LMFDB - Embedded newform 648.2.t.a.613.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [648,2,Mod(37,648)] 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("648.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(648, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 14])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 648 = 2^{3} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	648.t (of order $18$, degree $6$, 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:	$5.17430605098$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 216)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			613.22
Character	$\chi$	$=$	648.613
Dual form			648.2.t.a.37.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.644492 + 1.25882i) q^{2} +(-1.16926 + 1.62260i) q^{4} +(-1.34802 + 3.70366i) q^{5} +(0.00177522 - 0.0100678i) q^{7} +(-2.79614 - 0.426137i) q^{8} +(-5.53104 + 0.690061i) q^{10} +(-0.343808 - 0.944604i) q^{11} +(2.57400 + 3.06757i) q^{13} +(0.0138176 - 0.00425391i) q^{14} +(-1.26566 - 3.79448i) q^{16} +(0.948987 + 1.64369i) q^{17} +(-3.76245 - 2.17225i) q^{19} +(-4.43337 - 6.51785i) q^{20} +(0.967506 - 1.04158i) q^{22} +(-1.19728 - 6.79010i) q^{23} +(-8.06972 - 6.77130i) q^{25} +(-2.20260 + 5.21723i) q^{26} +(0.0142603 + 0.0146523i) q^{28} +(-3.82827 + 4.56236i) q^{29} +(1.38501 + 7.85480i) q^{31} +(3.96087 - 4.03875i) q^{32} +(-1.45750 + 2.25395i) q^{34} +(0.0348946 + 0.0201464i) q^{35} +(6.65823 - 3.84413i) q^{37} +(0.309608 - 6.13625i) q^{38} +(5.34753 - 9.78152i) q^{40} +(-4.44753 + 3.73192i) q^{41} +(-1.42511 - 3.91546i) q^{43} +(1.93471 + 0.546626i) q^{44} +(7.77588 - 5.88332i) q^{46} +(-1.37530 + 7.79973i) q^{47} +(6.57775 + 2.39411i) q^{49} +(3.32298 - 14.5224i) q^{50} +(-7.98712 + 0.589779i) q^{52} +2.25567i q^{53} +3.96195 q^{55} +(-0.00925402 + 0.0273944i) q^{56} +(-8.21048 - 1.87871i) q^{58} +(-2.24610 + 6.17111i) q^{59} +(-0.106836 - 0.0188381i) q^{61} +(-8.99516 + 6.80584i) q^{62} +(7.63681 + 2.38308i) q^{64} +(-14.8311 + 5.39806i) q^{65} +(2.47342 + 2.94771i) q^{67} +(-3.77667 - 0.382080i) q^{68} +(-0.00287143 + 0.0569102i) q^{70} +(-0.442665 - 0.766718i) q^{71} +(-7.26116 + 12.5767i) q^{73} +(9.13025 + 5.90401i) q^{74} +(7.92398 - 3.56502i) q^{76} +(-0.0101204 + 0.00178450i) q^{77} +(2.46319 + 2.06686i) q^{79} +(15.7596 + 0.427473i) q^{80} +(-7.56422 - 3.19345i) q^{82} +(9.76904 - 11.6423i) q^{83} +(-7.36694 + 1.29899i) q^{85} +(4.01039 - 4.31744i) q^{86} +(0.558804 + 2.78776i) q^{88} +(1.45362 - 2.51775i) q^{89} +(0.0354530 - 0.0204688i) q^{91} +(12.4175 + 5.99669i) q^{92} +(-10.7048 + 3.29560i) q^{94} +(13.1172 - 11.0066i) q^{95} +(-12.0217 + 4.37554i) q^{97} +(1.22556 + 9.82319i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) $ 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/648\mathbb{Z}\right)^\times$.

$n$	$325$	$487$	$569$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.644492	+	1.25882i	0.455725	+	0.890121i
$2$	0.644492	+	1.25882i	0.455725	+	0.890121i
$3$		0			0
$3$		0			0
$4$	−1.16926	+	1.62260i	−0.584630	+	0.811300i
$5$	−1.34802	+	3.70366i	−0.602854	+	1.65633i	0.142608	+	0.989779i	$0.454451\pi$
$5$	−1.34802	+	3.70366i	−0.602854	+	1.65633i	−0.745462	+	0.666548i	$0.767771\pi$
$6$		0			0
$7$	0.00177522	−	0.0100678i	0.000670970	−	0.00380526i	−0.984470	−	0.175550i	$-0.943829\pi$
$7$	0.00177522	−	0.0100678i	0.000670970	−	0.00380526i	0.985141	+	0.171745i	$0.0549406\pi$
$8$	−2.79614	−	0.426137i	−0.988585	−	0.150662i
$9$		0			0
$10$	−5.53104	+	0.690061i	−1.74907	+	0.218216i
$11$	−0.343808	−	0.944604i	−0.103662	−	0.284809i	0.877009	−	0.480474i	$-0.159535\pi$
$11$	−0.343808	−	0.944604i	−0.103662	−	0.284809i	−0.980671	+	0.195666i	$0.937313\pi$
$12$		0			0
$13$	2.57400	+	3.06757i	0.713899	+	0.850792i	0.994023	−	0.109172i	$-0.0348200\pi$
$13$	2.57400	+	3.06757i	0.713899	+	0.850792i	−0.280124	+	0.959964i	$0.590376\pi$
$14$	0.0138176	−	0.00425391i	0.00369292	−	0.00113691i
$15$		0			0
$16$	−1.26566	−	3.79448i	−0.316415	−	0.948621i
$17$	0.948987	+	1.64369i	0.230163	+	0.398654i	0.957856	−	0.287249i	$-0.0927407\pi$
$17$	0.948987	+	1.64369i	0.230163	+	0.398654i	−0.727693	+	0.685903i	$0.759407\pi$
$18$		0			0
$19$	−3.76245	−	2.17225i	−0.863166	−	0.498349i	0.00190536	−	0.999998i	$-0.499394\pi$
$19$	−3.76245	−	2.17225i	−0.863166	−	0.498349i	−0.865071	+	0.501649i	$0.832727\pi$
$20$	−4.43337	−	6.51785i	−0.991332	−	1.45743i
$21$		0			0
$22$	0.967506	−	1.04158i	0.206273	−	0.222066i
$23$	−1.19728	−	6.79010i	−0.249650	−	1.41583i	−0.809442	−	0.587200i	$-0.800230\pi$
$23$	−1.19728	−	6.79010i	−0.249650	−	1.41583i	0.559792	−	0.828633i	$-0.310881\pi$
$24$		0			0
$25$	−8.06972	−	6.77130i	−1.61394	−	1.35426i
$26$	−2.20260	+	5.21723i	−0.431966	+	1.02318i
$27$		0			0
$28$	0.0142603	+	0.0146523i	0.00269494	+	0.00276903i
$29$	−3.82827	+	4.56236i	−0.710892	+	0.847208i	−0.993712	−	0.111965i	$-0.964286\pi$
$29$	−3.82827	+	4.56236i	−0.710892	+	0.847208i	0.282820	+	0.959173i	$0.408730\pi$
$30$		0			0
$31$	1.38501	+	7.85480i	0.248756	+	1.41076i	0.811606	+	0.584205i	$0.198594\pi$
$31$	1.38501	+	7.85480i	0.248756	+	1.41076i	−0.562850	+	0.826559i	$0.690295\pi$
$32$	3.96087	−	4.03875i	0.700189	−	0.713957i
$33$		0			0
$34$	−1.45750	+	2.25395i	−0.249959	+	0.386550i
$35$	0.0348946	+	0.0201464i	0.00589826	+	0.00340536i
$36$		0			0
$37$	6.65823	−	3.84413i	1.09461	−	0.631971i	0.159807	−	0.987148i	$-0.448913\pi$
$37$	6.65823	−	3.84413i	1.09461	−	0.631971i	0.934799	+	0.355177i	$0.115579\pi$
$38$	0.309608	−	6.13625i	0.0502250	−	0.995432i
$39$		0			0
$40$	5.34753	−	9.78152i	0.845519	−	1.54659i
$41$	−4.44753	+	3.73192i	−0.694588	+	0.582828i	−0.920228	−	0.391382i	$-0.871997\pi$
$41$	−4.44753	+	3.73192i	−0.694588	+	0.582828i	0.225641	+	0.974211i	$0.427553\pi$
$42$		0			0
$43$	−1.42511	−	3.91546i	−0.217327	−	0.597102i	0.782341	−	0.622850i	$-0.214025\pi$
$43$	−1.42511	−	3.91546i	−0.217327	−	0.597102i	−0.999668	+	0.0257481i	$0.991803\pi$
$44$	1.93471	+	0.546626i	0.291669	+	0.0824069i
$45$		0			0
$46$	7.77588	−	5.88332i	1.14649	−	0.867448i
$47$	−1.37530	+	7.79973i	−0.200608	+	1.13771i	0.703594	+	0.710602i	$0.251578\pi$
$47$	−1.37530	+	7.79973i	−0.200608	+	1.13771i	−0.904202	+	0.427105i	$0.859534\pi$
$48$		0			0
$49$	6.57775	+	2.39411i	0.939679	+	0.342015i
$50$	3.32298	−	14.5224i	0.469941	−	2.05377i
$51$		0			0
$52$	−7.98712	+	0.589779i	−1.10761	+	0.0817876i
$53$			2.25567i			0.309840i	0.987927	+	0.154920i	$0.0495120\pi$
$53$			2.25567i			0.309840i	−0.987927	+	0.154920i	$0.950488\pi$
$54$		0			0
$55$	3.96195			0.534230
$56$	−0.00925402	+	0.0273944i	−0.00123662	+	0.00366074i
$57$		0			0
$58$	−8.21048	−	1.87871i	−1.07809	−	0.246686i
$59$	−2.24610	+	6.17111i	−0.292417	+	0.803410i	0.703294	+	0.710899i	$0.251712\pi$
$59$	−2.24610	+	6.17111i	−0.292417	+	0.803410i	−0.995712	+	0.0925111i	$0.970511\pi$
$60$		0			0
$61$	−0.106836	−	0.0188381i	−0.0136789	−	0.00241197i	0.166805	−	0.985990i	$-0.446655\pi$
$61$	−0.106836	−	0.0188381i	−0.0136789	−	0.00241197i	−0.180483	+	0.983578i	$0.557766\pi$
$62$	−8.99516	+	6.80584i	−1.14239	+	0.864343i
$63$		0			0
$64$	7.63681	+	2.38308i	0.954602	+	0.297885i
$65$	−14.8311	+	5.39806i	−1.83957	+	0.669547i
$66$		0			0
$67$	2.47342	+	2.94771i	0.302177	+	0.360120i	0.895670	−	0.444718i	$-0.146696\pi$
$67$	2.47342	+	2.94771i	0.302177	+	0.360120i	−0.593494	+	0.804839i	$0.702252\pi$
$68$	−3.77667	−	0.382080i	−0.457989	−	0.0463340i
$69$		0			0
$70$	−0.00287143	+	0.0569102i	−0.000343202	+	0.00680207i
$71$	−0.442665	−	0.766718i	−0.0525346	−	0.0909926i	0.838562	−	0.544806i	$-0.183397\pi$
$71$	−0.442665	−	0.766718i	−0.0525346	−	0.0909926i	−0.891097	+	0.453813i	$0.850063\pi$
$72$		0			0
$73$	−7.26116	+	12.5767i	−0.849854	+	1.47199i	0.0314838	+	0.999504i	$0.489977\pi$
$73$	−7.26116	+	12.5767i	−0.849854	+	1.47199i	−0.881338	+	0.472486i	$0.843357\pi$
$74$	9.13025	+	5.90401i	1.06137	+	0.686327i
$75$		0			0
$76$	7.92398	−	3.56502i	0.908943	−	0.408936i
$77$	−0.0101204	+	0.00178450i	−0.00115333	+	0.000203362i
$78$		0			0
$79$	2.46319	+	2.06686i	0.277131	+	0.232540i	0.770750	−	0.637138i	$-0.219882\pi$
$79$	2.46319	+	2.06686i	0.277131	+	0.232540i	−0.493619	+	0.869678i	$0.664326\pi$
$80$	15.7596	+	0.427473i	1.76198	+	0.0477930i
$81$		0			0
$82$	−7.56422	−	3.19345i	−0.835328	−	0.352658i
$83$	9.76904	−	11.6423i	1.07229	−	1.27791i	0.113579	−	0.993529i	$-0.463768\pi$
$83$	9.76904	−	11.6423i	1.07229	−	1.27791i	0.958712	−	0.284378i	$-0.0917872\pi$
$84$		0			0
$85$	−7.36694	+	1.29899i	−0.799057	+	0.140895i
$86$	4.01039	−	4.31744i	0.432452	−	0.465562i
$87$		0			0
$88$	0.558804	+	2.78776i	0.0595687	+	0.297176i
$89$	1.45362	−	2.51775i	0.154084	−	0.266881i	−0.778641	−	0.627469i	$-0.784091\pi$
$89$	1.45362	−	2.51775i	0.154084	−	0.266881i	0.932725	+	0.360588i	$0.117424\pi$
$90$		0			0
$91$	0.0354530	−	0.0204688i	0.00371649	−	0.00214572i
$92$	12.4175	+	5.99669i	1.29462	+	0.625198i
$93$		0			0
$94$	−10.7048	+	3.29560i	−1.10412	+	0.339915i
$95$	13.1172	−	11.0066i	1.34579	−	1.12925i
$96$		0			0
$97$	−12.0217	+	4.37554i	−1.22062	+	0.444269i	−0.870375	−	0.492389i	$-0.836124\pi$
$97$	−12.0217	+	4.37554i	−1.22062	+	0.444269i	−0.350244	+	0.936658i	$0.613901\pi$
$98$	1.22556	+	9.82319i	0.123800	+	0.992292i
$99$		0			0
$100$	20.4227	−	5.17651i	2.04227	−	0.517651i
$101$	8.25225	+	1.45509i	0.821129	+	0.144787i	0.568403	−	0.822751i	$-0.307562\pi$
$101$	8.25225	+	1.45509i	0.821129	+	0.144787i	0.252727	+	0.967538i	$0.418673\pi$
$102$		0			0
$103$	6.53199	+	2.37745i	0.643617	+	0.234257i	0.643147	−	0.765743i	$-0.277628\pi$
$103$	6.53199	+	2.37745i	0.643617	+	0.234257i	0.000469418		1.00000i	$0.499851\pi$
$104$	−5.89006	−	9.67424i	−0.577568	−	0.948638i
$105$		0			0
$106$	−2.83949	+	1.45376i	−0.275795	+	0.141202i
$107$			14.2756i			1.38007i	0.723776	+	0.690035i	$0.242405\pi$
$107$			14.2756i			1.38007i	−0.723776	+	0.690035i	$0.757595\pi$
$108$		0			0
$109$			4.88426i			0.467827i	0.972257	+	0.233914i	$0.0751533\pi$
$109$			4.88426i			0.467827i	−0.972257	+	0.233914i	$0.924847\pi$
$110$	2.55345	+	4.98739i	0.243462	+	0.475529i
$111$		0			0
$112$	−0.0404488	+	0.00600633i	−0.00382206	+	0.000567545i
$113$	−4.20463	−	1.53036i	−0.395538	−	0.143964i	0.136591	−	0.990628i	$-0.456386\pi$
$113$	−4.20463	−	1.53036i	−0.395538	−	0.143964i	−0.532129	+	0.846663i	$0.678608\pi$
$114$		0			0
$115$	26.7622	+	4.71889i	2.49559	+	0.440039i
$116$	−2.92663	−	11.5463i	−0.271731	−	1.07205i
$117$		0			0
$118$	−9.21591	+	1.14979i	−0.848394	+	0.105847i
$119$	0.0182330	−	0.00663627i	0.00167142	−	0.000608346i
$120$		0			0
$121$	7.65242	−	6.42114i	0.695674	−	0.583740i
$122$	−0.0451412	−	0.146628i	−0.00408689	−	0.0132751i
$123$		0			0
$124$	−14.3646	−	6.93699i	−1.28998	−	0.622960i
$125$	18.8902	−	10.9063i	1.68959	−	0.975485i
$126$		0			0
$127$	−0.733337	+	1.27018i	−0.0650731	+	0.112710i	−0.896726	−	0.442585i	$-0.854061\pi$
$127$	−0.733337	+	1.27018i	−0.0650731	+	0.112710i	0.831653	+	0.555295i	$0.187395\pi$
$128$	1.92199	+	11.1493i	0.169882	+	0.985464i
$129$		0			0
$130$	−16.3537	−	15.1906i	−1.43431	−	1.33231i
$131$	11.2373	−	1.98143i	0.981805	−	0.173119i	0.340366	−	0.940293i	$-0.389449\pi$
$131$	11.2373	−	1.98143i	0.981805	−	0.173119i	0.641439	+	0.767174i	$0.278338\pi$
$132$		0			0
$133$	−0.0285489	+	0.0340233i	−0.00247551	+	0.00295019i
$134$	−2.11654	+	5.01337i	−0.182841	+	0.433089i
$135$		0			0
$136$	−1.95306	−	5.00040i	−0.167474	−	0.428781i
$137$	−3.27137	−	2.74501i	−0.279492	−	0.234522i	0.492255	−	0.870451i	$-0.336173\pi$
$137$	−3.27137	−	2.74501i	−0.279492	−	0.234522i	−0.771748	+	0.635929i	$0.780617\pi$
$138$		0			0
$139$	1.04893	−	0.184955i	0.0889693	−	0.0156877i	−0.128986	−	0.991646i	$-0.541172\pi$
$139$	1.04893	−	0.184955i	0.0889693	−	0.0156877i	0.217956	+	0.975959i	$0.430061\pi$
$140$	−0.0734904	+	0.0330636i	−0.00621107	+	0.00279438i
$141$		0			0
$142$	0.679866	−	1.05138i	0.0570531	−	0.0882297i
$143$	2.01268	−	3.48606i	0.168309	−	0.291519i
$144$		0			0
$145$	−11.7368	−	20.3288i	−0.974690	−	1.68821i
$146$	−20.5116	−	1.03492i	−1.69755	−	0.0856506i
$147$		0			0
$148$	−1.54772	+	15.2984i	−0.127222	+	1.25752i
$149$	−1.34236	−	1.59976i	−0.109970	−	0.131058i	0.708251	−	0.705960i	$-0.249484\pi$
$149$	−1.34236	−	1.59976i	−0.109970	−	0.131058i	−0.818222	+	0.574903i	$0.805040\pi$
$150$		0			0
$151$	9.89970	−	3.60320i	0.805626	−	0.293224i	0.0938105	−	0.995590i	$-0.470095\pi$
$151$	9.89970	−	3.60320i	0.805626	−	0.293224i	0.711816	+	0.702366i	$0.247873\pi$
$152$	9.59467	+	7.67725i	0.778231	+	0.622707i
$153$		0			0
$154$	−0.00876888	−	0.0115897i	−0.000706616	−	0.000933922i
$155$	−30.9586	−	5.45883i	−2.48665	−	0.438464i
$156$		0			0
$157$	−7.61747	+	20.9288i	−0.607940	+	1.67030i	0.126779	+	0.991931i	$0.459536\pi$
$157$	−7.61747	+	20.9288i	−0.607940	+	1.67030i	−0.734720	+	0.678371i	$0.762686\pi$
$158$	−1.01430	+	4.43280i	−0.0806937	+	0.352654i
$159$		0			0
$160$	9.61883	+	20.1140i	0.760436	+	1.59015i
$161$	−0.0704866			−0.00555512
$162$		0			0
$163$			8.64571i			0.677184i	0.940933	+	0.338592i	$0.109951\pi$
$163$			8.64571i			0.677184i	−0.940933	+	0.338592i	$0.890049\pi$
$164$	−0.855093	−	11.5801i	−0.0667715	−	0.904258i
$165$		0			0
$166$	20.9516	+	4.79411i	1.62616	+	0.372095i
$167$	7.93163	+	2.88688i	0.613768	+	0.223393i	0.630151	−	0.776473i	$-0.282993\pi$
$167$	7.93163	+	2.88688i	0.613768	+	0.223393i	−0.0163833	+	0.999866i	$0.505215\pi$
$168$		0			0
$169$	−0.527105	+	2.98936i	−0.0405465	+	0.229951i
$170$	−6.38313	−	8.43647i	−0.489564	−	0.647048i
$171$		0			0
$172$	8.01955	+	2.26581i	0.611485	+	0.172766i
$173$	−4.65008	−	12.7760i	−0.353539	−	0.971340i	−0.981224	−	0.192872i	$-0.938220\pi$
$173$	−4.65008	−	12.7760i	−0.353539	−	0.971340i	0.627685	−	0.778467i	$-0.284003\pi$
$174$		0			0
$175$	−0.0824974	+	0.0692236i	−0.00623622	+	0.00523281i
$176$	−3.14914	+	2.50012i	−0.237375	+	0.188454i
$177$		0			0
$178$	4.10624	+	0.207183i	0.307776	+	0.0155290i
$179$	0.257187	−	0.148487i	0.0192231	−	0.0110985i	−0.490358	−	0.871521i	$-0.663134\pi$
$179$	0.257187	−	0.148487i	0.0192231	−	0.0110985i	0.509581	+	0.860423i	$0.329801\pi$
$180$		0			0
$181$	−1.63626	−	0.944694i	−0.121622	−	0.0702186i	0.437955	−	0.898997i	$-0.355703\pi$
$181$	−1.63626	−	0.944694i	−0.121622	−	0.0702186i	−0.559577	+	0.828778i	$0.689036\pi$
$182$	0.0486158	+	0.0314370i	0.00360364	+	0.00233027i
$183$		0			0
$184$	0.454243	+	19.4963i	0.0334873	+	1.43728i
$185$	5.26192	+	29.8418i	0.386864	+	2.19401i
$186$		0			0
$187$	1.22637	−	1.46153i	0.0896811	−	0.106878i
$188$	−11.0477	−	11.3515i	−0.805740	−	0.827892i
$189$		0			0
$190$	22.3092	+	9.41849i	1.61848	+	0.683289i
$191$	−10.6897	−	8.96976i	−0.773483	−	0.649029i	0.168116	−	0.985767i	$-0.446232\pi$
$191$	−10.6897	−	8.96976i	−0.773483	−	0.649029i	−0.941598	+	0.336738i	$0.890676\pi$
$192$		0			0
$193$	1.65530	+	9.38768i	0.119151	+	0.675740i	0.984611	+	0.174761i	$0.0559153\pi$
$193$	1.65530	+	9.38768i	0.119151	+	0.675740i	−0.865460	+	0.500979i	$0.832974\pi$
$194$	−13.2559	−	12.3132i	−0.951720	−	0.884034i
$195$		0			0
$196$	−11.5758	+	7.87372i	−0.826841	+	0.562409i
$197$	7.61046	+	4.39390i	0.542223	+	0.313052i	0.745979	−	0.665969i	$-0.231982\pi$
$197$	7.61046	+	4.39390i	0.542223	+	0.313052i	−0.203757	+	0.979022i	$0.565315\pi$
$198$		0			0
$199$	4.70991	+	8.15780i	0.333876	+	0.578291i	0.983268	−	0.182163i	$-0.0583098\pi$
$199$	4.70991	+	8.15780i	0.333876	+	0.578291i	−0.649392	+	0.760454i	$0.724977\pi$
$200$	19.6786	+	22.3723i	1.39149	+	1.58196i
$201$		0			0
$202$	3.48680	+	11.3259i	0.245331	+	0.796887i
$203$	0.0391368	+	0.0466414i	0.00274686	+	0.00327358i
$204$		0			0
$205$	−7.82640	−	21.5029i	−0.546619	−	1.50182i
$206$	1.21703	+	9.75486i	0.0847946	+	0.679653i
$207$		0			0
$208$	8.38205	−	13.6495i	0.581190	−	0.946423i
$209$	−0.758358	+	4.30086i	−0.0524567	+	0.297497i
$210$		0			0
$211$	4.12560	−	11.3350i	0.284018	−	0.780333i	−0.712855	−	0.701311i	$-0.752598\pi$
$211$	4.12560	−	11.3350i	0.284018	−	0.780333i	0.996873	−	0.0790214i	$-0.0251795\pi$
$212$	−3.66005	−	2.63747i	−0.251373	−	0.181142i
$213$		0			0
$214$	−17.9704	+	9.20048i	−1.22843	+	0.628932i
$215$	16.4226			1.12001
$216$		0			0
$217$	0.0815391			0.00553524
$218$	−6.14841	+	3.14786i	−0.416423	+	0.213200i
$219$		0			0
$220$	−4.63255	+	6.42866i	−0.312327	+	0.433420i
$221$	−2.59946	+	7.14195i	−0.174858	+	0.480420i
$222$		0			0
$223$	0.616341	−	3.49544i	0.0412732	−	0.234072i	−0.957192	−	0.289454i	$-0.906526\pi$
$223$	0.616341	−	3.49544i	0.0412732	−	0.234072i	0.998465	+	0.0553815i	$0.0176375\pi$
$224$	−0.0336298	−	0.0470468i	−0.00224699	−	0.00314345i
$225$		0			0
$226$	−0.783400	−	6.27918i	−0.0521110	−	0.417685i
$227$	−3.72066	−	10.2224i	−0.246949	−	0.678486i	−0.999794	−	0.0202886i	$-0.993542\pi$
$227$	−3.72066	−	10.2224i	−0.246949	−	0.678486i	0.752846	−	0.658197i	$-0.228681\pi$
$228$		0			0
$229$	5.05083	+	6.01935i	0.333769	+	0.397770i	0.906661	−	0.421861i	$-0.138623\pi$
$229$	5.05083	+	6.01935i	0.333769	+	0.397770i	−0.572892	+	0.819631i	$0.694179\pi$
$230$	11.3078	+	36.7301i	0.745612	+	2.42191i
$231$		0			0
$232$	12.6486	−	11.1256i	0.830420	−	0.730433i
$233$	−12.0985	−	20.9553i	−0.792602	−	1.37283i	−0.924351	−	0.381544i	$-0.875392\pi$
$233$	−12.0985	−	20.9553i	−0.792602	−	1.37283i	0.131749	−	0.991283i	$-0.457941\pi$
$234$		0			0
$235$	−27.0336	−	15.6079i	−1.76348	−	1.01814i
$236$	−7.38696	−	10.8602i	−0.480850	−	0.706936i
$237$		0			0
$238$	0.0201049	+	0.0186751i	0.00130321	+	0.00121052i
$239$	5.23764	+	29.7041i	0.338795	+	1.92140i	0.385963	+	0.922514i	$0.373869\pi$
$239$	5.23764	+	29.7041i	0.338795	+	1.92140i	−0.0471684	+	0.998887i	$0.515020\pi$
$240$		0			0
$241$	−1.91756	−	1.60903i	−0.123521	−	0.103647i	0.578935	−	0.815374i	$-0.303469\pi$
$241$	−1.91756	−	1.60903i	−0.123521	−	0.103647i	−0.702456	+	0.711727i	$0.747913\pi$
$242$	13.0150	+	5.49465i	0.836635	+	0.353209i
$243$		0			0
$244$	0.155486	−	0.151325i	0.00995396	−	0.00968762i
$245$	−17.7339	+	21.1344i	−1.13298	+	1.35023i
$246$		0			0
$247$	−3.02101	−	17.1330i	−0.192222	−	1.09015i
$248$	−0.525470	−	22.5534i	−0.0333674	−	1.43214i
$249$		0			0
$250$	25.9036	+	16.7504i	1.63829	+	1.05939i
$251$	−14.5027	−	8.37314i	−0.915402	−	0.528508i	−0.0332368	−	0.999448i	$-0.510582\pi$
$251$	−14.5027	−	8.37314i	−0.915402	−	0.528508i	−0.882165	+	0.470940i	$0.843915\pi$
$252$		0			0
$253$	−6.00232	+	3.46544i	−0.377363	+	0.217870i
$254$	−2.07156	−	0.104521i	−0.129981	−	0.00655825i
$255$		0			0
$256$	−12.7962	+	9.60505i	−0.799763	+	0.600316i
$257$	20.4870	−	17.1907i	1.27795	−	1.07232i	0.284423	−	0.958699i	$-0.408198\pi$
$257$	20.4870	−	17.1907i	1.27795	−	1.07232i	0.993524	−	0.113626i	$-0.0362465\pi$
$258$		0			0
$259$	−0.0268820	−	0.0738578i	−0.00167037	−	0.00458930i
$260$	8.58247	−	30.3766i	0.532262	−	1.88388i
$261$		0			0
$262$	9.73660	+	12.8687i	0.601529	+	0.795031i
$263$	0.762315	−	4.32330i	0.0470064	−	0.266586i	−0.952242	−	0.305343i	$-0.901229\pi$
$263$	0.762315	−	4.32330i	0.0470064	−	0.266586i	0.999249	+	0.0387571i	$0.0123398\pi$
$264$		0			0
$265$	−8.35424	−	3.04070i	−0.513197	−	0.186788i
$266$	−0.0612288	−	0.0140103i	−0.00375418	−	0.000859024i
$267$		0			0
$268$	−7.67503	+	0.566734i	−0.468827	+	0.0346188i
$269$		−	0.741050i		−	0.0451826i	−0.999745	−	0.0225913i	$-0.992808\pi$
$269$		−	0.741050i		−	0.0451826i	0.999745	−	0.0225913i	$-0.00719165\pi$
$270$		0			0
$271$	−14.1450			−0.859245			−0.429622	−	0.903009i	$-0.641353\pi$
$271$	−14.1450			−0.859245			−0.429622	+	0.903009i	$0.641353\pi$
$272$	5.03587	−	5.68127i	0.305345	−	0.344478i
$273$		0			0
$274$	1.34710	−	5.88721i	0.0813813	−	0.355659i
$275$	−3.62176	+	9.95071i	−0.218400	+	0.600050i
$276$		0			0
$277$	8.42697	+	1.48590i	0.506327	+	0.0892792i	0.420976	−	0.907072i	$-0.361688\pi$
$277$	8.42697	+	1.48590i	0.506327	+	0.0892792i	0.0853514	+	0.996351i	$0.472799\pi$
$278$	0.908854	+	1.20122i	0.0545094	+	0.0720442i
$279$		0			0
$280$	−0.0889851	−	0.0712021i	−0.00531788	−	0.00425514i
$281$	17.6483	−	6.42344i	1.05281	−	0.383191i	0.243086	−	0.970005i	$-0.421840\pi$
$281$	17.6483	−	6.42344i	1.05281	−	0.383191i	0.809722	+	0.586814i	$0.199618\pi$
$282$		0			0
$283$	−16.5234	−	19.6918i	−0.982214	−	1.17056i	−0.985347	−	0.170562i	$-0.945442\pi$
$283$	−16.5234	−	19.6918i	−0.982214	−	1.17056i	0.00313343	−	0.999995i	$-0.499003\pi$
$284$	1.76167	+	0.178225i	0.104536	+	0.0105757i
$285$		0			0
$286$	5.68549	+	0.286864i	0.336190	+	0.0169626i
$287$	0.0296768	+	0.0514017i	0.00175177	+	0.00303415i
$288$		0			0
$289$	6.69885	−	11.6027i	0.394050	−	0.682514i
$290$	18.0260	−	27.8763i	1.05852	−	1.63695i
$291$		0			0
$292$	−11.9168	−	26.4874i	−0.697375	−	1.55006i
$293$	−14.3663	+	2.53317i	−0.839288	+	0.147989i	−0.576738	−	0.816929i	$-0.695675\pi$
$293$	−14.3663	+	2.53317i	−0.839288	+	0.147989i	−0.262550	+	0.964918i	$0.584564\pi$
$294$		0			0
$295$	−19.8279	−	16.6376i	−1.15442	−	0.968678i
$296$	−20.2555	+	7.91142i	−1.17733	+	0.459842i
$297$		0			0
$298$	1.14868	−	2.72083i	0.0665410	−	0.157613i
$299$	17.7473	−	21.1504i	1.02635	−	1.22316i
$300$		0			0
$301$	−0.0419499	+	0.00739689i	−0.00241795	+	0.000426350i
$302$	10.9161	+	10.1397i	0.628149	+	0.583476i
$303$		0			0
$304$	−3.48059	+	17.0259i	−0.199626	+	0.976502i
$305$	0.213787	−	0.370290i	0.0122414	−	0.0212028i
$306$		0			0
$307$	−8.07578	+	4.66255i	−0.460909	+	0.266106i	−0.712426	−	0.701747i	$-0.752404\pi$
$307$	−8.07578	+	4.66255i	−0.460909	+	0.266106i	0.251517	+	0.967853i	$0.419070\pi$
$308$	0.00893785	−	0.0185079i	0.000509281	−	0.00105458i
$309$		0			0
$310$	−13.0809	−	42.4895i	−0.742942	−	2.41324i
$311$	6.15253	−	5.16259i	0.348878	−	0.292743i	−0.451461	−	0.892291i	$-0.649097\pi$
$311$	6.15253	−	5.16259i	0.348878	−	0.292743i	0.800339	+	0.599547i	$0.204653\pi$
$312$		0			0
$313$	31.0694	−	11.3083i	1.75615	−	0.639185i	0.756261	−	0.654269i	$-0.227024\pi$
$313$	31.0694	−	11.3083i	1.75615	−	0.639185i	0.999886	+	0.0150840i	$0.00480156\pi$
$314$	−31.2550	+	3.89943i	−1.76382	+	0.220057i
$315$		0			0
$316$	−6.23381	+	1.58007i	−0.350679	+	0.0888861i
$317$	25.6721	+	4.52669i	1.44189	+	0.254244i	0.839240	−	0.543762i	$-0.183000\pi$
$317$	25.6721	+	4.52669i	1.44189	+	0.254244i	0.602650	+	0.798006i	$0.294112\pi$
$318$		0			0
$319$	5.62581	+	2.04763i	0.314985	+	0.114645i
$320$	−19.1207	+	25.0717i	−1.06888	+	1.40155i
$321$		0			0
$322$	−0.0454280	−	0.0887300i	−0.00253161	−	0.00494473i
$323$		−	8.24576i		−	0.458806i
$324$		0			0
$325$		−	42.1838i		−	2.33993i
$326$	−10.8834	+	5.57209i	−0.602776	+	0.308609i
$327$		0			0
$328$	14.0262	−	8.53972i	0.774469	−	0.471527i
$329$	0.0760844	+	0.0276925i	0.00419467	+	0.00152674i
$330$		0			0
$331$	−2.73256	−	0.481823i	−0.150195	−	0.0264834i	0.0980451	−	0.995182i	$-0.468741\pi$
$331$	−2.73256	−	0.481823i	−0.150195	−	0.0264834i	−0.248240	+	0.968699i	$0.579852\pi$
$332$	7.46822	+	29.4641i	0.409872	+	1.61705i
$333$		0			0
$334$	1.47781	+	11.8451i	0.0808621	+	0.648133i
$335$	−14.2516	+	5.18714i	−0.778645	+	0.283404i
$336$		0			0
$337$	−10.0326	+	8.41837i	−0.546512	+	0.458578i	−0.873758	−	0.486361i	$-0.838324\pi$
$337$	−10.0326	+	8.41837i	−0.546512	+	0.458578i	0.327246	+	0.944939i	$0.393879\pi$
$338$	−4.10278	+	1.26309i	−0.223162	+	0.0687029i
$339$		0			0
$340$	6.50613	−	13.4725i	0.352844	−	0.730646i
$341$	6.94350	−	4.00883i	0.376012	−	0.217090i
$342$		0			0
$343$	0.0715611	−	0.123947i	0.00386393	−	0.00669253i
$344$	2.31629	+	11.5555i	0.124886	+	0.623029i
$345$		0			0
$346$	13.0857	−	14.0876i	0.703493	−	0.757356i
$347$	14.2864	−	2.51907i	0.766932	−	0.135231i	0.223523	−	0.974699i	$-0.428244\pi$
$347$	14.2864	−	2.51907i	0.766932	−	0.135231i	0.543409	+	0.839468i	$0.317133\pi$
$348$		0			0
$349$	−15.0245	+	17.9055i	−0.804242	+	0.958459i	−0.999753	−	0.0222430i	$-0.992919\pi$
$349$	−15.0245	+	17.9055i	−0.804242	+	0.958459i	0.195510	+	0.980702i	$0.437364\pi$
$350$	−0.140309	−	0.0592355i	−0.00749983	−	0.00316627i
$351$		0			0
$352$	−5.17680	−	2.35290i	−0.275924	−	0.125410i
$353$	26.1780	+	21.9660i	1.39332	+	1.16913i	0.963976	+	0.265988i	$0.0856981\pi$
$353$	26.1780	+	21.9660i	1.39332	+	1.16913i	0.429340	+	0.903143i	$0.358746\pi$
$354$		0			0
$355$	3.43638	−	0.605927i	0.182384	−	0.0321593i
$356$	2.38564	+	5.30255i	0.126438	+	0.281035i
$357$		0			0
$358$	0.352674	+	0.228054i	0.0186394	+	0.0120530i
$359$	13.5391	−	23.4504i	0.714565	−	1.23766i	−0.248562	−	0.968616i	$-0.579958\pi$
$359$	13.5391	−	23.4504i	0.714565	−	1.23766i	0.963127	−	0.269047i	$-0.0867088\pi$
$360$		0			0
$361$	−0.0626343	−	0.108486i	−0.00329654	−	0.00570978i
$362$	0.134646	−	2.66860i	0.00707682	−	0.140259i
$363$		0			0
$364$	−0.00824113	+	0.0814595i	−0.000431953	+	0.00426964i
$365$	−36.7916	−	43.8465i	−1.92576	−	2.29503i
$366$		0			0
$367$	4.30354	−	1.56636i	0.224643	−	0.0817633i	−0.227247	−	0.973837i	$-0.572972\pi$
$367$	4.30354	−	1.56636i	0.224643	−	0.0817633i	0.451890	+	0.892074i	$0.350750\pi$
$368$	−24.2496	+	13.1370i	−1.26410	+	0.684814i
$369$		0			0
$370$	−34.1742	+	25.8566i	−1.77663	+	1.34422i
$371$	0.0227096	+	0.00400432i	0.00117902	+	0.000207894i
$372$		0			0
$373$	−5.86591	+	16.1165i	−0.303725	+	0.834479i	0.690119	+	0.723696i	$0.257558\pi$
$373$	−5.86591	+	16.1165i	−0.303725	+	0.834479i	−0.993845	+	0.110783i	$0.964664\pi$
$374$	2.63019	+	0.601836i	0.136004	+	0.0311202i
$375$		0			0
$376$	7.16929	−	21.2231i	0.369728	−	1.09450i
$377$	−23.8493			−1.22830
$378$		0			0
$379$			0.380673i			0.0195538i	0.999952	+	0.00977692i	$0.00311214\pi$
$379$			0.380673i			0.0195538i	−0.999952	+	0.00977692i	$0.996888\pi$
$380$	2.52194	+	34.1535i	0.129373	+	1.75204i
$381$		0			0
$382$	4.40187	−	19.2374i	0.225219	−	0.984272i
$383$	−34.6697	−	12.6187i	−1.77154	−	0.644788i	−0.999963	−	0.00865253i	$-0.997246\pi$
$383$	−34.6697	−	12.6187i	−1.77154	−	0.644788i	−0.771578	−	0.636135i	$-0.780532\pi$
$384$		0			0
$385$	0.00703334	−	0.0398880i	0.000358452	−	0.00203288i
$386$	−10.7506	+	8.13401i	−0.547190	+	0.414010i
$387$		0			0
$388$	6.95675	−	24.6226i	0.353176	−	1.25002i
$389$	2.44660	+	6.72197i	0.124047	+	0.340817i	0.986136	−	0.165941i	$-0.0530660\pi$
$389$	2.44660	+	6.72197i	0.124047	+	0.340817i	−0.862088	+	0.506758i	$0.830844\pi$
$390$		0			0
$391$	10.0246	−	8.41167i	0.506968	−	0.425397i
$392$	−17.3721	−	9.49728i	−0.877424	−	0.479685i
$393$		0			0
$394$	−0.626255	+	12.4120i	−0.0315503	+	0.625309i
$395$	−10.9754	+	6.33665i	−0.552233	+	0.318832i
$396$		0			0
$397$	22.6986	+	13.1051i	1.13921	+	0.657724i	0.946235	−	0.323479i	$-0.104853\pi$
$397$	22.6986	+	13.1051i	1.13921	+	0.657724i	0.192976	+	0.981203i	$0.438186\pi$
$398$	−7.23371	+	11.1866i	−0.362593	+	0.560732i
$399$		0			0
$400$	−15.4801	+	39.1906i	−0.774003	+	1.95953i
$401$	−3.00071	−	17.0179i	−0.149848	−	0.849832i	−0.963346	−	0.268263i	$-0.913550\pi$
$401$	−3.00071	−	17.0179i	−0.149848	−	0.849832i	0.813497	−	0.581569i	$-0.197561\pi$
$402$		0			0
$403$	−20.5302	+	24.4669i	−1.02268	+	1.21878i
$404$	−12.0101	+	11.6887i	−0.597523	+	0.581535i
$405$		0			0
$406$	−0.0334898	+	0.0793262i	−0.00166207	+	0.00393689i
$407$	−5.92033	−	4.96775i	−0.293460	−	0.246242i
$408$		0			0
$409$	−4.27076	−	24.2207i	−0.211176	−	1.19764i	−0.887421	−	0.460960i	$-0.847505\pi$
$409$	−4.27076	−	24.2207i	−0.211176	−	1.19764i	0.676245	−	0.736677i	$-0.263606\pi$
$410$	22.0242	−	23.7105i	1.08770	−	1.17098i
$411$		0			0
$412$	−11.4953	+	7.81895i	−0.566331	+	0.385212i
$413$	0.0581420	+	0.0335683i	0.00286098	+	0.00165179i
$414$		0			0
$415$	29.9502	+	51.8753i	1.47020	+	2.54646i
$416$	22.5844	+	1.75450i	1.10729	+	0.0860216i
$417$		0			0
$418$	−5.90277	+	1.81723i	−0.288714	+	0.0888838i
$419$	8.86909	+	10.5698i	0.433283	+	0.516367i	0.937867	−	0.346996i	$-0.112798\pi$
$419$	8.86909	+	10.5698i	0.433283	+	0.516367i	−0.504583	+	0.863363i	$0.668354\pi$
$420$		0			0
$421$	−12.5029	−	34.3515i	−0.609355	−	1.67419i	−0.731637	−	0.681695i	$-0.761243\pi$
$421$	−12.5029	−	34.3515i	−0.609355	−	1.67419i	0.122281	−	0.992496i	$-0.460979\pi$
$422$	16.9276	−	2.11192i	0.824024	−	0.102807i
$423$		0			0
$424$	0.961226	−	6.30718i	0.0466813	−	0.306304i
$425$	3.47188	−	19.6900i	0.168411	−	0.955106i
$426$		0			0
$427$	−0.000379315		0.00104216i	−1.83563e−5		5.04336e-5i
$428$	−23.1635	−	16.6918i	−1.11965	−	0.806830i
$429$		0			0
$430$	10.5842	+	20.6731i	0.510418	+	0.996947i
$431$	−7.44743			−0.358730			−0.179365	−	0.983783i	$-0.557404\pi$
$431$	−7.44743			−0.358730			−0.179365	+	0.983783i	$0.557404\pi$
$432$		0			0
$433$	20.9407			1.00634			0.503172	−	0.864186i	$-0.332166\pi$
$433$	20.9407			1.00634			0.503172	+	0.864186i	$0.332166\pi$
$434$	0.0525513	+	0.102643i	0.00252254	+	0.00492703i
$435$		0			0
$436$	−7.92519	−	5.71097i	−0.379548	−	0.273506i
$437$	−10.2451	+	28.1482i	−0.490090	+	1.34651i
$438$		0			0
$439$	4.88555	−	27.7073i	0.233174	−	1.32240i	−0.613250	−	0.789889i	$-0.710138\pi$
$439$	4.88555	−	27.7073i	0.233174	−	1.32240i	0.846424	−	0.532509i	$-0.178751\pi$
$440$	−11.0782	−	1.68834i	−0.528132	−	0.0804882i
$441$		0			0
$442$	−10.6658	+	1.33068i	−0.507319	+	0.0632939i
$443$	5.98423	+	16.4415i	0.284319	+	0.781161i	0.996835	+	0.0795043i	$0.0253338\pi$
$443$	5.98423	+	16.4415i	0.284319	+	0.781161i	−0.712515	+	0.701657i	$0.752444\pi$
$444$		0			0
$445$	7.36537	+	8.77771i	0.349152	+	0.416103i
$446$	4.79736	−	1.47692i	0.227162	−	0.0699342i
$447$		0			0
$448$	0.0375493	−	0.0726552i	0.00177404	−	0.00343264i
$449$	2.99357	+	5.18501i	0.141275	+	0.244696i	0.927977	−	0.372637i	$-0.121546\pi$
$449$	2.99357	+	5.18501i	0.141275	+	0.244696i	−0.786702	+	0.617333i	$0.788213\pi$
$450$		0			0
$451$	5.05428	+	2.91809i	0.237997	+	0.137408i
$452$	7.39947	−	5.03304i	0.348042	−	0.236734i
$453$		0			0
$454$	10.4703	−	11.2719i	0.491394	−	0.529017i
$455$	0.0280181	+	0.158899i	0.00131351	+	0.00744928i
$456$		0			0
$457$	18.6279	+	15.6306i	0.871375	+	0.731170i	0.964387	−	0.264495i	$-0.0852052\pi$
$457$	18.6279	+	15.6306i	0.871375	+	0.731170i	−0.0930125	+	0.995665i	$0.529650\pi$
$458$	−4.32206	+	10.2375i	−0.201957	+	0.478368i
$459$		0			0
$460$	−38.9488	+	37.9067i	−1.81600	+	1.76741i
$461$	10.3010	−	12.2762i	0.479764	−	0.571761i	−0.470819	−	0.882230i	$-0.656042\pi$
$461$	10.3010	−	12.2762i	0.479764	−	0.571761i	0.950584	+	0.310469i	$0.100486\pi$
$462$		0			0
$463$	0.124840	+	0.708003i	0.00580181	+	0.0329037i	0.987571	−	0.157172i	$-0.0502377\pi$
$463$	0.124840	+	0.708003i	0.00580181	+	0.0329037i	−0.981769	+	0.190076i	$0.939127\pi$
$464$	22.1571	+	8.75192i	1.02862	+	0.406298i
$465$		0			0
$466$	18.5816	−	28.7354i	0.860774	−	1.33114i
$467$	16.8793	+	9.74528i	0.781082	+	0.450958i	0.836814	−	0.547488i	$-0.184416\pi$
$467$	16.8793	+	9.74528i	0.781082	+	0.450958i	−0.0557318	+	0.998446i	$0.517749\pi$
$468$		0			0
$469$	0.0340678	−	0.0196690i	0.00157310	−	0.000908231i
$470$	2.22456	−	44.0896i	0.102611	−	2.03370i
$471$		0			0
$472$	8.91015	−	16.2981i	0.410123	−	0.750183i
$473$	−3.20859	+	2.69233i	−0.147531	+	0.123794i
$474$		0			0
$475$	15.6530	+	43.0062i	0.718207	+	1.97326i
$476$	−0.0105511	+	0.0373444i	−0.000483610	+	0.00171168i
$477$		0			0
$478$	−34.0166	+	25.7373i	−1.55588	+	1.17720i
$479$	−1.69552	+	9.61575i	−0.0774701	+	0.439355i	0.921259	+	0.388950i	$0.127162\pi$
$479$	−1.69552	+	9.61575i	−0.0774701	+	0.439355i	−0.998729	+	0.0504046i	$0.983949\pi$
$480$		0			0
$481$	28.9304	+	10.5298i	1.31911	+	0.480118i
$482$	0.789623	−	3.45087i	0.0359663	−	0.157183i
$483$		0			0
$484$	1.47127	+	19.9248i	0.0668760	+	0.905672i
$485$		−	50.4227i		−	2.28958i
$486$		0			0
$487$	−40.7197			−1.84519			−0.922594	−	0.385773i	$-0.873935\pi$
$487$	−40.7197			−1.84519			−0.922594	+	0.385773i	$0.873935\pi$
$488$	0.290701	+	0.0982007i	0.0131594	+	0.00444534i
$489$		0			0
$490$	−38.0338	−	8.70284i	−1.71819	−	0.393154i
$491$	−4.27622	+	11.7488i	−0.192983	+	0.530217i	−0.998012	−	0.0630180i	$-0.979927\pi$
$491$	−4.27622	+	11.7488i	−0.192983	+	0.530217i	0.805029	+	0.593235i	$0.202150\pi$
$492$		0			0
$493$	−11.1321	−	1.96289i	−0.501365	−	0.0884041i
$494$	19.6203	−	14.8450i	0.882761	−	0.667907i
$495$		0			0
$496$	28.0520	−	15.1969i	1.25957	−	0.682362i
$497$	−0.00850497	+	0.00309555i	−0.000381500	+	0.000138855i
$498$		0			0
$499$	2.94192	+	3.50604i	0.131698	+	0.156952i	0.827863	−	0.560930i	$-0.189556\pi$
$499$	2.94192	+	3.50604i	0.131698	+	0.156952i	−0.696165	+	0.717882i	$0.745112\pi$
$500$	−4.39106	+	43.4035i	−0.196374	+	1.94106i
$501$		0			0
$502$	1.19341	−	23.6527i	0.0532644	−	1.05567i
$503$	9.68900	+	16.7818i	0.432011	+	0.748265i	0.997046	−	0.0768015i	$-0.0244708\pi$
$503$	9.68900	+	16.7818i	0.432011	+	0.748265i	−0.565035	+	0.825067i	$0.691137\pi$
$504$		0			0
$505$	−16.5134	+	28.6020i	−0.734836	+	1.27277i
$506$	−8.23081	−	5.32240i	−0.365904	−	0.236609i
$507$		0			0
$508$	−1.20353	−	2.67508i	−0.0533979	−	0.118688i
$509$	−2.30682	+	0.406755i	−0.102248	+	0.0180291i	−0.224538	−	0.974465i	$-0.572087\pi$
$509$	−2.30682	+	0.406755i	−0.102248	+	0.0180291i	0.122290	+	0.992494i	$0.460976\pi$
$510$		0			0
$511$	0.113729	+	0.0954301i	0.00503108	+	0.00422158i
$512$	−20.3381	−	9.91776i	−0.898825	−	0.438307i
$513$		0			0
$514$	34.8437	+	14.7103i	1.53689	+	0.648842i
$515$	−17.6105	+	20.9874i	−0.776014	+	0.924817i
$516$		0			0
$517$	7.84049	−	1.38249i	0.344824	−	0.0608018i
$518$	0.0756484	−	0.0814404i	0.00332380	−	0.00357829i
$519$		0			0
$520$	43.7701	−	8.77368i	1.91944	−	0.384751i
$521$	3.33988	−	5.78485i	0.146323	−	0.253439i	−0.783543	−	0.621338i	$-0.786589\pi$
$521$	3.33988	−	5.78485i	0.146323	−	0.253439i	0.929866	+	0.367899i	$0.119923\pi$
$522$		0			0
$523$	−25.4719	+	14.7062i	−1.11381	+	0.643057i	−0.939813	−	0.341690i	$-0.889001\pi$
$523$	−25.4719	+	14.7062i	−1.11381	+	0.643057i	−0.173994	+	0.984747i	$0.555667\pi$
$524$	−9.92422	+	20.5504i	−0.433542	+	0.897749i
$525$		0			0
$526$	5.93357	−	1.82672i	0.258716	−	0.0796486i
$527$	−11.5965	+	9.73065i	−0.505153	+	0.423874i
$528$		0			0
$529$	−23.0590	+	8.39280i	−1.00257	+	0.364904i
$530$	−1.55655	−	12.4762i	−0.0676122	−	0.541932i
$531$		0			0
$532$	−0.0218251	−	0.0861056i	−0.000946236	−	0.00373315i
$533$	−22.8959	−	4.03716i	−0.991731	−	0.174869i
$534$		0			0
$535$	−52.8718	−	19.2438i	−2.28585	−	0.831980i
$536$	−5.65991	−	9.29623i	−0.244471	−	0.401536i
$537$		0			0
$538$	0.932850	−	0.477601i	0.0402180	−	0.0205908i
$539$		−	7.03648i		−	0.303083i
$540$		0			0
$541$		−	1.09392i		−	0.0470312i	−0.999723	−	0.0235156i	$-0.992514\pi$
$541$		−	1.09392i		−	0.0470312i	0.999723	−	0.0235156i	$-0.00748594\pi$
$542$	−9.11631	−	17.8060i	−0.391579	−	0.764832i
$543$		0			0
$544$	10.3973	+	2.67773i	0.445780	+	0.114807i
$545$	−18.0896	−	6.58409i	−0.774875	−	0.282031i
$546$		0			0
$547$	11.4033	+	2.01070i	0.487568	+	0.0859714i	0.412028	−	0.911171i	$-0.364821\pi$
$547$	11.4033	+	2.01070i	0.487568	+	0.0859714i	0.0755403	+	0.997143i	$0.475932\pi$
$548$	8.27914	−	2.09850i	0.353667	−	0.0896435i
$549$		0			0
$550$	−14.8604	+	1.85400i	−0.633648	+	0.0790549i
$551$	24.3143	−	8.84968i	1.03582	−	0.377009i
$552$		0			0
$553$	0.0251814	−	0.0211297i	0.00107082	−	0.000898528i
$554$	3.56063	+	11.5657i	0.151277	+	0.491379i
$555$		0			0
$556$	−0.926368	+	1.91826i	−0.0392867	+	0.0813523i
$557$	−11.9979	+	6.92697i	−0.508366	+	0.293505i	−0.732162	−	0.681131i	$-0.761488\pi$
$557$	−11.9979	+	6.92697i	−0.508366	+	0.293505i	0.223796	+	0.974636i	$0.428155\pi$
$558$		0			0
$559$	8.34273	−	14.4500i	0.352860	−	0.611171i
$560$	0.0322805	−	0.157905i	0.00136410	−	0.00667272i
$561$		0			0
$562$	19.4601	+	18.0762i	0.820876	+	0.762496i
$563$	29.5384	−	5.20841i	1.24489	−	0.219508i	0.487882	−	0.872910i	$-0.337770\pi$
$563$	29.5384	−	5.20841i	1.24489	−	0.219508i	0.757012	+	0.653401i	$0.226659\pi$
$564$		0			0
$565$	11.3359	−	13.5096i	0.476903	−	0.568351i
$566$	14.1393	−	33.4912i	0.594318	−	1.40774i
$567$		0			0
$568$	0.911026	+	2.33249i	0.0382258	+	0.0978690i
$569$	13.1491	+	11.0334i	0.551241	+	0.462546i	0.875361	−	0.483470i	$-0.160624\pi$
$569$	13.1491	+	11.0334i	0.551241	+	0.462546i	−0.324120	+	0.946016i	$0.605068\pi$
$570$		0			0
$571$	16.7116	−	2.94670i	0.699357	−	0.123316i	0.187346	−	0.982294i	$-0.440012\pi$
$571$	16.7116	−	2.94670i	0.699357	−	0.123316i	0.512012	+	0.858978i	$0.328900\pi$
$572$	3.30314	+	7.34189i	0.138111	+	0.306980i
$573$		0			0
$574$	−0.0455791	+	0.0704858i	−0.00190244	+	0.00294202i
$575$	−36.3161	+	62.9013i	−1.51449	+	2.62317i
$576$		0			0
$577$	−4.49809	−	7.79092i	−0.187258	−	0.324340i	0.757077	−	0.653326i	$-0.226627\pi$
$577$	−4.49809	−	7.79092i	−0.187258	−	0.324340i	−0.944335	+	0.328985i	$0.893293\pi$
$578$	18.9231	+	0.954775i	0.787098	+	0.0397134i
$579$		0			0
$580$	46.7089	+	4.72547i	1.93948	+	0.196214i
$581$	−0.0998698	−	0.119020i	−0.00414330	−	0.00493779i
$582$		0			0
$583$	2.13072	−	0.775517i	0.0882453	−	0.0321186i
$584$	25.6626	−	32.0720i	1.06193	−	1.32715i
$585$		0			0
$586$	−12.4478	−	16.4520i	−0.514212	−	0.679626i
$587$	29.2734	+	5.16169i	1.20824	+	0.213046i	0.741258	−	0.671220i	$-0.234229\pi$
$587$	29.2734	+	5.16169i	1.20824	+	0.213046i	0.466984	+	0.884266i	$0.345340\pi$
$588$		0			0
$589$	11.8516	−	32.5619i	0.488336	−	1.34169i
$590$	8.16482	−	35.6826i	0.336140	−	1.46903i
$591$		0			0
$592$	−23.0136	−	20.3992i	−0.945851	−	0.838401i
$593$	21.5451			0.884750			0.442375	−	0.896830i	$-0.354136\pi$
$593$	21.5451			0.884750			0.442375	+	0.896830i	$0.354136\pi$
$594$		0			0
$595$			0.0764747i			0.00313516i
$596$	4.16535	−	0.307574i	0.170619	−	0.0125987i
$597$		0			0
$598$	38.0626	+	8.70942i	1.55650	+	0.356155i
$599$	10.2586	+	3.73384i	0.419156	+	0.152560i	0.542983	−	0.839743i	$-0.317295\pi$
$599$	10.2586	+	3.73384i	0.419156	+	0.152560i	−0.123827	+	0.992304i	$0.539517\pi$
$600$		0			0
$601$	−2.62710	+	14.8990i	−0.107162	+	0.607744i	0.883173	+	0.469047i	$0.155403\pi$
$601$	−2.62710	+	14.8990i	−0.107162	+	0.607744i	−0.990335	+	0.138697i	$0.955709\pi$
$602$	−0.0363477	−	0.0480401i	−0.00148142	−	0.00195797i
$603$		0			0
$604$	−5.72879	+	20.2763i	−0.233101	+	0.825032i
$605$	13.4661	+	36.9978i	0.547475	+	1.50417i
$606$		0			0
$607$	−18.8283	+	15.7988i	−0.764216	+	0.641253i	−0.939221	−	0.343314i	$-0.888450\pi$
$607$	−18.8283	+	15.7988i	−0.764216	+	0.641253i	0.175005	+	0.984568i	$0.444006\pi$
$608$	−23.6758	+	6.59161i	−0.960179	+	0.267325i
$609$		0			0
$610$	0.603913	+	0.0304707i	0.0244517	+	0.00123372i
$611$	−27.4663	+	15.8577i	−1.11117	+	0.641532i
$612$		0			0
$613$	15.6018	+	9.00768i	0.630149	+	0.363817i	0.780810	−	0.624769i	$-0.214807\pi$
$613$	15.6018	+	9.00768i	0.630149	+	0.363817i	−0.150661	+	0.988586i	$0.548140\pi$
$614$	−11.0741	−	7.16098i	−0.446914	−	0.288994i
$615$		0			0
$616$	0.0290585		0.000677033i	0.00117080		2.72784e-5i
$617$	4.06887	+	23.0757i	0.163807	+	0.928994i	0.950286	+	0.311378i	$0.100790\pi$
$617$	4.06887	+	23.0757i	0.163807	+	0.928994i	−0.786480	+	0.617616i	$0.788098\pi$
$618$		0			0
$619$	21.6871	−	25.8457i	0.871679	−	1.03883i	−0.127219	−	0.991875i	$-0.540605\pi$
$619$	21.6871	−	25.8457i	0.871679	−	1.03883i	0.998897	−	0.0469514i	$-0.0149506\pi$
$620$	45.0561	−	43.8506i	1.80950	−	1.76108i
$621$		0			0
$622$	10.4640	+	4.41769i	0.419569	+	0.177133i
$623$	−0.0227676	−	0.0191043i	−0.000912166	−	0.000765398i
$624$		0			0
$625$	5.78239	+	32.7936i	0.231296	+	1.31174i
$626$	34.2592	+	31.8227i	1.36927	+	1.27189i
$627$		0			0
$628$	−25.0523	−	36.8313i	−0.999695	−	1.46973i
$629$	12.6372	+	7.29606i	0.503876	+	0.290913i
$630$		0			0
$631$	−3.55095	−	6.15043i	−0.141361	−	0.244845i	0.786648	−	0.617401i	$-0.211815\pi$
$631$	−3.55095	−	6.15043i	−0.141361	−	0.244845i	−0.928009	+	0.372557i	$0.878481\pi$
$632$	−6.00667	−	6.82890i	−0.238932	−	0.271639i
$633$		0			0
$634$	10.8472	+	35.2340i	0.430797	+	1.39932i
$635$	−3.71575	−	4.42826i	−0.147455	−	0.175730i
$636$		0			0
$637$	9.58703	+	26.3402i	0.379852	+	1.04363i
$638$	1.04819	+	8.40157i	0.0414983	+	0.332621i
$639$		0			0
$640$	−43.8840	−	7.91104i	−1.73467	−	0.312711i
$641$	0.826096	−	4.68502i	0.0326288	−	0.185047i	−0.964137	−	0.265404i	$-0.914495\pi$
$641$	0.826096	−	4.68502i	0.0326288	−	0.185047i	0.996766	+	0.0803565i	$0.0256059\pi$
$642$		0			0
$643$	5.88956	−	16.1814i	0.232262	−	0.638134i	−0.767735	−	0.640768i	$-0.778616\pi$
$643$	5.88956	−	16.1814i	0.232262	−	0.638134i	0.999997	+	0.00263392i	$0.000838403\pi$
$644$	0.0824172	−	0.114372i	0.00324769	−	0.00450687i
$645$		0			0
$646$	10.3799	−	5.31433i	0.408393	−	0.209089i
$647$	−38.9704			−1.53208			−0.766042	−	0.642791i	$-0.777776\pi$
$647$	−38.9704			−1.53208			−0.766042	+	0.642791i	$0.777776\pi$
$648$		0			0
$649$	6.60148			0.259131
$650$	53.1018	−	27.1871i	2.08282	−	1.06637i
$651$		0			0
$652$	−14.0285	−	10.1091i	−0.549399	−	0.395902i
$653$	7.50821	−	20.6286i	0.293819	−	0.807261i	−0.701680	−	0.712492i	$-0.747566\pi$
$653$	7.50821	−	20.6286i	0.293819	−	0.807261i	0.995499	−	0.0947692i	$-0.0302113\pi$
$654$		0			0
$655$	−7.80953	+	44.2901i	−0.305144	+	1.73056i
$656$	19.7898	+	12.1527i	0.772661	+	0.474485i
$657$		0			0
$658$	0.0141759	+	0.113624i	0.000552636	+	0.00442953i
$659$	−10.8064	−	29.6905i	−0.420960	−	1.15658i	−0.951158	−	0.308703i	$-0.900105\pi$
$659$	−10.8064	−	29.6905i	−0.420960	−	1.15658i	0.530199	−	0.847873i	$-0.322117\pi$
$660$		0			0
$661$	0.564964	+	0.673298i	0.0219746	+	0.0261883i	0.776920	−	0.629600i	$-0.216781\pi$
$661$	0.564964	+	0.673298i	0.0219746	+	0.0261883i	−0.754945	+	0.655788i	$0.772337\pi$
$662$	−1.15458	−	3.75033i	−0.0448741	−	0.145761i
$663$		0			0
$664$	−32.2768	+	28.3905i	−1.25258	+	1.10177i
$665$	−0.0875262	−	0.151600i	−0.00339412	−	0.00587879i
$666$		0			0
$667$	35.5624	+	20.5319i	1.37698	+	0.795000i
$668$	−13.9584	+	9.49435i	−0.540066	+	0.367347i
$669$		0			0
$670$	−15.7147	−	14.5971i	−0.607111	−	0.563934i
$671$	0.0189365	+	0.107394i	0.000731036	+	0.00414591i
$672$		0			0
$673$	2.60760	+	2.18804i	0.100516	+	0.0843426i	0.691661	−	0.722223i	$-0.256879\pi$
$673$	2.60760	+	2.18804i	0.100516	+	0.0843426i	−0.591145	+	0.806565i	$0.701324\pi$
$674$	−17.0632	−	7.20371i	−0.657249	−	0.277477i
$675$		0			0
$676$	−4.23421	−	4.35062i	−0.162854	−	0.167331i
$677$	−12.0910	+	14.4095i	−0.464695	+	0.553802i	−0.946595	−	0.322424i	$-0.895502\pi$
$677$	−12.0910	+	14.4095i	−0.464695	+	0.553802i	0.481900	+	0.876226i	$0.339947\pi$
$678$		0			0
$679$	0.0227108	+	0.128799i	0.000871561	+	0.00494287i
$680$	21.1526	−	0.492833i	0.811163	−	0.0188993i
$681$		0			0
$682$	9.52143	+	6.15696i	0.364594	+	0.235762i
$683$	19.4488	+	11.2288i	0.744188	+	0.429657i	0.823590	−	0.567186i	$-0.191968\pi$
$683$	19.4488	+	11.2288i	0.744188	+	0.429657i	−0.0794021	+	0.996843i	$0.525301\pi$
$684$		0			0
$685$	14.5765	−	8.41573i	0.556938	−	0.321548i
$686$	0.202148	+	0.0101995i	0.00771805	+	0.000389418i
$687$		0			0
$688$	−13.0534	+	10.3632i	−0.497658	+	0.395093i
$689$	−6.91944	+	5.80610i	−0.263610	+	0.221195i
$690$		0			0
$691$	−14.6665	−	40.2960i	−0.557941	−	1.53293i	−0.822618	−	0.568594i	$-0.807488\pi$
$691$	−14.6665	−	40.2960i	−0.557941	−	1.53293i	0.264677	−	0.964337i	$-0.414735\pi$
$692$	26.1674	+	7.39323i	0.994737	+	0.281049i
$693$		0			0
$694$	12.3785	+	16.3605i	0.469882	+	0.621034i
$695$	−0.728974	+	4.13422i	−0.0276515	+	0.156820i
$696$		0			0
$697$	−10.3548	−	3.76883i	−0.392215	−	0.142755i
$698$	−32.2230	−	7.37320i	−1.21966	−	0.279080i
$699$		0			0
$700$	−0.0158612	−	0.214801i	−0.000599495	−	0.00811870i
$701$			30.9274i			1.16811i	0.811714	+	0.584055i	$0.198535\pi$
$701$			30.9274i			1.16811i	−0.811714	+	0.584055i	$0.801465\pi$
$702$		0			0
$703$	−33.4017			−1.25977
$704$	−0.374529	−	8.03308i	−0.0141156	−	0.302758i
$705$		0			0
$706$	−10.7797	+	47.1103i	−0.405699	+	1.77302i
$707$	0.0292991	−	0.0804987i	0.00110191	−	0.00302746i
$708$		0			0
$709$	10.5402	+	1.85852i	0.395845	+	0.0697982i	0.368028	−	0.929815i	$-0.380033\pi$
$709$	10.5402	+	1.85852i	0.395845	+	0.0697982i	0.0278175	+	0.999613i	$0.491144\pi$
$710$	2.97747	+	3.93528i	0.111743	+	0.147688i
$711$		0			0
$712$	−5.13744	+	6.42054i	−0.192534	+	0.240620i
$713$	51.6766	−	18.8088i	1.93531	−	0.704394i
$714$		0			0
$715$	10.1981	+	12.1536i	0.381386	+	0.454518i
$716$	−0.0597837	+	0.590932i	−0.00223422	+	0.0220842i
$717$		0			0
$718$	38.2456	+	1.92970i	1.42731	+	0.0720158i
$719$	−7.98318	−	13.8273i	−0.297723	−	0.515671i	0.677892	−	0.735161i	$-0.262894\pi$
$719$	−7.98318	−	13.8273i	−0.297723	−	0.515671i	−0.975615	+	0.219491i	$0.929560\pi$
$720$		0			0
$721$	0.0355314	−	0.0615422i	0.00132326	−	0.00229195i
$722$	0.0961969	−	0.148764i	0.00358008	−	0.00553641i
$723$		0			0
$724$	3.44607	−	1.55040i	0.128072	−	0.0576201i
$725$	61.7861	−	10.8946i	2.29468	−	0.404614i
$726$		0			0
$727$	18.0652	+	15.1585i	0.670002	+	0.562198i	0.913066	−	0.407812i	$-0.133708\pi$
$727$	18.0652	+	15.1585i	0.670002	+	0.562198i	−0.243064	+	0.970010i	$0.578153\pi$
$728$	−0.107854	+	0.0421259i	−0.00399735	+	0.00156129i
$729$		0			0
$730$	31.4830	−	74.5728i	1.16524	−	2.76006i
$731$	5.08341	−	6.05817i	0.188017	−	0.224069i
$732$		0			0
$733$	5.12011	−	0.902813i	0.189115	−	0.0333462i	−0.0782882	−	0.996931i	$-0.524945\pi$
$733$	5.12011	−	0.902813i	0.189115	−	0.0333462i	0.267404	+	0.963585i	$0.413834\pi$
$734$	4.74536	+	4.40788i	0.175155	+	0.162698i
$735$		0			0
$736$	−32.1658	−	22.0592i	−1.18565	−	0.813112i
$737$	1.93404	−	3.34985i	0.0712412	−	0.123393i
$738$		0			0
$739$	10.5638	−	6.09903i	0.388596	−	0.224356i	−0.292955	−	0.956126i	$-0.594639\pi$
$739$	10.5638	−	6.09903i	0.388596	−	0.224356i	0.681552	+	0.731770i	$0.261305\pi$
$740$	−54.5739	−	26.3549i	−2.00617	−	0.968824i
$741$		0			0
$742$	0.00959544	+	0.0311681i	0.000352260	+	0.00114422i
$743$	11.5486	−	9.69040i	0.423676	−	0.355506i	−0.405883	−	0.913925i	$-0.633036\pi$
$743$	11.5486	−	9.69040i	0.423676	−	0.355506i	0.829559	+	0.558419i	$0.188592\pi$
$744$		0			0
$745$	7.73451	−	2.81513i	0.283371	−	0.103138i
$746$	−24.0683	+	3.00279i	−0.881202	+	0.109940i
$747$		0			0
$748$	0.937534	+	3.69882i	0.0342796	+	0.135242i
$749$	0.143723	+	0.0253422i	0.00525153	+	0.000925986i
$750$		0			0
$751$	−1.35242	−	0.492239i	−0.0493504	−	0.0179621i	0.317227	−	0.948350i	$-0.397248\pi$
$751$	−1.35242	−	0.492239i	−0.0493504	−	0.0179621i	−0.366577	+	0.930388i	$0.619471\pi$
$752$	31.3366	−	4.65324i	1.14273	−	0.169686i
$753$		0			0
$754$	−15.3707	−	30.0220i	−0.559768	−	1.09334i
$755$			41.5223i			1.51115i
$756$		0			0
$757$			15.3476i			0.557818i	0.960318	+	0.278909i	$0.0899727\pi$
$757$			15.3476i			0.557818i	−0.960318	+	0.278909i	$0.910027\pi$
$758$	−0.479199	+	0.245340i	−0.0174053	+	0.00891116i
$759$		0			0
$760$	−41.3678	+	25.1863i	−1.50057	+	0.913603i
$761$	3.86991	+	1.40853i	0.140284	+	0.0510593i	0.411208	−	0.911541i	$-0.365107\pi$
$761$	3.86991	+	1.40853i	0.140284	+	0.0510593i	−0.270924	+	0.962601i	$0.587329\pi$
$762$		0			0
$763$	0.0491736	+	0.00867063i	0.00178020	+	0.000313898i
$764$	27.0534	−	6.85719i	0.978759	−	0.248084i
$765$		0			0
$766$	−6.45961	−	51.7757i	−0.233395	−	1.87073i
$767$	−24.7118	+	8.99435i	−0.892291	+	0.324767i
$768$		0			0
$769$	36.4911	−	30.6197i	1.31590	−	1.10417i	0.328748	−	0.944418i	$-0.393373\pi$
$769$	36.4911	−	30.6197i	1.31590	−	1.10417i	0.987156	−	0.159757i	$-0.0510710\pi$
$770$	0.0547448	−	0.0168538i	0.00197287	−	0.000607369i
$771$		0			0
$772$	−17.1679	−	8.29075i	−0.617887	−	0.298391i
$773$	−4.04314	+	2.33431i	−0.145422	+	0.0839592i	−0.570945	−	0.820988i	$-0.693423\pi$
$773$	−4.04314	+	2.33431i	−0.145422	+	0.0839592i	0.425524	+	0.904947i	$0.360090\pi$
$774$		0			0
$775$	42.0105	−	72.7644i	1.50906	−	2.61377i
$776$	35.4790	−	7.11174i	1.27362	−	0.255297i
$777$		0			0
$778$	−6.88494	+	7.41208i	−0.246837	+	0.265736i
$779$	24.8403	−	4.38001i	0.889996	−	0.156930i
$780$		0			0
$781$	−0.572053	+	0.681746i	−0.0204697	+	0.0243948i
$782$	17.0496	+	7.19797i	0.609692	+	0.257399i
$783$		0			0
$784$	0.759198	−	27.9893i	0.0271142	−	0.999617i
$785$	−67.2447	−	56.4250i	−2.40007	−	2.01390i
$786$		0			0
$787$	−16.1106	+	2.84073i	−0.574279	+	0.101261i	−0.453243	−	0.891387i	$-0.649733\pi$
$787$	−16.1106	+	2.84073i	−0.574279	+	0.101261i	−0.121037	+	0.992648i	$0.538622\pi$
$788$	−16.0281	+	7.21111i	−0.570979	+	0.256885i
$789$		0			0
$790$	−15.0503	−	9.73215i	−0.535465	−	0.346254i
$791$	−0.0228715	+	0.0396145i	−0.000813215	+	0.00140853i
$792$		0			0
$793$	−0.217209	−	0.376216i	−0.00771330	−	0.0133598i
$794$	−1.86784	+	37.0196i	−0.0662872	+	1.31378i
$795$		0			0
$796$	−18.7439	−	1.89630i	−0.664362	−	0.0672125i
$797$	6.71611	+	8.00395i	0.237897	+	0.283514i	0.871762	−	0.489929i	$-0.162977\pi$
$797$	6.71611	+	8.00395i	0.237897	+	0.283514i	−0.633866	+	0.773443i	$0.718533\pi$
$798$		0			0
$799$	−14.1255	+	5.14126i	−0.499725	+	0.181885i
$800$	−59.3107	+	5.77138i	−2.09695	+	0.204049i
$801$		0			0
$802$	19.4885	−	14.7452i	0.688164	−	0.520672i
$803$	14.3764	+	2.53495i	0.507333	+	0.0894566i
$804$		0			0
$805$	0.0950175	−	0.261058i	0.00334893	−	0.00920110i
$806$	−44.0310	−	10.0751i	−1.55092	−	0.354880i
$807$		0			0
$808$	−22.4544	−	7.58524i	−0.789942	−	0.266848i
$809$	−5.87774			−0.206650			−0.103325	−	0.994648i	$-0.532948\pi$
$809$	−5.87774			−0.206650			−0.103325	+	0.994648i	$0.532948\pi$
$810$		0			0
$811$			40.3341i			1.41632i	0.706052	+	0.708160i	$0.250475\pi$
$811$			40.3341i			1.41632i	−0.706052	+	0.708160i	$0.749525\pi$
$812$	−0.121441	+	0.00896738i	−0.00426176	+	0.000314693i
$813$		0			0
$814$	2.43790	−	10.6543i	0.0854484	−	0.373433i
$815$	−32.0208	−	11.6546i	−1.12164	−	0.408243i
$816$		0			0
$817$	−3.14346	+	17.8274i	−0.109976	+	0.623703i
$818$	27.7371	−	20.9862i	0.969803	−	0.733764i
$819$		0			0
$820$	44.0416	+	12.4433i	1.53800	+	0.434540i
$821$	8.31903	+	22.8563i	0.290336	+	0.797692i	0.996017	+	0.0891622i	$0.0284190\pi$
$821$	8.31903	+	22.8563i	0.290336	+	0.797692i	−0.705681	+	0.708530i	$0.749359\pi$
$822$		0			0
$823$	−22.0384	+	18.4924i	−0.768211	+	0.644605i	−0.940250	−	0.340485i	$-0.889409\pi$
$823$	−22.0384	+	18.4924i	−0.768211	+	0.644605i	0.172039	+	0.985090i	$0.444964\pi$
$824$	−17.2513	−	9.43122i	−0.600976	−	0.328552i
$825$		0			0
$826$	−0.00478443	+	0.0948249i	−0.000166472	+	0.00329938i
$827$	−12.6598	+	7.30915i	−0.440225	+	0.254164i	−0.703693	−	0.710504i	$-0.748467\pi$
$827$	−12.6598	+	7.30915i	−0.440225	+	0.254164i	0.263468	+	0.964668i	$0.415134\pi$
$828$		0			0
$829$	38.2098	+	22.0604i	1.32708	+	0.766191i	0.984847	−	0.173424i	$-0.0554830\pi$
$829$	38.2098	+	22.0604i	1.32708	+	0.766191i	0.342234	+	0.939615i	$0.388816\pi$
$830$	−45.9990	+	71.1351i	−1.59665	+	2.46914i
$831$		0			0
$832$	12.3469	+	29.5605i	0.428051	+	1.02483i
$833$	2.30702	+	13.0838i	0.0799336	+	0.453326i
$834$		0			0
$835$	−21.3840	+	25.4845i	−0.740025	+	0.881927i
$836$	−6.09186	−	6.25934i	−0.210691	−	0.216484i
$837$		0			0
$838$	−7.58939	+	17.9767i	−0.262171	+	0.620995i
$839$	28.2388	+	23.6951i	0.974911	+	0.818047i	0.983314	−	0.181917i	$-0.0582303\pi$
$839$	28.2388	+	23.6951i	0.974911	+	0.818047i	−0.00840301	+	0.999965i	$0.502675\pi$
$840$		0			0
$841$	−1.12364	−	6.37246i	−0.0387461	−	0.219740i
$842$	35.1844	−	37.8782i	1.21253	−	1.30537i
$843$		0			0
$844$	13.5683	+	19.9478i	0.467038	+	0.686630i
$845$	−10.3610	−	5.98194i	−0.356430	−	0.205785i
$846$		0			0
$847$	−0.0510619	−	0.0884417i	−0.00175451	−	0.00303889i
$848$	8.55911	−	2.85491i	0.293921	−	0.0980381i
$849$		0			0
$850$	27.0238	−	8.31958i	0.926909	−	0.285359i
$851$	−34.0738	−	40.6075i	−1.16803	−	1.39201i
$852$		0			0
$853$	12.7574	+	35.0506i	0.436804	+	1.20011i	0.941560	+	0.336846i	$0.109360\pi$
$853$	12.7574	+	35.0506i	0.436804	+	1.20011i	−0.504756	+	0.863262i	$0.668417\pi$
$854$	−0.00155636		0.000194174i	−5.32574e−5		6.64448e-6i
$855$		0			0
$856$	6.08334	−	39.9165i	0.207924	−	1.36432i
$857$	2.38265	−	13.5127i	0.0813899	−	0.461585i	−0.916687	−	0.399605i	$-0.869147\pi$
$857$	2.38265	−	13.5127i	0.0813899	−	0.461585i	0.998077	−	0.0619803i	$-0.0197416\pi$
$858$		0			0
$859$	10.4655	−	28.7538i	0.357079	−	0.981067i	−0.622958	−	0.782255i	$-0.714069\pi$
$859$	10.4655	−	28.7538i	0.357079	−	0.981067i	0.980038	−	0.198812i	$-0.0637083\pi$
$860$	−19.2023	+	26.6473i	−0.654794	+	0.908667i
$861$		0			0
$862$	−4.79981	−	9.37498i	−0.163482	−	0.319313i
$863$	7.80840			0.265801			0.132900	−	0.991129i	$-0.457571\pi$
$863$	7.80840			0.265801			0.132900	+	0.991129i	$0.457571\pi$
$864$		0			0
$865$	53.5863			1.82199
$866$	13.4961	+	26.3606i	0.458616	+	0.895768i
$867$		0			0
$868$	−0.0953405	+	0.132305i	−0.00323607	+	0.00449074i
$869$	1.10550	−	3.03735i	0.0375016	−	0.103035i
$870$		0			0
$871$	−2.67573	+	15.1748i	−0.0906636	+	0.514179i
$872$	2.08136	−	13.6571i	0.0704839	−	0.462487i
$873$		0			0
$874$	−42.0364	+	5.24453i	−1.42190	+	0.177399i
$875$	−0.0762675	−	0.209543i	−0.00257831	−	0.00708385i
$876$		0			0
$877$	−22.5373	−	26.8589i	−0.761029	−	0.906959i	0.236883	−	0.971538i	$-0.423874\pi$
$877$	−22.5373	−	26.8589i	−0.761029	−	0.906959i	−0.997913	+	0.0645787i	$0.979430\pi$
$878$	38.0273	−	11.7071i	1.28336	−	0.395096i
$879$		0			0
$880$	−5.01448	−	15.0336i	−0.169038	−	0.506781i
$881$	17.3596	+	30.0677i	0.584859	+	1.01301i	0.994893	+	0.100936i	$0.0321836\pi$
$881$	17.3596	+	30.0677i	0.584859	+	1.01301i	−0.410034	+	0.912070i	$0.634483\pi$
$882$		0			0
$883$	−48.4749	−	27.9870i	−1.63131	−	0.941837i	−0.983690	−	0.179874i	$-0.942431\pi$
$883$	−48.4749	−	27.9870i	−1.63131	−	0.941837i	−0.647620	−	0.761963i	$-0.724236\pi$
$884$	−8.54909	−	12.5687i	−0.287537	−	0.422731i
$885$		0			0
$886$	−16.8402	+	18.1295i	−0.565756	+	0.609073i
$887$	−5.13500	−	29.1221i	−0.172417	−	0.977823i	−0.941084	−	0.338174i	$-0.890191\pi$
$887$	−5.13500	−	29.1221i	−0.172417	−	0.977823i	0.768667	−	0.639649i	$-0.220920\pi$
$888$		0			0
$889$	0.0114860	+	0.00963792i	0.000385229	+	0.000323245i
$890$	−6.30264	+	14.9289i	−0.211265	+	0.500416i
$891$		0			0
$892$	4.95104	+	5.08716i	0.165773	+	0.170331i
$893$	22.1175	−	26.3586i	0.740134	−	0.882057i
$894$		0			0
$895$	0.203252	+	1.15270i	0.00679396	+	0.0385305i
$896$	0.115660		0.000442194i	0.00386394		1.47726e-5i
$897$		0			0
$898$	−4.59767	+	7.11007i	−0.153426	+	0.237266i
$899$	−41.1386	−	23.7514i	−1.37205	−	0.792154i
$900$		0			0
$901$	−3.70763	+	2.14060i	−0.123519	+	0.0713138i
$902$	−0.415911	+	8.24312i	−0.0138483	+	0.274466i
$903$		0			0
$904$	11.1046	+	6.07085i	0.369333	+	0.201913i
$905$	5.70454	−	4.78668i	0.189625	−	0.159115i
$906$		0			0
$907$	11.8324	+	32.5093i	0.392889	+	1.07945i	0.965676	+	0.259749i	$0.0836399\pi$
$907$	11.8324	+	32.5093i	0.392889	+	1.07945i	−0.572787	+	0.819704i	$0.694138\pi$
$908$	20.9373	+	5.91553i	0.694829	+	0.196314i
$909$		0			0
$910$	−0.181967	+	0.137679i	−0.00603216	+	0.00456400i
$911$	2.10465	−	11.9361i	0.0697303	−	0.395460i	−0.929888	−	0.367842i	$-0.880097\pi$
$911$	2.10465	−	11.9361i	0.0697303	−	0.395460i	0.999619	−	0.0276180i	$-0.00879219\pi$
$912$		0			0
$913$	−14.3560	−	5.22516i	−0.475115	−	0.172928i
$914$	−7.67066	+	33.5230i	−0.253723	+	1.10884i
$915$		0			0
$916$	−15.6727	+	1.15729i	−0.517842	+	0.0382381i
$917$		−	0.116652i		−	0.00385218i
$918$		0			0
$919$	11.2018			0.369514			0.184757	−	0.982784i	$-0.440850\pi$
$919$	11.2018			0.369514			0.184757	+	0.982784i	$0.440850\pi$
$920$	−72.8199	−	24.5991i	−2.40080	−	0.811007i
$921$		0			0
$922$	22.0925	+	5.05516i	0.727577	+	0.166483i
$923$	1.21254	−	3.33144i	0.0399114	−	0.109656i
$924$		0			0
$925$	−79.7598	−	14.0638i	−2.62249	−	0.462415i
$926$	−0.810790	+	0.613453i	−0.0266442	+	0.0201593i
$927$		0			0
$928$	3.26295	+	33.5323i	0.107112	+	1.10075i
$929$	−33.5582	+	12.2142i	−1.10101	+	0.400734i	−0.827687	−	0.561189i	$-0.810344\pi$
$929$	−33.5582	+	12.2142i	−1.10101	+	0.400734i	−0.273320	+	0.961923i	$0.588122\pi$
$930$		0			0
$931$	−19.5479	−	23.2962i	−0.640656	−	0.763504i
$932$	48.1484	+	4.87110i	1.57715	+	0.159558i
$933$		0			0
$934$	−1.38898	+	27.5288i	−0.0454488	+	0.900770i
$935$	3.75984	+	6.51224i	0.122960	+	0.212973i
$936$		0			0
$937$	−13.9023	+	24.0795i	−0.454169	+	0.786643i	−0.998640	−	0.0521363i	$-0.983397\pi$
$937$	−13.9023	+	24.0795i	−0.454169	+	0.786643i	0.544471	+	0.838779i	$0.316730\pi$
$938$	0.0467162	+	0.0302087i	0.00152534	+	0.000986348i
$939$		0			0
$940$	56.9346	−	25.6151i	1.85700	−	0.835471i
$941$	−17.4040	+	3.06880i	−0.567355	+	0.100040i	−0.449965	−	0.893046i	$-0.648564\pi$
$941$	−17.4040	+	3.06880i	−0.567355	+	0.100040i	−0.117390	+	0.993086i	$0.537453\pi$
$942$		0			0
$943$	30.6650	+	25.7310i	0.998591	+	0.837917i
$944$	26.2590	+	0.712264i	0.854657	+	0.0231822i
$945$		0			0
$946$	−5.45708	−	2.30386i	−0.177425	−	0.0749050i
$947$	−31.1472	+	37.1197i	−1.01215	+	1.20623i	−0.0337637	+	0.999430i	$0.510749\pi$
$947$	−31.1472	+	37.1197i	−1.01215	+	1.20623i	−0.978383	+	0.206800i	$0.933695\pi$
$948$		0			0
$949$	−57.2701	+	10.0983i	−1.85907	+	0.327804i
$950$	−44.0488	+	47.4214i	−1.42913	+	1.53855i
$951$		0			0
$952$	−0.0538100	+	0.0107862i	−0.00174399	+	0.000349582i
$953$	−6.84000	+	11.8472i	−0.221569	+	0.383770i	−0.955285	−	0.295688i	$-0.904451\pi$
$953$	−6.84000	+	11.8472i	−0.221569	+	0.383770i	0.733715	+	0.679457i	$0.237785\pi$
$954$		0			0
$955$	47.6310	−	27.4998i	1.54130	−	0.889871i
$956$	−54.3221	−	26.2333i	−1.75690	−	0.848445i
$957$		0			0
$958$	−13.1973	+	4.06292i	−0.426384	+	0.131267i
$959$	−0.0334435	+	0.0280625i	−0.00107995	+	0.000906184i
$960$		0			0
$961$	−30.6492	+	11.1554i	−0.988684	+	0.359852i
$962$	5.39028	+	43.2046i	0.173789	+	1.39297i
$963$		0			0
$964$	4.85294	−	1.23007i	0.156303	−	0.0396178i
$965$	−37.0002	−	6.52413i	−1.19108	−	0.210019i
$966$		0			0
$967$	28.0120	+	10.1955i	0.900806	+	0.327867i	0.750576	−	0.660785i	$-0.229776\pi$
$967$	28.0120	+	10.1955i	0.900806	+	0.327867i	0.150230	+	0.988651i	$0.451999\pi$
$968$	−24.1335	+	14.6934i	−0.775681	+	0.472265i
$969$		0			0
$970$	63.4731	−	32.4970i	2.03800	−	1.04342i
$971$		−	31.5563i		−	1.01269i	−0.862331	−	0.506345i	$-0.830996\pi$
$971$		−	31.5563i		−	1.01269i	0.862331	−	0.506345i	$-0.169004\pi$
$972$		0			0
$973$		−	0.0108888i		−	0.000349078i
$974$	−26.2435	−	51.2589i	−0.840897	−	1.64244i
$975$		0			0
$976$	0.0637373	+	0.429230i	0.00204018	+	0.0137393i
$977$	−26.2819	−	9.56585i	−0.840834	−	0.306039i	−0.114536	−	0.993419i	$-0.536538\pi$
$977$	−26.2819	−	9.56585i	−0.840834	−	0.306039i	−0.726297	+	0.687381i	$0.758760\pi$
$978$		0			0
$979$	−2.87804	−	0.507477i	−0.0919827	−	0.0162190i
$980$	−13.5572	−	53.4867i	−0.433069	−	1.70857i
$981$		0			0
$982$	−17.5457	+	2.18902i	−0.559905	+	0.0698546i
$983$	−23.5384	+	8.56727i	−0.750758	+	0.273253i	−0.688925	−	0.724833i	$-0.741917\pi$
$983$	−23.5384	+	8.56727i	−0.750758	+	0.273253i	−0.0618331	+	0.998087i	$0.519695\pi$
$984$		0			0
$985$	−26.5326	+	22.2635i	−0.845398	+	0.709373i
$986$	−4.70362	−	15.2784i	−0.149794	−	0.486563i
$987$		0			0
$988$	31.3323	+	15.1310i	0.996813	+	0.481382i
$989$	−24.8801	+	14.3645i	−0.791141	+	0.456766i
$990$		0			0
$991$	11.3147	−	19.5976i	0.359422	−	0.622537i	−0.628442	−	0.777856i	$-0.716307\pi$
$991$	11.3147	−	19.5976i	0.359422	−	0.622537i	0.987864	+	0.155319i	$0.0496405\pi$
$992$	37.2095	+	25.5181i	1.18140	+	0.810201i
$993$		0			0
$994$	−0.00937813	−	0.00871117i	−0.000297456	−	0.000276302i
$995$	−36.5628	+	6.44700i	−1.15912	+	0.204384i
$996$		0			0
$997$	−6.16806	+	7.35081i	−0.195344	+	0.232802i	−0.854821	−	0.518922i	$-0.826333\pi$
$997$	−6.16806	+	7.35081i	−0.195344	+	0.232802i	0.659477	+	0.751725i	$0.270778\pi$
$998$	−2.51744	+	5.96297i	−0.0796881	+	0.188754i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	648.2.t.a.613.22		204
3.2	odd	2		216.2.t.a.205.13	yes	204
8.5	even	2	inner	648.2.t.a.613.31		204
12.11	even	2		864.2.bf.a.529.16		204
24.5	odd	2		216.2.t.a.205.4	yes	204
24.11	even	2		864.2.bf.a.529.19		204
27.5	odd	18		216.2.t.a.157.4	✓	204
27.22	even	9	inner	648.2.t.a.37.31		204
108.59	even	18		864.2.bf.a.49.19		204
216.5	odd	18		216.2.t.a.157.13	yes	204
216.59	even	18		864.2.bf.a.49.16		204
216.157	even	18	inner	648.2.t.a.37.22		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.157.4	✓	204	27.5	odd	18
216.2.t.a.157.13	yes	204	216.5	odd	18
216.2.t.a.205.4	yes	204	24.5	odd	2
216.2.t.a.205.13	yes	204	3.2	odd	2
648.2.t.a.37.22		204	216.157	even	18	inner
648.2.t.a.37.31		204	27.22	even	9	inner
648.2.t.a.613.22		204	1.1	even	1	trivial
648.2.t.a.613.31		204	8.5	even	2	inner
864.2.bf.a.49.16		204	216.59	even	18
864.2.bf.a.49.19		204	108.59	even	18
864.2.bf.a.529.16		204	12.11	even	2
864.2.bf.a.529.19		204	24.11	even	2

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:	\( N \)	\(=\)	\( 648 = 2^{3} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	648.t (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.644492 + 1.25882i) q^{2} +(-1.16926 + 1.62260i) q^{4} +(-1.34802 + 3.70366i) q^{5} +(0.00177522 - 0.0100678i) q^{7} +(-2.79614 - 0.426137i) q^{8} +(-5.53104 + 0.690061i) q^{10} +(-0.343808 - 0.944604i) q^{11} +(2.57400 + 3.06757i) q^{13} +(0.0138176 - 0.00425391i) q^{14} +(-1.26566 - 3.79448i) q^{16} +(0.948987 + 1.64369i) q^{17} +(-3.76245 - 2.17225i) q^{19} +(-4.43337 - 6.51785i) q^{20} +(0.967506 - 1.04158i) q^{22} +(-1.19728 - 6.79010i) q^{23} +(-8.06972 - 6.77130i) q^{25} +(-2.20260 + 5.21723i) q^{26} +(0.0142603 + 0.0146523i) q^{28} +(-3.82827 + 4.56236i) q^{29} +(1.38501 + 7.85480i) q^{31} +(3.96087 - 4.03875i) q^{32} +(-1.45750 + 2.25395i) q^{34} +(0.0348946 + 0.0201464i) q^{35} +(6.65823 - 3.84413i) q^{37} +(0.309608 - 6.13625i) q^{38} +(5.34753 - 9.78152i) q^{40} +(-4.44753 + 3.73192i) q^{41} +(-1.42511 - 3.91546i) q^{43} +(1.93471 + 0.546626i) q^{44} +(7.77588 - 5.88332i) q^{46} +(-1.37530 + 7.79973i) q^{47} +(6.57775 + 2.39411i) q^{49} +(3.32298 - 14.5224i) q^{50} +(-7.98712 + 0.589779i) q^{52} +2.25567i q^{53} +3.96195 q^{55} +(-0.00925402 + 0.0273944i) q^{56} +(-8.21048 - 1.87871i) q^{58} +(-2.24610 + 6.17111i) q^{59} +(-0.106836 - 0.0188381i) q^{61} +(-8.99516 + 6.80584i) q^{62} +(7.63681 + 2.38308i) q^{64} +(-14.8311 + 5.39806i) q^{65} +(2.47342 + 2.94771i) q^{67} +(-3.77667 - 0.382080i) q^{68} +(-0.00287143 + 0.0569102i) q^{70} +(-0.442665 - 0.766718i) q^{71} +(-7.26116 + 12.5767i) q^{73} +(9.13025 + 5.90401i) q^{74} +(7.92398 - 3.56502i) q^{76} +(-0.0101204 + 0.00178450i) q^{77} +(2.46319 + 2.06686i) q^{79} +(15.7596 + 0.427473i) q^{80} +(-7.56422 - 3.19345i) q^{82} +(9.76904 - 11.6423i) q^{83} +(-7.36694 + 1.29899i) q^{85} +(4.01039 - 4.31744i) q^{86} +(0.558804 + 2.78776i) q^{88} +(1.45362 - 2.51775i) q^{89} +(0.0354530 - 0.0204688i) q^{91} +(12.4175 + 5.99669i) q^{92} +(-10.7048 + 3.29560i) q^{94} +(13.1172 - 11.0066i) q^{95} +(-12.0217 + 4.37554i) q^{97} +(1.22556 + 9.82319i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q + 6 q^{2} - 6 q^{4} - 12 q^{7} + 3 q^{8} - 3 q^{10} + 21 q^{14} - 6 q^{16} + 6 q^{17} - 15 q^{20} - 6 q^{22} + 12 q^{23} - 12 q^{25} + 30 q^{26} - 12 q^{28} - 12 q^{31} + 36 q^{32} + 42 q^{38} - 21 q^{40}+ \cdots - 54 q^{98}+O(q^{100}) \) 204 * q + 6 * q^2 - 6 * q^4 - 12 * q^7 + 3 * q^8 - 3 * q^10 + 21 * q^14 - 6 * q^16 + 6 * q^17 - 15 * q^20 - 6 * q^22 + 12 * q^23 - 12 * q^25 + 30 * q^26 - 12 * q^28 - 12 * q^31 + 36 * q^32 + 42 * q^38 - 21 * q^40 + 24 * q^41 - 21 * q^44 - 3 * q^46 + 12 * q^47 - 12 * q^49 + 99 * q^50 - 33 * q^52 - 24 * q^55 - 99 * q^56 + 21 * q^58 + 36 * q^62 - 3 * q^64 + 12 * q^65 - 75 * q^68 + 9 * q^70 + 90 * q^71 - 6 * q^73 - 9 * q^74 - 18 * q^76 - 12 * q^79 - 78 * q^80 - 12 * q^82 + 30 * q^86 - 30 * q^88 + 6 * q^89 - 111 * q^92 - 33 * q^94 + 42 * q^95 - 12 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

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Database

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