519i
$134$		0			0
$135$	22.4885	−	15.2101i	1.93550	−	1.30908i
$136$		0			0
$137$	−2.43382	−	3.34986i	−0.207935	−	0.286198i	0.692293	−	0.721616i	$-0.256600\pi$
$137$	−2.43382	−	3.34986i	−0.207935	−	0.286198i	−0.900228	+	0.435418i	$0.856600\pi$
$138$		0			0
$139$	−5.91784	+	8.14520i	−0.501944	+	0.690867i	−0.982535	−	0.186078i	$-0.940422\pi$
$139$	−5.91784	+	8.14520i	−0.501944	+	0.690867i	0.480591	+	0.876945i	$0.340422\pi$
$140$		0			0
$141$	−16.5386	−	22.7635i	−1.39280	−	1.91703i
$142$		0			0
$143$			13.6741i			1.14349i
$144$		0			0
$145$	0.0969343	−	2.88038i	0.00804996	−	0.239202i
$146$		0			0
$147$	3.92948	+	12.0937i	0.324098	+	0.997472i
$148$		0			0
$149$			13.6951i			1.12195i	0.827834	+	0.560973i	$0.189573\pi$
$149$			13.6951i			1.12195i	−0.827834	+	0.560973i	$0.810427\pi$
$150$		0			0
$151$	12.0927			0.984088			0.492044	−	0.870570i	$-0.336250\pi$
$151$	12.0927			0.984088			0.492044	+	0.870570i	$0.336250\pi$
$152$		0			0
$153$	17.4175	−	5.65928i	1.40812	−	0.457525i
$154$		0			0
$155$	−2.07149	−	1.61420i	−0.166386	−	0.129656i
$156$		0			0
$157$	12.6051			1.00599			0.502997	−	0.864288i	$-0.332231\pi$
$157$	12.6051			1.00599			0.502997	+	0.864288i	$0.332231\pi$
$158$		0			0
$159$	−8.97273	+	6.51907i	−0.711584	+	0.516996i
$160$		0			0
$161$	0.931268	+	0.676606i	0.0733942	+	0.0533240i
$162$		0			0
$163$	−9.55541	+	6.94241i	−0.748438	+	0.543772i	−0.895342	−	0.445379i	$-0.853069\pi$
$163$	−9.55541	+	6.94241i	−0.748438	+	0.543772i	0.146904	+	0.989151i	$0.453069\pi$
$164$		0			0
$165$	9.93233	−	12.7460i	0.773231	−	0.992277i
$166$		0			0
$167$	−10.4420	−	3.39280i	−0.808023	−	0.262543i	−0.124263	−	0.992249i	$-0.539657\pi$
$167$	−10.4420	−	3.39280i	−0.808023	−	0.262543i	−0.683760	+	0.729707i	$0.739657\pi$
$168$		0			0
$169$	6.89835	−	21.2309i	0.530642	−	1.63315i
$170$		0			0
$171$	−37.6309	+	12.2270i	−2.87771	+	0.935024i
$172$		0			0
$173$	12.2681	+	8.91328i	0.932725	+	0.677664i	0.946659	−	0.322238i	$-0.104435\pi$
$173$	12.2681	+	8.91328i	0.932725	+	0.677664i	−0.0139334	+	0.999903i	$0.504435\pi$
$174$		0			0
$175$	5.50486	−	6.59427i	0.416128	−	0.498480i
$176$		0			0
$177$	11.2490	−	15.4829i	0.845527	−	1.16377i
$178$		0			0
$179$	20.5530	−	6.67808i	1.53620	−	0.499143i	0.585878	−	0.810399i	$-0.300750\pi$
$179$	20.5530	−	6.67808i	1.53620	−	0.499143i	0.950326	+	0.311256i	$0.100750\pi$
$180$		0			0
$181$	−8.26366	−	2.68502i	−0.614233	−	0.199576i	−0.0146547	−	0.999893i	$-0.504665\pi$
$181$	−8.26366	−	2.68502i	−0.614233	−	0.199576i	−0.599578	+	0.800316i	$0.704665\pi$
$182$		0			0
$183$	2.75524	+	0.895233i	0.203673	+	0.0661775i
$184$		0			0
$185$	2.26000	+	7.84406i	0.166158	+	0.576707i
$186$		0			0
$187$	4.96511	−	3.60736i	0.363085	−	0.263796i
$188$		0			0
$189$	12.2607	−	16.8753i	0.891831	−	1.22750i
$190$		0			0
$191$	−0.689197	+	0.500731i	−0.0498686	+	0.0362316i	−0.612440	−	0.790517i	$-0.709812\pi$
$191$	−0.689197	+	0.500731i	−0.0498686	+	0.0362316i	0.562572	+	0.826748i	$0.309812\pi$
$192$		0			0
$193$			10.7404i			0.773113i	0.922266	+	0.386557i	$0.126336\pi$
$193$			10.7404i			0.773113i	−0.922266	+	0.386557i	$0.873664\pi$
$194$		0			0
$195$	−34.5765	+	23.3859i	−2.47607	+	1.67470i
$196$		0			0
$197$	−6.98882	−	21.5094i	−0.497933	−	1.53248i	−0.812336	−	0.583190i	$-0.801804\pi$
$197$	−6.98882	−	21.5094i	−0.497933	−	1.53248i	0.314403	−	0.949290i	$-0.398196\pi$
$198$		0			0
$199$	−0.706769			−0.0501015			−0.0250508	−	0.999686i	$-0.507975\pi$
$199$	−0.706769			−0.0501015			−0.0250508	+	0.999686i	$0.507975\pi$
$200$		0			0
$201$	−48.1879			−3.39891
$202$		0			0
$203$	−0.684250	−	2.10590i	−0.0480249	−	0.147806i
$204$		0			0
$205$	4.75679	+	16.5100i	0.332229	+	1.15311i
$206$		0			0
$207$			4.60013i			0.319731i
$208$		0			0
$209$	−10.7273	+	7.79381i	−0.742020	+	0.539109i
$210$		0			0
$211$	10.7903	−	14.8516i	0.742834	−	1.02242i	−0.255616	−	0.966778i	$-0.582278\pi$
$211$	10.7903	−	14.8516i	0.742834	−	1.02242i	0.998451	−	0.0556452i	$-0.0177216\pi$
$212$		0			0
$213$	15.8445	−	11.5117i	1.08565	−	0.788770i
$214$		0			0
$215$	−2.86096	+	7.89150i	−0.195116	+	0.538196i
$216$		0			0
$217$	−1.91895	−	0.623506i	−0.130267	−	0.0423263i
$218$		0			0
$219$	15.9782	+	5.19164i	1.07971	+	0.350818i
$220$		0			0
$221$	−15.0779	+	4.89911i	−1.01425	+	0.329550i
$222$		0			0
$223$	4.51123	−	6.20918i	0.302094	−	0.415797i	−0.630801	−	0.775945i	$-0.717274\pi$
$223$	4.51123	−	6.20918i	0.302094	−	0.415797i	0.932895	+	0.360147i	$0.117274\pi$
$224$		0			0
$225$	34.2501	+	2.30788i	2.28334	+	0.153858i
$226$		0			0
$227$	−9.47829	−	6.88638i	−0.629096	−	0.457065i	0.226991	−	0.973897i	$-0.427111\pi$
$227$	−9.47829	−	6.88638i	−0.629096	−	0.457065i	−0.856087	+	0.516832i	$0.827111\pi$
$228$		0			0
$229$	25.6372	−	8.33003i	1.69415	−	0.550464i	0.706582	−	0.707631i	$-0.250236\pi$
$229$	25.6372	−	8.33003i	1.69415	−	0.550464i	0.987572	+	0.157167i	$0.0502361\pi$
$230$		0			0
$231$	3.83649	−	11.8075i	0.252422	−	0.776876i
$232$		0			0
$233$	13.2560	+	4.30712i	0.868426	+	0.282169i	0.709144	−	0.705064i	$-0.249082\pi$
$233$	13.2560	+	4.30712i	0.868426	+	0.282169i	0.159283	+	0.987233i	$0.449082\pi$
$234$		0			0
$235$	0.673733	−	20.0198i	0.0439495	−	1.30595i
$236$		0			0
$237$	−1.03305	+	0.750558i	−0.0671041	+	0.0487540i
$238$		0			0
$239$	−7.73830	−	5.62220i	−0.500549	−	0.363670i	0.308678	−	0.951167i	$-0.400114\pi$
$239$	−7.73830	−	5.62220i	−0.500549	−	0.363670i	−0.809227	+	0.587497i	$0.800114\pi$
$240$		0			0
$241$	20.3460	−	14.7823i	1.31060	−	0.952210i	0.310606	−	0.950539i	$-0.399468\pi$
$241$	20.3460	−	14.7823i	1.31060	−	0.952210i	0.999999	−	0.00167085i	$-0.000531849\pi$
$242$		0			0
$243$	18.6651			1.19737
$244$		0			0
$245$	−3.08543	+	8.51066i	−0.197121	+	0.543726i
$246$		0			0
$247$	32.5763	−	10.5847i	2.07278	−	0.673486i
$248$		0			0
$249$	3.62757			0.229888
$250$		0			0
$251$			6.91776i			0.436645i	0.975877	+	0.218323i	$0.0700585\pi$
$251$			6.91776i			0.436645i	−0.975877	+	0.218323i	$0.929941\pi$
$252$		0			0
$253$	0.476370	+	1.46612i	0.0299492	+	0.0921740i
$254$		0			0
$255$	17.6130	+	6.38538i	1.10297	+	0.399868i
$256$		0			0
$257$		−	29.8090i		−	1.85943i	−0.368277	−	0.929716i	$-0.620052\pi$
$257$		−	29.8090i		−	1.85943i	0.368277	−	0.929716i	$-0.379948\pi$
$258$		0			0
$259$	3.68650	+	5.07403i	0.229068	+	0.315285i
$260$		0			0
$261$	5.20121	−	7.15885i	0.321947	−	0.443122i
$262$		0			0
$263$	15.5573	+	21.4128i	0.959304	+	1.32037i	0.947269	+	0.320441i	$0.103831\pi$
$263$	15.5573	+	21.4128i	0.959304	+	1.32037i	0.0120353	+	0.999928i	$0.496169\pi$
$264$		0			0
$265$	−7.89125	−	0.265567i	−0.484755	−	0.0163137i
$266$		0			0
$267$	−4.01813	+	12.3665i	−0.245906	+	0.756820i
$268$		0			0
$269$	7.64014	+	2.48243i	0.465827	+	0.151357i	0.532521	−	0.846417i	$-0.321245\pi$
$269$	7.64014	+	2.48243i	0.465827	+	0.151357i	−0.0666932	+	0.997774i	$0.521245\pi$
$270$		0			0
$271$	−2.87827	−	8.85842i	−0.174843	−	0.538111i	0.824784	−	0.565449i	$-0.191297\pi$
$271$	−2.87827	−	8.85842i	−0.174843	−	0.538111i	−0.999626	+	0.0273381i	$0.991297\pi$
$272$		0			0
$273$	−18.8510	+	25.9461i	−1.14091	+	1.57033i
$274$		0			0
$275$	11.1549	−	2.81125i	0.672667	−	0.169525i
$276$		0			0
$277$	−3.05174	−	2.21722i	−0.183361	−	0.133220i	0.492318	−	0.870415i	$-0.336150\pi$
$277$	−3.05174	−	2.21722i	−0.183361	−	0.133220i	−0.675679	+	0.737196i	$0.736150\pi$
$278$		0			0
$279$	−2.49169	−	7.66863i	−0.149173	−	0.459109i
$280$		0			0
$281$	−6.62409	+	20.3869i	−0.395160	+	1.21618i	0.533676	+	0.845689i	$0.320810\pi$
$281$	−6.62409	+	20.3869i	−0.395160	+	1.21618i	−0.928837	+	0.370489i	$0.879190\pi$
$282$		0			0
$283$	−0.286114	+	0.880568i	−0.0170077	+	0.0523443i	−0.959200	−	0.282728i	$-0.908761\pi$
$283$	−0.286114	+	0.880568i	−0.0170077	+	0.0523443i	0.942192	+	0.335072i	$0.108761\pi$
$284$		0			0
$285$	−38.0535	−	13.7958i	−2.25409	−	0.817193i
$286$		0			0
$287$	7.75925	+	10.6797i	0.458014	+	0.630402i
$288$		0			0
$289$	−7.99672	−	5.80996i	−0.470395	−	0.341762i
$290$		0			0
$291$	−28.0277	−	38.5769i	−1.64301	−	2.26142i
$292$		0			0
$293$	−13.3571			−0.780332			−0.390166	−	0.920744i	$-0.627582\pi$
$293$	−13.3571			−0.780332			−0.390166	+	0.920744i	$0.627582\pi$
$294$		0			0
$295$	13.0919	−	3.77199i	0.762241	−	0.219614i
$296$		0			0
$297$	26.5673	−	8.63223i	1.54159	−	0.500893i
$298$		0			0
$299$		−	3.98223i		−	0.230298i
$300$		0			0
$301$			6.44929i			0.371731i
$302$		0			0
$303$	−41.0815	+	13.3482i	−2.36007	+	0.766833i
$304$		0			0
$305$	1.15546	+	1.70837i	0.0661612	+	0.0978207i
$306$		0			0
$307$	14.1781			0.809186			0.404593	−	0.914497i	$-0.367413\pi$
$307$	14.1781			0.809186			0.404593	+	0.914497i	$0.367413\pi$
$308$		0			0
$309$	−16.1668	−	22.2516i	−0.919695	−	1.26585i
$310$		0			0
$311$	−0.386936	−	0.281125i	−0.0219411	−	0.0159412i	0.576761	−	0.816913i	$-0.304317\pi$
$311$	−0.386936	−	0.281125i	−0.0219411	−	0.0159412i	−0.598702	+	0.800972i	$0.704317\pi$
$312$		0			0
$313$	−6.67701	−	9.19012i	−0.377407	−	0.519456i	0.577488	−	0.816399i	$-0.304033\pi$
$313$	−6.67701	−	9.19012i	−0.377407	−	0.519456i	−0.954895	+	0.296943i	$0.904033\pi$
$314$		0			0
$315$	25.3435	−	7.30187i	1.42794	−	0.411414i
$316$		0			0
$317$	−4.27173	+	13.1470i	−0.239924	+	0.738411i	0.756505	+	0.653987i	$0.226905\pi$
$317$	−4.27173	+	13.1470i	−0.239924	+	0.738411i	−0.996430	+	0.0844241i	$0.973095\pi$
$318$		0			0
$319$	0.916348	−	2.82023i	0.0513056	−	0.157902i
$320$		0			0
$321$	3.39081	+	10.4358i	0.189257	+	0.582472i
$322$		0			0
$323$	−12.4372	−	9.03618i	−0.692026	−	0.502786i
$324$		0			0
$325$	−29.6496	−	1.99788i	−1.64466	−	0.110822i
$326$		0			0
$327$	−8.05866	+	11.0918i	−0.445645	+	0.613378i
$328$		0			0
$329$	−4.75581	−	14.6369i	−0.262197	−	0.806958i
$330$		0			0
$331$	6.42804	+	2.08860i	0.353317	+	0.114800i	0.480298	−	0.877105i	$-0.340529\pi$
$331$	6.42804	+	2.08860i	0.353317	+	0.114800i	−0.126981	+	0.991905i	$0.540529\pi$
$332$		0			0
$333$	−7.74516	+	23.8372i	−0.424432	+	1.30627i
$334$		0			0
$335$	−27.0597	−	21.0863i	−1.47843	−	1.15207i
$336$		0			0
$337$	−9.77379	−	13.4525i	−0.532412	−	0.732803i	0.455083	−	0.890449i	$-0.349609\pi$
$337$	−9.77379	−	13.4525i	−0.532412	−	0.732803i	−0.987496	+	0.157646i	$0.949609\pi$
$338$		0			0
$339$	2.81392	−	3.87303i	0.152831	−	0.210354i
$340$		0			0
$341$	−1.58826	−	2.18606i	−0.0860093	−	0.118382i
$342$		0			0
$343$			18.9813i			1.02489i
$344$		0			0
$345$	−2.89253	+	3.71194i	−0.155728	+	0.199844i
$346$		0			0
$347$	−0.155098	−	0.477342i	−0.00832608	−	0.0256250i	0.946807	−	0.321801i	$-0.104288\pi$
$347$	−0.155098	−	0.477342i	−0.00832608	−	0.0256250i	−0.955133	+	0.296176i	$0.904288\pi$
$348$		0			0
$349$			1.38740i			0.0742660i	0.999310	+	0.0371330i	$0.0118225\pi$
$349$			1.38740i			0.0742660i	−0.999310	+	0.0371330i	$0.988177\pi$
$350$		0			0
$351$	−72.1613			−3.85169
$352$		0			0
$353$	−27.1323	+	8.81582i	−1.44411	+	0.469218i	−0.923175	−	0.384380i	$-0.874415\pi$
$353$	−27.1323	+	8.81582i	−1.44411	+	0.469218i	−0.520931	+	0.853599i	$0.674415\pi$
$354$		0			0
$355$	13.9348	+	0.468952i	0.739582	+	0.0248894i
$356$		0			0
$357$	14.3942			0.761820
$358$		0			0
$359$	18.7073	−	13.5917i	0.987336	−	0.717342i	0.0279998	−	0.999608i	$-0.491086\pi$
$359$	18.7073	−	13.5917i	0.987336	−	0.717342i	0.959336	+	0.282266i	$0.0910862\pi$
$360$		0			0
$361$	11.4997	+	8.35500i	0.605246	+	0.439737i
$362$		0			0
$363$	−14.5009	+	10.5355i	−0.761099	+	0.552971i
$364$		0			0
$365$	6.70073	+	9.90716i	0.350732	+	0.518565i
$366$		0			0
$367$	−26.8195	−	8.71417i	−1.39996	−	0.454876i	−0.490785	−	0.871281i	$-0.663290\pi$
$367$	−26.8195	−	8.71417i	−1.39996	−	0.454876i	−0.909179	+	0.416405i	$0.863290\pi$
$368$		0			0
$369$	−16.3018	+	50.1719i	−0.848640	+	2.61184i
$370$		0			0
$371$	−5.76946	+	1.87461i	−0.299535	+	0.0973250i
$372$		0			0
$373$	−14.5528	−	10.5732i	−0.753515	−	0.547461i	0.143399	−	0.989665i	$-0.454197\pi$
$373$	−14.5528	−	10.5732i	−0.753515	−	0.547461i	−0.896914	+	0.442204i	$0.854197\pi$
$374$		0			0
$375$	26.1860	+	23.3985i	1.35224	+	1.20829i
$376$		0			0
$377$	−4.50257	+	6.19726i	−0.231894	+	0.319175i
$378$		0			0
$379$	−5.18753	+	1.68553i	−0.266466	+	0.0865799i	−0.439203	−	0.898388i	$-0.644739\pi$
$379$	−5.18753	+	1.68553i	−0.266466	+	0.0865799i	0.172737	+	0.984968i	$0.444739\pi$
$380$		0			0
$381$	50.7814	+	16.4999i	2.60161	+	0.845315i
$382$		0			0
$383$	13.2382	+	4.30135i	0.676440	+	0.219789i	0.627036	−	0.778990i	$-0.284268\pi$
$383$	13.2382	+	4.30135i	0.676440	+	0.219789i	0.0494042	+	0.998779i	$0.484268\pi$
$384$		0			0
$385$	7.32114	−	4.95166i	0.373120	−	0.252360i
$386$		0			0
$387$	−20.8508	+	15.1490i	−1.05990	+	0.770066i
$388$		0			0
$389$	21.7230	−	29.8991i	1.10140	−	1.51594i	0.267880	−	0.963452i	$-0.413677\pi$
$389$	21.7230	−	29.8991i	1.10140	−	1.51594i	0.833518	−	0.552492i	$-0.186323\pi$
$390$		0			0
$391$	−1.44596	+	1.05055i	−0.0731251	+	0.0531285i
$392$		0			0
$393$			18.8777i			0.952255i
$394$		0			0
$395$	−0.908540	−	0.0305754i	−0.0457136	−	0.00153842i
$396$		0			0
$397$	7.32490	+	22.5437i	0.367626	+	1.13144i	0.948320	+	0.317315i	$0.102781\pi$
$397$	7.32490	+	22.5437i	0.367626	+	1.13144i	−0.580694	+	0.814122i	$0.697219\pi$
$398$		0			0
$399$	−31.0990			−1.55690
$400$		0			0
$401$	−0.881338			−0.0440119			−0.0220060	−	0.999758i	$-0.507005\pi$
$401$	−0.881338			−0.0440119			−0.0220060	+	0.999758i	$0.507005\pi$
$402$		0			0
$403$	2.15700	+	6.63856i	0.107448	+	0.330690i
$404$		0			0
$405$	30.9354	+	24.1063i	1.53719	+	1.19785i
$406$		0			0
$407$			8.39925i			0.416335i
$408$		0			0
$409$	28.9714	−	21.0489i	1.43254	−	1.04080i	0.443005	−	0.896519i	$-0.353912\pi$
$409$	28.9714	−	21.0489i	1.43254	−	1.04080i	0.989536	−	0.144283i	$-0.0460876\pi$
$410$		0			0
$411$	7.64449	−	10.5217i	0.377075	−	0.518999i
$412$		0			0
$413$	8.46866	−	6.15285i	0.416716	−	0.302762i
$414$		0			0
$415$	2.03705	+	1.58737i	0.0999949	+	0.0779209i
$416$		0			0
$417$	−30.0754	−	9.77209i	−1.47280	−	0.478541i
$418$		0			0
$419$	−18.1069	−	5.88329i	−0.884581	−	0.287418i	−0.168723	−	0.985664i	$-0.553964\pi$
$419$	−18.1069	−	5.88329i	−0.884581	−	0.287418i	−0.715858	+	0.698246i	$0.753964\pi$
$420$		0			0
$421$	−8.42477	+	2.73737i	−0.410598	+	0.133411i	−0.507031	−	0.861928i	$-0.669257\pi$
$421$	−8.42477	+	2.73737i	−0.410598	+	0.133411i	0.0964323	+	0.995340i	$0.469257\pi$
$422$		0			0
$423$	36.1505	−	49.7569i	1.75770	−	2.41926i
$424$		0			0
$425$	7.09639	+	11.2929i	0.344225	+	0.547785i
$426$		0			0
$427$	1.28196	+	0.931395i	0.0620382	+	0.0450734i
$428$		0			0
$429$	−40.8476	+	13.2722i	−1.97214	+	0.640788i
$430$		0			0
$431$	−0.956566	+	2.94401i	−0.0460762	+	0.141808i	−0.971448	−	0.237253i	$-0.923753\pi$
$431$	−0.956566	+	2.94401i	−0.0460762	+	0.141808i	0.925372	+	0.379061i	$0.123753\pi$
$432$		0			0
$433$	8.67407	+	2.81837i	0.416849	+	0.135442i	0.509930	−	0.860216i	$-0.329671\pi$
$433$	8.67407	+	2.81837i	0.416849	+	0.135442i	−0.0930806	+	0.995659i	$0.529671\pi$
$434$		0			0
$435$	8.69840	−	2.50615i	0.417056	−	0.120161i
$436$		0			0
$437$	3.12403	−	2.26974i	0.149443	−	0.108576i
$438$		0			0
$439$	−31.0958	−	22.5924i	−1.48412	−	1.07828i	−0.976200	−	0.216872i	$-0.930415\pi$
$439$	−31.0958	−	22.5924i	−1.48412	−	1.07828i	−0.507920	−	0.861404i	$-0.669585\pi$
$440$		0			0
$441$	−22.4867	+	16.3375i	−1.07080	+	0.777978i
$442$		0			0
$443$	−33.8214			−1.60690			−0.803451	−	0.595371i	$-0.797005\pi$
$443$	−33.8214			−1.60690			−0.803451	+	0.595371i	$0.797005\pi$
$444$		0			0
$445$	−7.66777	+	5.18611i	−0.363487	+	0.245845i
$446$		0			0
$447$	−40.9102	+	13.2925i	−1.93499	+	0.628715i
$448$		0			0
$449$	11.7494			0.554489			0.277245	−	0.960799i	$-0.410579\pi$
$449$	11.7494			0.554489			0.277245	+	0.960799i	$0.410579\pi$
$450$		0			0
$451$			17.6785i			0.832450i
$452$		0			0
$453$	11.7372	+	36.1235i	0.551463	+	1.69723i
$454$		0			0
$455$	−21.9393	+	6.32107i	−1.02853	+	0.296336i
$456$		0			0
$457$			12.5132i			0.585342i	0.956213	+	0.292671i	$0.0945441\pi$
$457$			12.5132i			0.585342i	−0.956213	+	0.292671i	$0.905456\pi$
$458$		0			0
$459$	19.0368	+	26.2019i	0.888562	+	1.22300i
$460$		0			0
$461$	−7.24736	+	9.97513i	−0.337543	+	0.464588i	−0.943722	−	0.330740i	$-0.892702\pi$
$461$	−7.24736	+	9.97513i	−0.337543	+	0.464588i	0.606179	+	0.795328i	$0.292702\pi$
$462$		0			0
$463$	9.71829	+	13.3761i	0.451647	+	0.621639i	0.972751	−	0.231854i	$-0.0744793\pi$
$463$	9.71829	+	13.3761i	0.451647	+	0.621639i	−0.521103	+	0.853494i	$0.674479\pi$
$464$		0			0
$465$	2.81138	−	7.75474i	0.130375	−	0.359617i
$466$		0			0
$467$	−4.96826	+	15.2907i	−0.229904	+	0.707571i	0.767853	+	0.640626i	$0.221325\pi$
$467$	−4.96826	+	15.2907i	−0.229904	+	0.707571i	−0.997757	+	0.0669450i	$0.978675\pi$
$468$		0			0
$469$	−25.0672	−	8.14484i	−1.15750	−	0.376094i
$470$		0			0
$471$	12.2346	+	37.6541i	0.563739	+	1.73501i
$472$		0			0
$473$	−5.07663	+	6.98739i	−0.233424	+	0.321280i
$474$		0			0
$475$	−15.3320	−	24.3986i	−0.703478	−	1.11948i
$476$		0			0
$477$	−19.6128	−	14.2495i	−0.898008	−	0.652441i
$478$		0			0
$479$	6.65413	+	20.4793i	0.304035	+	0.935723i	0.980036	+	0.198822i	$0.0637116\pi$
$479$	6.65413	+	20.4793i	0.304035	+	0.935723i	−0.676001	+	0.736901i	$0.736288\pi$
$480$		0			0
$481$	6.70481	−	20.6353i	0.305713	−	0.940889i
$482$		0			0
$483$	−1.11727	+	3.43862i	−0.0508378	+	0.156463i
$484$		0			0
$485$	1.14176	−	33.9272i	0.0518448	−	1.54055i
$486$		0			0
$487$	−15.7256	−	21.6444i	−0.712593	−	0.980800i	−0.999737	−	0.0229129i	$-0.992706\pi$
$487$	−15.7256	−	21.6444i	−0.712593	−	0.980800i	0.287144	−	0.957887i	$-0.407294\pi$
$488$		0			0
$489$	−30.0131	−	21.8058i	−1.35724	−	0.986091i
$490$		0			0
$491$	−0.191575	−	0.263680i	−0.00864564	−	0.0118997i	0.804672	−	0.593719i	$-0.202341\pi$
$491$	−0.191575	−	0.263680i	−0.00864564	−	0.0118997i	−0.813318	+	0.581820i	$0.802341\pi$
$492$		0			0
$493$	3.43806			0.154842
$494$		0			0
$495$	33.2058	+	12.0383i	1.49249	+	0.541083i
$496$		0			0
$497$	10.1880	−	3.31029i	0.456995	−	0.148487i
$498$		0			0
$499$		−	23.2206i		−	1.03950i	−0.854320	−	0.519748i	$-0.826026\pi$
$499$		−	23.2206i		−	1.03950i	0.854320	−	0.519748i	$-0.173974\pi$
$500$		0			0
$501$		−	34.4855i		−	1.54070i
$502$		0			0
$503$	8.85545	−	2.87731i	0.394845	−	0.128293i	−0.104863	−	0.994487i	$-0.533441\pi$
$503$	8.85545	−	2.87731i	0.394845	−	0.128293i	0.499708	+	0.866194i	$0.333441\pi$
$504$		0			0
$505$	−28.9101	−	10.4810i	−1.28648	−	0.466398i
$506$		0			0
$507$	70.1170			3.11401
$508$		0			0
$509$	11.8276	+	16.2793i	0.524249	+	0.721567i	0.986240	−	0.165318i	$-0.0528650\pi$
$509$	11.8276	+	16.2793i	0.524249	+	0.721567i	−0.461992	+	0.886884i	$0.652865\pi$
$510$		0			0
$511$	7.43433	+	5.40135i	0.328875	+	0.238942i
$512$		0			0
$513$	−41.1296	−	56.6100i	−1.81592	−	2.49939i
$514$		0			0
$515$	0.658584	−	19.5696i	0.0290207	−	0.862341i
$516$		0			0
$517$	6.36899	−	19.6017i	0.280108	−	0.862083i
$518$		0			0
$519$	−14.7185	+	45.2987i	−0.646068	+	1.98839i
$520$		0			0
$521$	5.18227	+	15.9494i	0.227039	+	0.698755i	0.998078	+	0.0619670i	$0.0197373\pi$
$521$	5.18227	+	15.9494i	0.227039	+	0.698755i	−0.771039	+	0.636788i	$0.780263\pi$
$522$		0			0
$523$	−0.0366350	−	0.0266169i	−0.00160194	−	0.00116388i	0.586984	−	0.809599i	$-0.300315\pi$
$523$	−0.0366350	−	0.0266169i	−0.00160194	−	0.00116388i	−0.588586	+	0.808435i	$0.700315\pi$
$524$		0			0
$525$	25.0416	+	10.0438i	1.09290	+	0.438347i
$526$		0			0
$527$	1.84144	−	2.53452i	0.0802144	−	0.110406i
$528$		0			0
$529$	6.96866	+	21.4473i	0.302985	+	0.932493i
$530$		0			0
$531$	39.7848	+	12.9268i	1.72651	+	0.560978i
$532$		0			0
$533$	14.1121	−	43.4327i	0.611265	−	1.88128i
$534$		0			0
$535$	−2.66246	+	7.34397i	−0.115108	+	0.317508i
$536$		0			0
$537$	39.8978	+	54.9146i	1.72172	+	2.36974i
$538$		0			0
$539$	−5.47494	+	7.53561i	−0.235822	+	0.324582i
$540$		0			0
$541$	−10.3777	−	14.2837i	−0.446173	−	0.614104i	0.525397	−	0.850857i	$-0.323917\pi$
$541$	−10.3777	−	14.2837i	−0.446173	−	0.614104i	−0.971570	+	0.236753i	$0.923917\pi$
$542$		0			0
$543$		−	27.2915i		−	1.17119i
$544$		0			0
$545$	−9.37891	+	2.70221i	−0.401748	+	0.115750i
$546$		0			0
$547$	−10.9369	−	33.6604i	−0.467630	−	1.43922i	−0.855645	−	0.517563i	$-0.826839\pi$
$547$	−10.9369	−	33.6604i	−0.467630	−	1.43922i	0.388015	−	0.921653i	$-0.373161\pi$
$548$		0			0
$549$			6.33240i			0.270260i
$550$		0			0
$551$	−7.42802			−0.316444
$552$		0			0
$553$	−0.664253	+	0.215829i	−0.0282469	+	0.00917798i
$554$		0			0
$555$	−21.2384	+	14.3646i	−0.901518	+	0.609744i
$556$		0			0
$557$	−27.7529			−1.17593			−0.587964	−	0.808887i	$-0.700070\pi$
$557$	−27.7529			−1.17593			−0.587964	+	0.808887i	$0.700070\pi$
$558$		0			0
$559$	18.0501	−	13.1141i	0.763436	−	0.554669i
$560$		0			0
$561$	15.5951	+	11.3305i	0.658428	+	0.478376i
$562$		0			0
$563$	23.5565	−	17.1148i	0.992788	−	0.721303i	0.0322580	−	0.999480i	$-0.489730\pi$
$563$	23.5565	−	17.1148i	0.992788	−	0.721303i	0.960530	+	0.278177i	$0.0897302\pi$
$564$		0			0
$565$	3.27493	−	0.943558i	0.137777	−	0.0396958i
$566$		0			0
$567$	28.6575	+	9.31138i	1.20350	+	0.391041i
$568$		0			0
$569$	5.68191	−	17.4871i	0.238198	−	0.733098i	−0.758483	−	0.651693i	$-0.774059\pi$
$569$	5.68191	−	17.4871i	0.238198	−	0.733098i	0.996681	−	0.0814052i	$-0.0259408\pi$
$570$		0			0
$571$	−20.4740	+	6.65241i	−0.856811	+	0.278395i	−0.704296	−	0.709906i	$-0.748737\pi$
$571$	−20.4740	+	6.65241i	−0.856811	+	0.278395i	−0.152515	+	0.988301i	$0.548737\pi$
$572$		0			0
$573$	−2.16473	−	1.57277i	−0.0904330	−	0.0657034i
$574$		0			0
$575$	−3.24857	+	0.818702i	−0.135475	+	0.0341422i
$576$		0			0
$577$	1.65018	−	2.27128i	0.0686978	−	0.0945545i	−0.773285	−	0.634058i	$-0.781388\pi$
$577$	1.65018	−	2.27128i	0.0686978	−	0.0945545i	0.841983	+	0.539504i	$0.181388\pi$
$578$		0			0
$579$	−32.0840	+	10.4247i	−1.33337	+	0.433237i
$580$		0			0
$581$	1.88705	+	0.613141i	0.0782882	+	0.0254374i
$582$		0			0
$583$	−7.72646	−	2.51048i	−0.319997	−	0.103973i
$584$		0			0
$585$	−71.9704	−	56.0828i	−2.97561	−	2.31874i
$586$		0			0
$587$	9.41724	−	6.84202i	0.388691	−	0.282401i	−0.376228	−	0.926527i	$-0.622779\pi$
$587$	9.41724	−	6.84202i	0.388691	−	0.282401i	0.764919	+	0.644127i	$0.222779\pi$
$588$		0			0
$589$	−3.97848	+	5.47591i	−0.163931	+	0.225631i
$590$		0			0
$591$	57.4698	−	41.7543i	2.36399	−	1.71754i
$592$		0			0
$593$			12.6560i			0.519720i	0.965646	+	0.259860i	$0.0836765\pi$
$593$			12.6560i			0.519720i	−0.965646	+	0.259860i	$0.916324\pi$
$594$		0			0
$595$	8.08298	+	6.29866i	0.331370	+	0.258220i
$596$		0			0
$597$	−0.685994	−	2.11127i	−0.0280759	−	0.0864087i
$598$		0			0
$599$	20.9771			0.857101			0.428550	−	0.903518i	$-0.359024\pi$
$599$	20.9771			0.857101			0.428550	+	0.903518i	$0.359024\pi$
$600$		0			0
$601$	23.0207			0.939032			0.469516	−	0.882924i	$-0.344428\pi$
$601$	23.0207			0.939032			0.469516	+	0.882924i	$0.344428\pi$
$602$		0			0
$603$	−32.5488	−	100.175i	−1.32549	−	4.07944i
$604$		0			0
$605$	−12.7531	−	0.429184i	−0.518487	−	0.0174488i
$606$		0			0
$607$		−	26.0419i		−	1.05701i	−0.848931	−	0.528504i	$-0.822753\pi$
$607$		−	26.0419i		−	1.05701i	0.848931	−	0.528504i	$-0.177247\pi$
$608$		0			0
$609$	5.62666	−	4.08801i	0.228004	−	0.165654i
$610$		0			0
$611$	−31.2947	+	43.0734i	−1.26605	+	1.74257i
$612$		0			0
$613$	−13.6825	+	9.94089i	−0.552629	+	0.401509i	−0.828754	−	0.559613i	$-0.810950\pi$
$613$	−13.6825	+	9.94089i	−0.552629	+	0.401509i	0.276125	+	0.961122i	$0.410950\pi$
$614$		0			0
$615$	−44.7020	+	30.2343i	−1.80256	+	1.21916i
$616$		0			0
$617$	5.20768	+	1.69208i	0.209653	+	0.0681205i	0.411961	−	0.911202i	$-0.364844\pi$
$617$	5.20768	+	1.69208i	0.209653	+	0.0681205i	−0.202308	+	0.979322i	$0.564844\pi$
$618$		0			0
$619$	−15.1429	−	4.92021i	−0.608643	−	0.197760i	−0.0115514	−	0.999933i	$-0.503677\pi$
$619$	−15.1429	−	4.92021i	−0.608643	−	0.197760i	−0.597091	+	0.802173i	$0.703677\pi$
$620$		0			0
$621$	−7.73701	+	2.51391i	−0.310476	+	0.100880i
$622$		0			0
$623$	−4.18044	+	5.75389i	−0.167486	+	0.230525i
$624$		0			0
$625$	4.46582	+	24.5979i	0.178633	+	0.983916i
$626$		0			0
$627$	−33.6938	−	24.4799i	−1.34560	−	0.977635i
$628$		0			0
$629$	−9.26151	+	3.00925i	−0.369281	+	0.119987i
$630$		0			0
$631$	15.0147	−	46.2106i	0.597727	−	1.83961i	0.0570726	−	0.998370i	$-0.481823\pi$
$631$	15.0147	−	46.2106i	0.597727	−	1.83961i	0.540654	−	0.841245i	$-0.318177\pi$
$632$		0			0
$633$	54.8380	+	17.8179i	2.17961	+	0.708200i
$634$		0			0
$635$	21.2960	+	31.4866i	0.845107	+	1.24951i
$636$		0			0
$637$	19.4662	−	14.1431i	0.771280	−	0.560368i
$638$		0			0
$639$	34.6333	+	25.1626i	1.37007	+	0.995417i
$640$		0			0
$641$	15.1755	−	11.0256i	0.599396	−	0.435486i	−0.246269	−	0.969202i	$-0.579205\pi$
$641$	15.1755	−	11.0256i	0.599396	−	0.435486i	0.845664	+	0.533715i	$0.179205\pi$
$642$		0			0
$643$	37.8673			1.49334			0.746669	−	0.665195i	$-0.231652\pi$
$643$	37.8673			1.49334			0.746669	+	0.665195i	$0.231652\pi$
$644$		0			0
$645$	−26.3505	−	0.886783i	−1.03755	−	0.0349171i
$646$		0			0
$647$	37.5073	−	12.1869i	1.47456	−	0.479115i	0.542080	−	0.840327i	$-0.317637\pi$
$647$	37.5073	−	12.1869i	1.47456	−	0.479115i	0.932484	+	0.361212i	$0.117637\pi$
$648$		0			0
$649$	14.0185			0.550276
$650$		0			0
$651$		−	6.33752i		−	0.248387i
$652$		0			0
$653$	−6.71891	−	20.6787i	−0.262931	−	0.809219i	−0.992163	−	0.124952i	$-0.960122\pi$
$653$	−6.71891	−	20.6787i	−0.262931	−	0.809219i	0.729232	−	0.684267i	$-0.239878\pi$
$654$		0			0
$655$	−8.26059	+	10.6007i	−0.322768	+	0.414204i
$656$		0			0
$657$			36.7229i			1.43270i
$658$		0			0
$659$	−3.19947	−	4.40369i	−0.124634	−	0.171543i	0.742141	−	0.670244i	$-0.233811\pi$
$659$	−3.19947	−	4.40369i	−0.124634	−	0.171543i	−0.866774	+	0.498701i	$0.833811\pi$
$660$		0			0
$661$	26.8362	−	36.9368i	1.04381	−	1.43668i	0.149747	−	0.988724i	$-0.452154\pi$
$661$	26.8362	−	36.9368i	1.04381	−	1.43668i	0.894058	−	0.447951i	$-0.147846\pi$
$662$		0			0
$663$	−29.2694	−	40.2859i	−1.13673	−	1.56458i
$664$		0			0
$665$	−17.4635	−	13.6084i	−0.677206	−	0.527712i
$666$		0			0
$667$	−0.266862	+	0.821317i	−0.0103329	+	0.0318015i
$668$		0			0
$669$	22.9268	+	7.44937i	0.886402	+	0.288009i
$670$		0			0
$671$	0.655758	+	2.01821i	0.0253152	+	0.0779123i
$672$		0			0
$673$	25.2847	−	34.8014i	0.974654	−	1.34150i	0.0349929	−	0.999388i	$-0.488859\pi$
$673$	25.2847	−	34.8014i	0.974654	−	1.34150i	0.939661	−	0.342108i	$-0.111141\pi$
$674$		0			0
$675$	14.8356	+	58.8669i	0.571021	+	2.26579i
$676$		0			0
$677$	−37.8808	−	27.5220i	−1.45588	−	1.05776i	−0.984413	−	0.175873i	$-0.943725\pi$
$677$	−37.8808	−	27.5220i	−1.45588	−	1.05776i	−0.471466	−	0.881884i	$-0.656275\pi$
$678$		0			0
$679$	−8.05960	−	24.8049i	−0.309299	−	0.951924i
$680$		0			0
$681$	11.3714	−	34.9977i	0.435755	−	1.34111i
$682$		0			0
$683$	0.331130	−	1.01911i	0.0126703	−	0.0389953i	−0.944521	−	0.328450i	$-0.893474\pi$
$683$	0.331130	−	1.01911i	0.0126703	−	0.0389953i	0.957192	+	0.289454i	$0.0934739\pi$
$684$		0			0
$685$	8.89688	−	2.56333i	0.339932	−	0.0979399i
$686$		0			0
$687$	49.7673	+	68.4988i	1.89874	+	2.61339i
$688$		0			0
$689$	16.9784	+	12.3355i	0.646824	+	0.469945i
$690$		0			0
$691$	8.71658	+	11.9973i	0.331595	+	0.456401i	0.941963	−	0.335717i	$-0.108979\pi$
$691$	8.71658	+	11.9973i	0.331595	+	0.456401i	−0.610368	+	0.792118i	$0.708979\pi$
$692$		0			0
$693$	27.1373			1.03086
$694$		0			0
$695$	−12.6126	−	18.6480i	−0.478424	−	0.707359i
$696$		0			0
$697$	−19.4934	+	6.33379i	−0.738366	+	0.239910i
$698$		0			0
$699$			43.7790i			1.65587i
$700$		0			0
$701$		−	6.33651i		−	0.239327i	−0.992815	−	0.119663i	$-0.961818\pi$
$701$		−	6.33651i		−	0.239327i	0.992815	−	0.119663i	$-0.0381815\pi$
$702$		0			0
$703$	20.0098	−	6.50156i	0.754682	−	0.245211i
$704$		0			0
$705$	60.4574	−	17.4187i	2.27696	−	0.656027i
$706$		0			0
$707$	−23.6266			−0.888571
$708$		0			0
$709$	25.4810	+	35.0716i	0.956960	+	1.31714i	0.948366	+	0.317179i	$0.102736\pi$
$709$	25.4810	+	35.0716i	0.956960	+	1.31714i	0.00859395	+	0.999963i	$0.497264\pi$
$710$		0			0
$711$	−2.25807	−	1.64059i	−0.0846843	−	0.0615268i
$712$		0			0
$713$	0.462540	+	0.636631i	0.0173222	+	0.0238420i
$714$		0			0
$715$	−28.7455	−	10.4213i	−1.07502	−	0.389736i
$716$		0			0
$717$	9.28391	−	28.5729i	0.346714	−	1.06708i
$718$		0			0
$719$	−2.82195	+	8.68507i	−0.105241	+	0.323898i	−0.989787	−	0.142555i	$-0.954468\pi$
$719$	−2.82195	+	8.68507i	−0.105241	+	0.323898i	0.884546	+	0.466453i	$0.154468\pi$
$720$		0			0
$721$	−4.64888	−	14.3078i	−0.173133	−	0.532850i
$722$		0			0
$723$	63.9059	+	46.4303i	2.37669	+	1.72676i
$724$		0			0
$725$	5.98120	+	2.39896i	0.222136	+	0.0890953i
$726$		0			0
$727$	−24.3866	+	33.5653i	−0.904449	+	1.24487i	0.0645777	+	0.997913i	$0.479430\pi$
$727$	−24.3866	+	33.5653i	−0.904449	+	1.24487i	−0.969027	+	0.246955i	$0.920570\pi$
$728$		0			0
$729$	1.85677	+	5.71454i	0.0687691	+	0.211649i
$730$		0			0
$731$	−9.52354	−	3.09439i	−0.352241	−	0.114450i
$732$		0			0
$733$	−11.2254	+	34.5481i	−0.414619	+	1.27606i	0.497973	+	0.867193i	$0.334078\pi$
$733$	−11.2254	+	34.5481i	−0.414619	+	1.27606i	−0.912592	+	0.408872i	$0.865922\pi$
$734$		0			0
$735$	−28.4179	−	0.956359i	−1.04821	−	0.0352758i
$736$		0			0
$737$	−20.7474	−	28.5564i	−0.764241	−	1.05189i
$738$		0			0
$739$	−27.2866	+	37.5567i	−1.00375	+	1.38155i	−0.0807577	+	0.996734i	$0.525734\pi$
$739$	−27.2866	+	37.5567i	−1.00375	+	1.38155i	−0.922995	+	0.384813i	$0.874266\pi$
$740$		0			0
$741$	63.2375	+	87.0389i	2.32309	+	3.19745i
$742$		0			0
$743$		−	43.8156i		−	1.60744i	−0.595008	−	0.803720i	$-0.702851\pi$
$743$		−	43.8156i		−	1.60744i	0.595008	−	0.803720i	$-0.297149\pi$
$744$		0			0
$745$	−28.7896	−	10.4373i	−1.05477	−	0.382393i
$746$		0			0
$747$	2.45027	+	7.54115i	0.0896506	+	0.275916i
$748$		0			0
$749$			6.00182i			0.219302i
$750$		0			0
$751$	−0.0692442			−0.00252676			−0.00126338	−	0.999999i	$-0.500402\pi$
$751$	−0.0692442			−0.00252676			−0.00126338	+	0.999999i	$0.500402\pi$
$752$		0			0
$753$	−20.6649	+	6.71442i	−0.753070	+	0.244687i
$754$		0			0
$755$	−9.21607	+	25.4210i	−0.335407	+	0.925166i
$756$		0			0
$757$	17.1602			0.623700			0.311850	−	0.950131i	$-0.399051\pi$
$757$	17.1602			0.623700			0.311850	+	0.950131i	$0.399051\pi$
$758$		0			0
$759$	−3.91725	+	2.84605i	−0.142187	+	0.103305i
$760$		0			0
$761$	8.77922	+	6.37847i	0.318246	+	0.231220i	0.735427	−	0.677604i	$-0.236982\pi$
$761$	8.77922	+	6.37847i	0.318246	+	0.231220i	−0.417180	+	0.908824i	$0.636982\pi$
$762$		0			0
$763$	−6.06686	+	4.40783i	−0.219635	+	0.159574i
$764$		0			0
$765$	−1.37736	+	40.9277i	−0.0497984	+	1.47975i
$766$		0			0
$767$	−34.4408	−	11.1905i	−1.24358	−	0.404065i
$768$		0			0
$769$	5.30296	−	16.3208i	0.191230	−	0.588545i	−0.808770	−	0.588125i	$-0.799866\pi$
$769$	5.30296	−	16.3208i	0.191230	−	0.588545i	1.00000		0.000419828i	$-0.000133635\pi$
$770$		0			0
$771$	89.0459	−	28.9328i	3.20691	−	1.04199i
$772$		0			0
$773$	−29.9036	−	21.7262i	−1.07556	−	0.781437i	−0.0986535	−	0.995122i	$-0.531454\pi$
$773$	−29.9036	−	21.7262i	−1.07556	−	0.781437i	−0.976903	+	0.213685i	$0.931454\pi$
$774$		0			0
$775$	4.97207	−	3.12443i	0.178602	−	0.112233i
$776$		0			0
$777$	−11.5791	+	15.9372i	−0.415398	+	0.571746i
$778$		0			0
$779$	42.1161	−	13.6843i	1.50896	−	0.490292i
$780$		0			0
$781$	13.6438	+	4.43314i	0.488214	+	0.158630i
$782$		0			0
$783$	14.8829	+	4.83576i	0.531873	+	0.172816i
$784$		0			0
$785$	−9.60657	+	26.4982i	−0.342873	+	0.945760i
$786$		0			0
$787$	19.5842	−	14.2288i	0.698102	−	0.507201i	−0.181212	−	0.983444i	$-0.558002\pi$
$787$	19.5842	−	14.2288i	0.698102	−	0.507201i	0.879313	+	0.476244i	$0.158002\pi$
$788$		0			0
$789$	−48.8646	+	67.2564i	−1.73963	+	2.39439i
$790$		0			0
$791$	2.11843	−	1.53913i	0.0753225	−	0.0547250i
$792$		0			0
$793$		−	5.48182i		−	0.194665i
$794$		0			0
$795$	−6.86599	−	23.8306i	−0.243511	−	0.845186i
$796$		0			0
$797$	−0.311905	−	0.959946i	−0.0110483	−	0.0340030i	0.945380	−	0.325969i	$-0.105691\pi$
$797$	−0.311905	−	0.959946i	−0.0110483	−	0.0340030i	−0.956429	+	0.291966i	$0.905691\pi$
$798$		0			0
$799$	23.8959			0.845375
$800$		0			0
$801$	−28.4221			−1.00425
$802$		0			0
$803$	3.80287	+	11.7040i	0.134200	+	0.413027i
$804$		0			0
$805$	−2.13209	+	1.44204i	−0.0751462	+	0.0508253i
$806$		0			0
$807$			25.2322i			0.888217i
$808$		0			0
$809$	−14.0834	+	10.2322i	−0.495147	+	0.359745i	−0.807160	−	0.590332i	$-0.798997\pi$
$809$	−14.0834	+	10.2322i	−0.495147	+	0.359745i	0.312013	+	0.950078i	$0.398997\pi$
$810$		0			0
$811$	4.13632	−	5.69316i	0.145246	−	0.199914i	−0.730195	−	0.683238i	$-0.760571\pi$
$811$	4.13632	−	5.69316i	0.145246	−	0.199914i	0.875441	+	0.483325i	$0.160571\pi$
$812$		0			0
$813$	23.6684	−	17.1961i	0.830086	−	0.603093i
$814$		0			0
$815$	−7.31186	−	25.3782i	−0.256123	−	0.888959i
$816$		0			0
$817$	20.5759	+	6.68551i	0.719859	+	0.233896i
$818$		0			0
$819$	−66.6709	−	21.6627i	−2.32967	−	0.756956i
$820$		0			0
$821$	−24.4826	+	7.95489i	−0.854450	+	0.277628i	−0.703309	−	0.710884i	$-0.748295\pi$
$821$	−24.4826	+	7.95489i	−0.854450	+	0.277628i	−0.151141	+	0.988512i	$0.548295\pi$
$822$		0			0
$823$	−24.5580	+	33.8012i	−0.856038	+	1.17823i	0.126462	+	0.991971i	$0.459638\pi$
$823$	−24.5580	+	33.8012i	−0.856038	+	1.17823i	−0.982500	+	0.186264i	$0.940362\pi$
$824$		0			0
$825$	19.2249	+	30.5936i	0.669324	+	1.06513i
$826$		0			0
$827$	21.0719	+	15.3096i	0.732741	+	0.532368i	0.890429	−	0.455121i	$-0.150404\pi$
$827$	21.0719	+	15.3096i	0.732741	+	0.532368i	−0.157688	+	0.987489i	$0.550404\pi$
$828$		0			0
$829$	3.94736	−	1.28257i	0.137097	−	0.0445457i	−0.239665	−	0.970856i	$-0.577037\pi$
$829$	3.94736	−	1.28257i	0.137097	−	0.0445457i	0.376762	+	0.926310i	$0.377037\pi$
$830$		0			0
$831$	3.66128	−	11.2683i	0.127008	−	0.390892i
$832$		0			0
$833$	−10.2707	−	3.33717i	−0.355860	−	0.115626i
$834$		0			0
$835$	15.0903	−	19.3652i	0.522222	−	0.670160i
$836$		0			0
$837$	11.5363	−	8.38160i	0.398752	−	0.289710i
$838$		0			0
$839$	31.5974	+	22.9568i	1.09086	+	0.792557i	0.979545	−	0.201227i	$-0.0644930\pi$
$839$	31.5974	+	22.9568i	1.09086	+	0.792557i	0.111317	+	0.993785i	$0.464493\pi$
$840$		0			0
$841$	−22.1176	+	16.0693i	−0.762674	+	0.554115i
$842$		0			0
$843$	−67.3294			−2.31895
$844$		0			0
$845$	39.3739	+	30.6821i	1.35450	+	1.05550i
$846$		0			0
$847$	−9.32406	+	3.02957i	−0.320378	+	0.104097i
$848$		0			0
$849$	−2.90815			−0.0998075
$850$		0			0
$851$		−	2.44606i		−	0.0838498i
$852$		0			0
$853$	3.09392	+	9.52211i	0.105934	+	0.326031i	0.989948	−	0.141428i	$-0.0451695\pi$
$853$	3.09392	+	9.52211i	0.105934	+	0.326031i	−0.884015	+	0.467459i	$0.845169\pi$
$854$		0			0
$855$	2.97582	−	88.4256i	0.101771	−	3.02409i
$856$		0			0
$857$		−	31.6591i		−	1.08146i	−0.841198	−	0.540728i	$-0.818149\pi$
$857$		−	31.6591i		−	1.08146i	0.841198	−	0.540728i	$-0.181851\pi$
$858$		0			0
$859$	10.6822	+	14.7028i	0.364473	+	0.501654i	0.951388	−	0.307994i	$-0.0996577\pi$
$859$	10.6822	+	14.7028i	0.364473	+	0.501654i	−0.586915	+	0.809649i	$0.699658\pi$
$860$		0			0
$861$	−24.3714	+	33.5444i	−0.830575	+	1.14319i
$862$		0			0
$863$	−1.06034	−	1.45943i	−0.0360944	−	0.0496797i	0.790588	−	0.612348i	$-0.209775\pi$
$863$	−1.06034	−	1.45943i	−0.0360944	−	0.0496797i	−0.826683	+	0.562668i	$0.809775\pi$
$864$		0			0
$865$	−28.0871	+	18.9968i	−0.954990	+	0.645909i
$866$		0			0
$867$	9.59395	−	29.5271i	0.325828	−	1.00279i
$868$		0			0
$869$	−0.889568	−	0.289038i	−0.0301765	−	0.00980495i
$870$		0			0
$871$	28.1768	+	86.7193i	0.954735	+	2.93837i
$872$		0			0
$873$	61.2636	−	84.3221i	2.07346	−	2.85387i
$874$		0			0
$875$	9.66700	+	16.5978i	0.326804	+	0.561110i
$876$		0			0
$877$	25.8054	+	18.7487i	0.871387	+	0.633100i	0.930959	−	0.365124i	$-0.118974\pi$
$877$	25.8054	+	18.7487i	0.871387	+	0.633100i	−0.0595719	+	0.998224i	$0.518974\pi$
$878$		0			0
$879$	−12.9645	−	39.9007i	−0.437282	−	1.34582i
$880$		0			0
$881$	5.46376	−	16.8157i	0.184079	−	0.566536i	−0.815852	−	0.578260i	$-0.803732\pi$
$881$	5.46376	−	16.8157i	0.184079	−	0.566536i	0.999931	+	0.0117237i	$0.00373186\pi$
$882$		0			0
$883$	−3.19347	+	9.82850i	−0.107469	+	0.330755i	−0.990302	−	0.138932i	$-0.955633\pi$
$883$	−3.19347	+	9.82850i	−0.107469	+	0.330755i	0.882833	+	0.469687i	$0.155633\pi$
$884$		0			0
$885$	23.9749	+	35.4473i	0.805906	+	1.19155i
$886$		0			0
$887$	−18.9891	−	26.1362i	−0.637591	−	0.877568i	0.360894	−	0.932607i	$-0.382472\pi$
$887$	−18.9891	−	26.1362i	−0.637591	−	0.877568i	−0.998484	+	0.0550388i	$0.982472\pi$
$888$		0			0
$889$	23.6275	+	17.1664i	0.792442	+	0.575742i
$890$		0			0
$891$	23.7190	+	32.6464i	0.794615	+	1.09369i
$892$		0			0
$893$	−51.6277			−1.72766
$894$		0			0
$895$	−1.62531	+	48.2957i	−0.0543282	+	1.61435i
$896$		0			0
$897$	11.8958	−	3.86518i	0.397189	−	0.129055i
$898$		0			0
$899$		−	1.51372i		−	0.0504854i
$900$		0			0
$901$		−	9.41910i		−	0.313796i
$902$		0			0
$903$	−19.2654	+	6.25972i	−0.641113	+	0.208310i
$904$		0			0
$905$	11.9423	−	15.3254i	0.396976	−	0.509434i
$906$		0			0
$907$	−38.2694			−1.27071			−0.635357	−	0.772219i	$-0.719147\pi$
$907$	−38.2694			−1.27071			−0.635357	+	0.772219i	$0.719147\pi$
$908$		0			0
$909$	−55.4975	−	76.3858i	−1.84074	−	2.53356i
$910$		0			0
$911$	39.1122	+	28.4167i	1.29584	+	0.941486i	0.999906	−	0.0137212i	$-0.00436774\pi$
$911$	39.1122	+	28.4167i	1.29584	+	0.941486i	0.295938	+	0.955207i	$0.404368\pi$
$912$		0			0
$913$	1.56186	+	2.14972i	0.0516901	+	0.0711453i
$914$		0			0
$915$	−3.98177	+	5.10975i	−0.131633	+	0.168923i
$916$		0			0
$917$	−3.19076	+	9.82014i	−0.105368	+	0.324290i
$918$		0			0
$919$	2.97260	−	9.14872i	0.0980570	−	0.301788i	−0.889981	−	0.455997i	$-0.849283\pi$
$919$	2.97260	−	9.14872i	0.0980570	−	0.301788i	0.988038	+	0.154209i	$0.0492828\pi$
$920$		0			0
$921$	13.7613	+	42.3531i	0.453452	+	1.39558i
$922$		0			0
$923$	−29.9813	−	21.7827i	−0.986847	−	0.716986i
$924$		0			0
$925$	−18.2120	−	1.22718i	−0.598808	−	0.0403495i
$926$		0			0
$927$	35.3377	−	48.6381i	1.16064	−	1.59749i
$928$		0			0
$929$	5.02685	+	15.4710i	0.164926	+	0.507589i	0.999031	−	0.0440168i	$-0.0140155\pi$
$929$	5.02685	+	15.4710i	0.164926	+	0.507589i	−0.834105	+	0.551605i	$0.814015\pi$
$930$		0			0
$931$	22.1902	+	7.21004i	0.727255	+	0.236300i
$932$		0			0
$933$	0.464221	−	1.42872i	0.0151979	−	0.0467743i
$934$		0			0
$935$	3.79933	+	13.1868i	0.124251	+	0.431255i
$936$		0			0
$937$	2.13418	+	2.93745i	0.0697207	+	0.0959623i	0.842453	−	0.538769i	$-0.181111\pi$
$937$	2.13418	+	2.93745i	0.0697207	+	0.0959623i	−0.772733	+	0.634732i	$0.781111\pi$
$938$		0			0
$939$	20.9721	−	28.8657i	0.684400	−	0.941996i
$940$		0			0
$941$	23.9722	+	32.9948i	0.781470	+	1.07560i	0.995118	+	0.0986904i	$0.0314654\pi$
$941$	23.9722	+	32.9948i	0.781470	+	1.07560i	−0.213648	+	0.976911i	$0.568535\pi$
$942$		0			0
$943$		−	5.14841i		−	0.167655i
$944$		0			0
$945$	26.1310	+	38.6352i	0.850041	+	1.25680i
$946$		0			0
$947$	−7.79156	−	23.9800i	−0.253192	−	0.779244i	−0.994181	−	0.107727i	$-0.965643\pi$
$947$	−7.79156	−	23.9800i	−0.253192	−	0.779244i	0.740989	−	0.671517i	$-0.234357\pi$
$948$		0			0
$949$		−	31.7902i		−	1.03195i
$950$		0			0
$951$	−43.4193			−1.40797
$952$		0			0
$953$	22.2071	−	7.21551i	0.719357	−	0.233733i	0.0736128	−	0.997287i	$-0.476547\pi$
$953$	22.2071	−	7.21551i	0.719357	−	0.233733i	0.645745	+	0.763554i	$0.276547\pi$
$954$		0			0
$955$	−0.527378	−	1.83044i	−0.0170655	−	0.0592315i
$956$		0			0
$957$	9.31405			0.301081
$958$		0			0
$959$	5.75505	−	4.18129i	0.185840	−	0.135021i
$960$		0			0
$961$	23.9636	+	17.4106i	0.773020	+	0.561632i
$962$		0			0
$963$	−19.4041	+	14.0979i	−0.625289	+	0.454299i
$964$		0			0
$965$	−22.5784	−	8.18550i	−0.726823	−	0.263500i
$966$		0			0
$967$	23.8786	+	7.75862i	0.767883	+	0.249500i	0.666659	−	0.745363i	$-0.267724\pi$
$967$	23.8786	+	7.75862i	0.767883	+	0.249500i	0.101225	+	0.994864i	$0.467724\pi$
$968$		0			0
$969$	14.9214	−	45.9233i	0.479344	−	1.47527i
$970$		0			0
$971$	9.54087	−	3.10002i	0.306181	−	0.0994843i	−0.151897	−	0.988396i	$-0.548538\pi$
$971$	9.54087	−	3.10002i	0.306181	−	0.0994843i	0.458078	+	0.888912i	$0.348538\pi$
$972$		0			0
$973$	−13.9934	−	10.1668i	−0.448609	−	0.325934i
$974$		0			0
$975$	−22.8100	−	90.5089i	−0.730503	−	2.89860i
$976$		0			0
$977$	12.8529	−	17.6906i	0.411202	−	0.565971i	−0.552309	−	0.833640i	$-0.686253\pi$
$977$	12.8529	−	17.6906i	0.411202	−	0.565971i	0.963511	+	0.267668i	$0.0862531\pi$
$978$		0			0
$979$	−9.05848	+	2.94328i	−0.289510	+	0.0940676i
$980$		0			0
$981$	−28.5014	−	9.26065i	−0.909978	−	0.295670i
$982$		0			0
$983$	17.7241	+	5.75890i	0.565311	+	0.183681i	0.577709	−	0.816243i	$-0.303947\pi$
$983$	17.7241	+	5.75890i	0.565311	+	0.183681i	−0.0123987	+	0.999923i	$0.503947\pi$
$984$		0			0
$985$	50.5430	+	1.70094i	1.61043	+	0.0541965i
$986$		0			0
$987$	39.1076	−	28.4133i	1.24481	−	0.904406i
$988$		0			0
$989$	1.47843	−	2.03489i	0.0470115	−	0.0647058i
$990$		0			0
$991$	−29.3074	+	21.2931i	−0.930981	+	0.676398i	−0.946233	−	0.323486i	$-0.895145\pi$
$991$	−29.3074	+	21.2931i	−0.930981	+	0.676398i	0.0152515	+	0.999884i	$0.495145\pi$
$992$		0			0
$993$			21.2292i			0.673688i
$994$		0			0
$995$	0.538643	−	1.48576i	0.0170761	−	0.0471017i
$996$		0			0
$997$	5.62136	+	17.3008i	0.178030	+	0.547921i	0.999759	−	0.0219581i	$-0.00699003\pi$
$997$	5.62136	+	17.3008i	0.178030	+	0.547921i	−0.821729	+	0.569879i	$0.806990\pi$
$998$		0			0
$999$	−44.3246			−1.40237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	800.2.be.a.209.28		112
4.3	odd	2		200.2.o.a.109.17	✓	112
8.3	odd	2		200.2.o.a.109.24	yes	112
8.5	even	2	inner	800.2.be.a.209.1		112
20.3	even	4		1000.2.t.b.701.4		224
20.7	even	4		1000.2.t.b.701.53		224
20.19	odd	2		1000.2.o.a.549.12		112
25.14	even	10	inner	800.2.be.a.689.1		112
40.3	even	4		1000.2.t.b.701.19		224
40.19	odd	2		1000.2.o.a.549.5		112
40.27	even	4		1000.2.t.b.701.38		224
100.11	odd	10		1000.2.o.a.949.5		112
100.23	even	20		1000.2.t.b.301.19		224
100.27	even	20		1000.2.t.b.301.38		224
100.39	odd	10		200.2.o.a.189.24	yes	112
200.11	odd	10		1000.2.o.a.949.12		112
200.27	even	20		1000.2.t.b.301.53		224
200.123	even	20		1000.2.t.b.301.4		224
200.139	odd	10		200.2.o.a.189.17	yes	112
200.189	even	10	inner	800.2.be.a.689.28		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.17	✓	112	4.3	odd	2
200.2.o.a.109.24	yes	112	8.3	odd	2
200.2.o.a.189.17	yes	112	200.139	odd	10
200.2.o.a.189.24	yes	112	100.39	odd	10
800.2.be.a.209.1		112	8.5	even	2	inner
800.2.be.a.209.28		112	1.1	even	1	trivial
800.2.be.a.689.1		112	25.14	even	10	inner
800.2.be.a.689.28		112	200.189	even	10	inner
1000.2.o.a.549.5		112	40.19	odd	2
1000.2.o.a.549.12		112	20.19	odd	2
1000.2.o.a.949.5		112	100.11	odd	10
1000.2.o.a.949.12		112	200.11	odd	10
1000.2.t.b.301.4		224	200.123	even	20
1000.2.t.b.301.19		224	100.23	even	20
1000.2.t.b.301.38		224	100.27	even	20
1000.2.t.b.301.53		224	200.27	even	20
1000.2.t.b.701.4		224	20.3	even	4
1000.2.t.b.701.19		224	40.3	even	4
1000.2.t.b.701.38		224	40.27	even	4
1000.2.t.b.701.53		224	20.7	even	4

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:	\( N \)	\(=\)	\( 800 = 2^{5} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	800.be (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.970606 + 2.98722i) q^{3} +(-0.762120 + 2.10218i) q^{5} +1.71800i q^{7} +(-5.55435 + 4.03547i) q^{9} +(-1.35234 + 1.86134i) q^{11} +(4.80828 - 3.49342i) q^{13} +(-7.01940 - 0.236226i) q^{15} +(-2.53693 - 0.824300i) q^{17} +(5.48112 + 1.78092i) q^{19} +(-5.13203 + 1.66750i) q^{21} +(0.393834 - 0.542066i) q^{23} +(-3.83835 - 3.20423i) q^{25} +(-9.82268 - 7.13660i) q^{27} +(-1.22579 + 0.398283i) q^{29} +(-0.362926 + 1.11697i) q^{31} +(-6.87282 - 2.23312i) q^{33} +(-3.61155 - 1.30932i) q^{35} +(2.95345 - 2.14581i) q^{37} +(15.1026 + 10.9726i) q^{39} +(6.21636 - 4.51645i) q^{41} +3.75396 q^{43} +(-4.25022 - 14.7518i) q^{45} +(-8.51974 + 2.76823i) q^{47} +4.04848 q^{49} -8.37845i q^{51} +(1.09116 + 3.35825i) q^{53} +(-2.88223 - 4.26144i) q^{55} +18.1019i q^{57} +(-3.58141 - 4.92938i) q^{59} +(0.542140 - 0.746192i) q^{61} +(-6.93293 - 9.54236i) q^{63} +(3.67932 + 12.7703i) q^{65} +(-4.74089 + 14.5910i) q^{67} +(2.00153 + 0.650336i) q^{69} +(-1.92683 - 5.93017i) q^{71} +(3.14398 - 4.32732i) q^{73} +(5.84621 - 14.5760i) q^{75} +(-3.19778 - 2.32332i) q^{77} +(0.125628 + 0.386644i) q^{79} +(5.41990 - 16.6807i) q^{81} +(0.356893 - 1.09840i) q^{83} +(3.66628 - 4.70489i) q^{85} +(-2.37952 - 3.27513i) q^{87} +(3.34918 + 2.43332i) q^{89} +(6.00168 + 8.26061i) q^{91} -3.68890 q^{93} +(-7.92110 + 10.1650i) q^{95} +(-14.4383 + 4.69127i) q^{97} -15.7959i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 30 q^{9} + 2 q^{15} - 10 q^{17} + 10 q^{23} - 6 q^{25} + 18 q^{31} - 10 q^{33} + 10 q^{39} - 10 q^{41} + 10 q^{47} - 80 q^{49} + 34 q^{55} - 60 q^{63} + 40 q^{65} - 22 q^{71} - 10 q^{73} - 14 q^{79}+ \cdots - 50 q^{97}+O(q^{100}) \) 112 * q - 30 * q^9 + 2 * q^15 - 10 * q^17 + 10 * q^23 - 6 * q^25 + 18 * q^31 - 10 * q^33 + 10 * q^39 - 10 * q^41 + 10 * q^47 - 80 * q^49 + 34 * q^55 - 60 * q^63 + 40 * q^65 - 22 * q^71 - 10 * q^73 - 14 * q^79 - 6 * q^81 + 10 * q^87 + 24 * q^89 + 86 * q^95 - 50 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more