LMFDB - Embedded newform 540.2.be.a.11.71

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, degree $6$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.71
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.71

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41339 + 0.0483239i) q^{2} +(-0.924312 + 1.46480i) q^{3} +(1.99533 + 0.136601i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.37720 + 2.02567i) q^{6} +(3.29465 + 0.580935i) q^{7} +(2.81357 + 0.289492i) q^{8} +(-1.29129 - 2.70787i) q^{9} +(-0.528817 + 1.31162i) q^{10} +(3.29684 - 1.19995i) q^{11} +(-2.04440 + 2.79650i) q^{12} +(-2.45658 + 2.06131i) q^{13} +(4.62854 + 0.980297i) q^{14} +(-1.06033 - 1.36956i) q^{15} +(3.96268 + 0.545127i) q^{16} +(-1.99049 + 1.14921i) q^{17} +(-1.69424 - 3.88967i) q^{18} +(-6.21007 - 3.58539i) q^{19} +(-0.810806 + 1.82828i) q^{20} +(-3.89624 + 4.28904i) q^{21} +(4.71769 - 1.53668i) q^{22} +(1.19803 + 6.79437i) q^{23} +(-3.02467 + 3.85375i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-3.57171 + 2.79472i) q^{26} +(5.16005 + 0.611427i) q^{27} +(6.49455 + 1.60921i) q^{28} +(-3.26084 + 3.88612i) q^{29} +(-1.43248 - 1.98696i) q^{30} +(10.2081 - 1.79996i) q^{31} +(5.57446 + 0.961969i) q^{32} +(-1.28962 + 5.93834i) q^{33} +(-2.86887 + 1.52809i) q^{34} +(-1.67274 + 2.89726i) q^{35} +(-2.20666 - 5.57949i) q^{36} +(-1.43654 - 2.48815i) q^{37} +(-8.60398 - 5.36764i) q^{38} +(-0.748772 - 5.50370i) q^{39} +(-1.23433 + 2.54488i) q^{40} +(-1.45919 - 1.73899i) q^{41} +(-5.71416 + 5.87380i) q^{42} +(-4.01448 - 11.0297i) q^{43} +(6.74219 - 1.94395i) q^{44} +(2.98621 - 0.287273i) q^{45} +(1.36495 + 9.66098i) q^{46} +(-1.41945 + 8.05011i) q^{47} +(-4.46126 + 5.30068i) q^{48} +(3.93937 + 1.43381i) q^{49} +(-1.05166 - 0.945526i) q^{50} +(0.156469 - 3.97791i) q^{51} +(-5.18326 + 3.77743i) q^{52} -13.0945i q^{53} +(7.26361 + 1.11354i) q^{54} +3.50842i q^{55} +(9.10156 + 2.58828i) q^{56} +(10.9919 - 5.78251i) q^{57} +(-4.79663 + 5.33502i) q^{58} +(-5.66375 - 2.06144i) q^{59} +(-1.92863 - 2.87757i) q^{60} +(0.987751 - 5.60182i) q^{61} +(14.5149 - 2.05074i) q^{62} +(-2.68126 - 9.67164i) q^{63} +(7.83239 + 1.62901i) q^{64} +(-1.09680 - 3.01344i) q^{65} +(-2.10969 + 8.33086i) q^{66} +(-1.64134 - 1.95607i) q^{67} +(-4.12867 + 2.02115i) q^{68} +(-11.0598 - 4.52524i) q^{69} +(-2.50423 + 4.01413i) q^{70} +(-2.05687 - 3.56261i) q^{71} +(-2.84924 - 7.99261i) q^{72} +(1.31500 - 2.27765i) q^{73} +(-1.91014 - 3.58614i) q^{74} +(1.64962 - 0.527967i) q^{75} +(-11.9014 - 8.00233i) q^{76} +(11.5590 - 2.03816i) q^{77} +(-0.792345 - 7.81504i) q^{78} +(4.37177 - 5.21007i) q^{79} +(-1.86757 + 3.53726i) q^{80} +(-5.66512 + 6.99331i) q^{81} +(-1.97836 - 2.52838i) q^{82} +(11.3190 + 9.49778i) q^{83} +(-8.36017 + 8.02583i) q^{84} +(-0.399117 - 2.26350i) q^{85} +(-5.14101 - 15.7832i) q^{86} +(-2.67836 - 8.36848i) q^{87} +(9.62326 - 2.42174i) q^{88} +(-3.68021 - 2.12477i) q^{89} +(4.23456 - 0.261723i) q^{90} +(-9.29104 + 5.36419i) q^{91} +(1.46235 + 13.7207i) q^{92} +(-6.79885 + 16.6165i) q^{93} +(-2.39525 + 11.3093i) q^{94} +(5.49313 - 4.60928i) q^{95} +(-6.56164 + 7.27633i) q^{96} +(5.16206 - 1.87884i) q^{97} +(5.49857 + 2.21690i) q^{98} +(-7.50649 - 7.37792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	1.41339	+	0.0483239i	0.999416	+	0.0341702i
$2$	1.41339	+	0.0483239i	0.999416	+	0.0341702i
$3$	−0.924312	+	1.46480i	−0.533652	+	0.845704i
$3$	−0.924312	+	1.46480i	−0.533652	+	0.845704i
$4$	1.99533	+	0.136601i	0.997665	+	0.0683004i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−1.37720	+	2.02567i	−0.562238	+	0.826975i
$7$	3.29465	+	0.580935i	1.24526	+	0.219573i	0.757168	−	0.653220i	$-0.226582\pi$
$7$	3.29465	+	0.580935i	1.24526	+	0.219573i	0.488091	+	0.872793i	$0.337693\pi$
$8$	2.81357	+	0.289492i	0.994748	+	0.102351i
$9$	−1.29129	−	2.70787i	−0.430431	−	0.902623i
$10$	−0.528817	+	1.31162i	−0.167227	+	0.414771i
$11$	3.29684	−	1.19995i	0.994033	−	0.361799i	0.206753	−	0.978393i	$-0.433710\pi$
$11$	3.29684	−	1.19995i	0.994033	−	0.361799i	0.787281	+	0.616595i	$0.211488\pi$
$12$	−2.04440	+	2.79650i	−0.590168	+	0.807281i
$13$	−2.45658	+	2.06131i	−0.681332	+	0.571705i	−0.916395	−	0.400275i	$-0.868915\pi$
$13$	−2.45658	+	2.06131i	−0.681332	+	0.571705i	0.235063	+	0.971980i	$0.424470\pi$
$14$	4.62854	+	0.980297i	1.23703	+	0.261995i
$15$	−1.06033	−	1.36956i	−0.273776	−	0.353619i
$16$	3.96268	+	0.545127i	0.990670	+	0.136282i
$17$	−1.99049	+	1.14921i	−0.482765	+	0.278725i	−0.721568	−	0.692344i	$-0.756578\pi$
$17$	−1.99049	+	1.14921i	−0.482765	+	0.278725i	0.238803	+	0.971068i	$0.423245\pi$
$18$	−1.69424	−	3.88967i	−0.399337	−	0.916804i
$19$	−6.21007	−	3.58539i	−1.42469	−	0.822544i	−0.427993	−	0.903782i	$-0.640779\pi$
$19$	−6.21007	−	3.58539i	−1.42469	−	0.822544i	−0.996695	+	0.0812381i	$0.974113\pi$
$20$	−0.810806	+	1.82828i	−0.181302	+	0.408815i
$21$	−3.89624	+	4.28904i	−0.850229	+	0.935946i
$22$	4.71769	−	1.53668i	1.00582	−	0.327621i
$23$	1.19803	+	6.79437i	0.249807	+	1.41672i	0.809059	+	0.587727i	$0.199977\pi$
$23$	1.19803	+	6.79437i	0.249807	+	1.41672i	−0.559252	+	0.828997i	$0.688912\pi$
$24$	−3.02467	+	3.85375i	−0.617408	+	0.786643i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	−3.57171	+	2.79472i	−0.700469	+	0.548090i
$27$	5.16005	+	0.611427i	0.993053	+	0.117669i
$28$	6.49455	+	1.60921i	1.22735	+	0.304112i
$29$	−3.26084	+	3.88612i	−0.605523	+	0.721634i	−0.978509	−	0.206203i	$-0.933889\pi$
$29$	−3.26084	+	3.88612i	−0.605523	+	0.721634i	0.372986	+	0.927837i	$0.378334\pi$
$30$	−1.43248	−	1.98696i	−0.261533	−	0.362768i
$31$	10.2081	−	1.79996i	1.83342	−	0.323282i	0.853260	−	0.521485i	$-0.174622\pi$
$31$	10.2081	−	1.79996i	1.83342	−	0.323282i	0.980161	+	0.198204i	$0.0635108\pi$
$32$	5.57446	+	0.961969i	0.985435	+	0.170054i
$33$	−1.28962	+	5.93834i	−0.224493	+	1.03373i
$34$	−2.86887	+	1.52809i	−0.492007	+	0.262066i
$35$	−1.67274	+	2.89726i	−0.282744	+	0.489727i
$36$	−2.20666	−	5.57949i	−0.367777	−	0.929914i
$37$	−1.43654	−	2.48815i	−0.236165	−	0.409050i	0.723446	−	0.690381i	$-0.242557\pi$
$37$	−1.43654	−	2.48815i	−0.236165	−	0.409050i	−0.959611	+	0.281332i	$0.909224\pi$
$38$	−8.60398	−	5.36764i	−1.39575	−	0.870745i
$39$	−0.748772	−	5.50370i	−0.119899	−	0.881297i
$40$	−1.23433	+	2.54488i	−0.195165	+	0.402381i
$41$	−1.45919	−	1.73899i	−0.227887	−	0.271585i	0.639969	−	0.768400i	$-0.278947\pi$
$41$	−1.45919	−	1.73899i	−0.227887	−	0.271585i	−0.867856	+	0.496816i	$0.834503\pi$
$42$	−5.71416	+	5.87380i	−0.881714	+	0.906347i
$43$	−4.01448	−	11.0297i	−0.612202	−	1.68201i	−0.725305	−	0.688427i	$-0.758301\pi$
$43$	−4.01448	−	11.0297i	−0.612202	−	1.68201i	0.113103	−	0.993583i	$-0.463921\pi$
$44$	6.74219	−	1.94395i	1.01642	−	0.293061i
$45$	2.98621	−	0.287273i	0.445159	−	0.0428241i
$46$	1.36495	+	9.66098i	0.201251	+	1.42443i
$47$	−1.41945	+	8.05011i	−0.207048	+	1.17423i	0.687136	+	0.726529i	$0.258868\pi$
$47$	−1.41945	+	8.05011i	−0.207048	+	1.17423i	−0.894184	+	0.447700i	$0.852243\pi$
$48$	−4.46126	+	5.30068i	−0.643927	+	0.765087i
$49$	3.93937	+	1.43381i	0.562767	+	0.204831i
$50$	−1.05166	−	0.945526i	−0.148727	−	0.133718i
$51$	0.156469	−	3.97791i	0.0219100	−	0.557018i
$52$	−5.18326	+	3.77743i	−0.718788	+	0.523835i
$53$		−	13.0945i		−	1.79866i	−0.437266	−	0.899332i	$-0.644053\pi$
$53$		−	13.0945i		−	1.79866i	0.437266	−	0.899332i	$-0.355947\pi$
$54$	7.26361	+	1.11354i	0.988452	+	0.151533i
$55$			3.50842i			0.473075i
$56$	9.10156	+	2.58828i	1.21625	+	0.345873i
$57$	10.9919	−	5.78251i	1.45592	−	0.765912i
$58$	−4.79663	+	5.33502i	−0.629828	+	0.700522i
$59$	−5.66375	−	2.06144i	−0.737358	−	0.268376i	−0.0540819	−	0.998537i	$-0.517223\pi$
$59$	−5.66375	−	2.06144i	−0.737358	−	0.268376i	−0.683276	+	0.730160i	$0.739445\pi$
$60$	−1.92863	−	2.87757i	−0.248985	−	0.371493i
$61$	0.987751	−	5.60182i	0.126469	−	0.717239i	−0.853956	−	0.520345i	$-0.825803\pi$
$61$	0.987751	−	5.60182i	0.126469	−	0.717239i	0.980425	−	0.196894i	$-0.0630855\pi$
$62$	14.5149	−	2.05074i	1.84340	−	0.260444i
$63$	−2.68126	−	9.67164i	−0.337807	−	1.21851i
$64$	7.83239	+	1.62901i	0.979049	+	0.203627i
$65$	−1.09680	−	3.01344i	−0.136041	−	0.373771i
$66$	−2.10969	+	8.33086i	−0.259685	+	1.02546i
$67$	−1.64134	−	1.95607i	−0.200521	−	0.238972i	0.656408	−	0.754406i	$-0.272075\pi$
$67$	−1.64134	−	1.95607i	−0.200521	−	0.238972i	−0.856929	+	0.515434i	$0.827631\pi$
$68$	−4.12867	+	2.02115i	−0.500675	+	0.245101i
$69$	−11.0598	−	4.52524i	−1.33144	−	0.544775i
$70$	−2.50423	+	4.01413i	−0.299313	+	0.479780i
$71$	−2.05687	−	3.56261i	−0.244106	−	0.422804i	0.717774	−	0.696276i	$-0.245161\pi$
$71$	−2.05687	−	3.56261i	−0.244106	−	0.422804i	−0.961880	+	0.273472i	$0.911828\pi$
$72$	−2.84924	−	7.99261i	−0.335786	−	0.941938i
$73$	1.31500	−	2.27765i	0.153909	−	0.266579i	−0.778752	−	0.627332i	$-0.784147\pi$
$73$	1.31500	−	2.27765i	0.153909	−	0.266579i	0.932661	+	0.360753i	$0.117480\pi$
$74$	−1.91014	−	3.58614i	−0.222050	−	0.416881i
$75$	1.64962	−	0.527967i	0.190482	−	0.0609644i
$76$	−11.9014	−	8.00233i	−1.36518	−	0.917930i
$77$	11.5590	−	2.03816i	1.31727	−	0.232270i
$78$	−0.792345	−	7.81504i	−0.0897154	−	0.884879i
$79$	4.37177	−	5.21007i	0.491862	−	0.586179i	−0.461828	−	0.886970i	$-0.652806\pi$
$79$	4.37177	−	5.21007i	0.491862	−	0.586179i	0.953690	+	0.300791i	$0.0972506\pi$
$80$	−1.86757	+	3.53726i	−0.208801	+	0.395477i
$81$	−5.66512	+	6.99331i	−0.629458	+	0.777035i
$82$	−1.97836	−	2.52838i	−0.218474	−	0.279213i
$83$	11.3190	+	9.49778i	1.24242	+	1.04252i	0.997331	+	0.0730170i	$0.0232627\pi$
$83$	11.3190	+	9.49778i	1.24242	+	1.04252i	0.245092	+	0.969500i	$0.421182\pi$
$84$	−8.36017	+	8.02583i	−0.912169	+	0.875689i
$85$	−0.399117	−	2.26350i	−0.0432903	−	0.245511i
$86$	−5.14101	−	15.7832i	−0.554370	−	1.70195i
$87$	−2.67836	−	8.36848i	−0.287151	−	0.897195i
$88$	9.62326	−	2.42174i	1.02584	−	0.258158i
$89$	−3.68021	−	2.12477i	−0.390102	−	0.225225i	0.292102	−	0.956387i	$-0.405645\pi$
$89$	−3.68021	−	2.12477i	−0.390102	−	0.225225i	−0.682204	+	0.731162i	$0.738979\pi$
$90$	4.23456	−	0.261723i	0.446362	−	0.0275880i
$91$	−9.29104	+	5.36419i	−0.973966	+	0.562319i
$92$	1.46235	+	13.7207i	0.152461	+	1.43048i
$93$	−6.79885	+	16.6165i	−0.705008	+	1.72305i
$94$	−2.39525	+	11.3093i	−0.247051	+	1.16647i
$95$	5.49313	−	4.60928i	0.563583	−	0.472902i
$96$	−6.56164	+	7.27633i	−0.669694	+	0.742637i
$97$	5.16206	−	1.87884i	0.524128	−	0.190767i	−0.0663867	−	0.997794i	$-0.521147\pi$
$97$	5.16206	−	1.87884i	0.524128	−	0.190767i	0.590514	+	0.807027i	$0.298925\pi$
$98$	5.49857	+	2.21690i	0.555439	+	0.223941i
$99$	−7.50649	−	7.37792i	−0.754431	−	0.741508i
$100$	−1.44071	−	1.38722i	−0.144071	−	0.138722i
$101$	−19.5765	−	3.45187i	−1.94794	−	0.343474i	−0.999661	−	0.0260250i	$-0.991715\pi$
$101$	−19.5765	−	3.45187i	−1.94794	−	0.343474i	−0.948275	−	0.317449i	$-0.897174\pi$
$102$	0.413379	−	5.61476i	0.0409306	−	0.555944i
$103$	0.567658	−	1.55963i	0.0559331	−	0.153675i	−0.908579	−	0.417712i	$-0.862832\pi$
$103$	0.567658	−	1.55963i	0.0559331	−	0.153675i	0.964512	+	0.264037i	$0.0850542\pi$
$104$	−7.50849	+	5.08849i	−0.736268	+	0.498968i
$105$	−2.69779	−	5.12821i	−0.263277	−	0.500462i
$106$	0.632776	−	18.5076i	0.0614607	−	1.79761i
$107$	7.95602			0.769137			0.384569	−	0.923096i	$-0.374350\pi$
$107$	7.95602			0.769137			0.384569	+	0.923096i	$0.374350\pi$
$108$	10.2125	+	1.92487i	0.982697	+	0.185220i
$109$	8.28431			0.793493			0.396747	−	0.917928i	$-0.370139\pi$
$109$	8.28431			0.793493			0.396747	+	0.917928i	$0.370139\pi$
$110$	−0.169541	+	4.95876i	−0.0161651	+	0.472799i
$111$	4.97246	+	0.195589i	0.471965	+	0.0185645i
$112$	12.7390	+	4.09806i	1.20372	+	0.387231i
$113$	0.384656	−	1.05683i	0.0361854	−	0.0994187i	−0.920284	−	0.391251i	$-0.872043\pi$
$113$	0.384656	−	1.05683i	0.0361854	−	0.0994187i	0.956470	+	0.291832i	$0.0942648\pi$
$114$	15.8153	−	7.64176i	1.48124	−	0.715716i
$115$	−6.79437	−	1.19803i	−0.633578	−	0.111717i
$116$	−7.03730	+	7.30866i	−0.653397	+	0.678592i
$117$	8.75393	+	3.99033i	0.809301	+	0.368906i
$118$	−7.90546	−	3.18731i	−0.727757	−	0.293415i
$119$	−7.22558	+	2.62990i	−0.662368	+	0.241082i
$120$	−2.58684	−	4.16032i	−0.236145	−	0.379783i
$121$	1.00276	−	0.841413i	0.0911597	−	0.0764921i
$122$	1.66678	−	7.86981i	0.150903	−	0.712499i
$123$	3.89602	−	0.530050i	0.351293	−	0.0477930i
$124$	20.6143	−	2.19708i	1.85122	−	0.197303i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	−3.32229	−	13.7993i	−0.295973	−	1.22934i
$127$	8.85407	+	5.11190i	0.785672	+	0.453608i	0.838437	−	0.544999i	$-0.183470\pi$
$127$	8.85407	+	5.11190i	0.785672	+	0.453608i	−0.0527647	+	0.998607i	$0.516803\pi$
$128$	10.9915	+	2.68092i	0.971519	+	0.236962i
$129$	19.8669	+	4.31446i	1.74919	+	0.379867i
$130$	−1.40458	−	4.31216i	−0.123190	−	0.378201i
$131$	0.916038	+	5.19511i	0.0800346	+	0.453899i	0.998318	+	0.0579751i	$0.0184644\pi$
$131$	0.916038	+	5.19511i	0.0800346	+	0.453899i	−0.918283	+	0.395924i	$0.870424\pi$
$132$	−3.38439	+	11.6728i	−0.294573	+	1.01599i
$133$	−18.3771	−	15.4202i	−1.59350	−	1.33710i
$134$	−2.22532	−	2.84400i	−0.192238	−	0.245684i
$135$	−2.33940	+	4.63974i	−0.201343	+	0.399326i
$136$	−5.93308	+	2.65716i	−0.508757	+	0.227849i
$137$	−0.188784	+	0.224983i	−0.0161289	+	0.0192216i	−0.774049	−	0.633126i	$-0.781771\pi$
$137$	−0.188784	+	0.224983i	−0.0161289	+	0.0192216i	0.757920	+	0.652348i	$0.226216\pi$
$138$	−15.4131	−	6.93037i	−1.31205	−	0.589953i
$139$	0.720591	−	0.127060i	0.0611198	−	0.0107771i	−0.143005	−	0.989722i	$-0.545676\pi$
$139$	0.720591	−	0.127060i	0.0611198	−	0.0107771i	0.204124	+	0.978945i	$0.434565\pi$
$140$	−3.73343	+	5.55250i	−0.315532	+	0.469272i
$141$	−10.4798	−	9.52003i	−0.882559	−	0.801731i
$142$	−2.73500	−	5.13474i	−0.229516	−	0.430898i
$143$	−5.62546	+	9.74358i	−0.470424	+	0.814799i
$144$	−3.64085	−	11.4343i	−0.303404	−	0.952862i
$145$	−2.53648	−	4.39332i	−0.210644	−	0.364845i
$146$	1.96867	−	3.15566i	0.162929	−	0.261164i
$147$	−5.74146	+	4.44511i	−0.473548	+	0.366626i
$148$	−2.52648	−	5.16092i	−0.207675	−	0.424225i
$149$	−1.27069	−	1.51435i	−0.104099	−	0.124061i	0.711479	−	0.702707i	$-0.248026\pi$
$149$	−1.27069	−	1.51435i	−0.104099	−	0.124061i	−0.815579	+	0.578646i	$0.803581\pi$
$150$	2.35707	−	0.666507i	0.192454	−	0.0544200i
$151$	−5.01436	−	13.7768i	−0.408062	−	1.12114i	−0.958208	−	0.286073i	$-0.907650\pi$
$151$	−5.01436	−	13.7768i	−0.408062	−	1.12114i	0.550145	−	0.835069i	$-0.314572\pi$
$152$	−16.4345	−	11.8855i	−1.33302	−	0.964042i
$153$	5.68222	+	3.90602i	0.459380	+	0.315783i
$154$	16.4358	−	2.32214i	1.32444	−	0.187123i
$155$	−1.79996	+	10.2081i	−0.144576	+	0.819931i
$156$	−0.742238	−	11.0840i	−0.0594266	−	0.887428i
$157$	−6.87422	−	2.50201i	−0.548622	−	0.199682i	0.0528119	−	0.998604i	$-0.483182\pi$
$157$	−6.87422	−	2.50201i	−0.548622	−	0.199682i	−0.601434	+	0.798922i	$0.705404\pi$
$158$	6.43078	−	7.15259i	0.511605	−	0.569030i
$159$	19.1808	+	12.1034i	1.52114	+	0.959861i
$160$	−2.81053	+	4.90927i	−0.222192	+	0.388112i
$161$			23.0810i			1.81904i
$162$	−8.34496	+	9.61050i	−0.655642	+	0.755072i
$163$		−	5.01110i		−	0.392500i	−0.980554	−	0.196250i	$-0.937124\pi$
$163$		−	5.01110i		−	0.392500i	0.980554	−	0.196250i	$-0.0628763\pi$
$164$	−2.67401	−	3.66919i	−0.208805	−	0.286515i
$165$	−5.13914	−	3.24288i	−0.400082	−	0.252457i
$166$	15.5392	+	13.9710i	1.20607	+	1.08436i
$167$	−0.0590359	−	0.0214873i	−0.00456833	−	0.00166274i	0.339735	−	0.940521i	$-0.389663\pi$
$167$	−0.0590359	−	0.0214873i	−0.00456833	−	0.00166274i	−0.344303	+	0.938858i	$0.611885\pi$
$168$	−12.2040	+	10.9396i	−0.941559	+	0.844009i
$169$	−0.471668	+	2.67496i	−0.0362821	+	0.205766i
$170$	−0.454725	−	3.21849i	−0.0348758	−	0.246847i
$171$	−1.68973	+	21.4459i	−0.129217	+	1.64001i
$172$	−6.50354	−	22.5562i	−0.495890	−	1.71990i
$173$	7.43436	+	20.4257i	0.565224	+	1.55294i	0.811873	+	0.583834i	$0.198448\pi$
$173$	7.43436	+	20.4257i	0.565224	+	1.55294i	−0.246649	+	0.969105i	$0.579330\pi$
$174$	−3.38117	−	11.9573i	−0.256326	−	0.906483i
$175$	−2.15043	−	2.56278i	−0.162557	−	0.193728i
$176$	13.7184	−	2.95782i	1.03407	−	0.222954i
$177$	8.25468	−	6.39087i	0.620459	−	0.480367i
$178$	−5.09889	−	3.18097i	−0.382178	−	0.238424i
$179$	−0.858099	−	1.48627i	−0.0641373	−	0.111089i	0.832174	−	0.554515i	$-0.187096\pi$
$179$	−0.858099	−	1.48627i	−0.0641373	−	0.111089i	−0.896311	+	0.443426i	$0.853763\pi$
$180$	5.99772	−	0.165285i	0.447044	−	0.0123196i
$181$	2.23461	−	3.87045i	0.166097	−	0.287689i	−0.770947	−	0.636899i	$-0.780217\pi$
$181$	2.23461	−	3.87045i	0.166097	−	0.287689i	0.937044	+	0.349210i	$0.113550\pi$
$182$	−13.3911	+	7.13269i	−0.992612	+	0.528711i
$183$	7.29257	+	6.62469i	0.539082	+	0.489711i
$184$	1.40383	+	19.4633i	0.103492	+	1.43485i
$185$	2.82942	−	0.498904i	0.208023	−	0.0366801i
$186$	−10.4124	+	23.1570i	−0.763473	+	1.69796i
$187$	−5.18333	+	6.17725i	−0.379042	+	0.451725i
$188$	−3.93192	+	15.8687i	−0.286765	+	1.15735i
$189$	16.6454	+	5.01209i	1.21077	+	0.364576i
$190$	7.98666	−	6.24925i	0.579413	−	0.453369i
$191$	−4.98368	−	4.18181i	−0.360607	−	0.302585i	0.444426	−	0.895816i	$-0.353408\pi$
$191$	−4.98368	−	4.18181i	−0.360607	−	0.302585i	−0.805033	+	0.593231i	$0.797852\pi$
$192$	−9.62576	+	9.96719i	−0.694679	+	0.719320i
$193$	0.433360	+	2.45771i	0.0311939	+	0.176910i	0.996424	−	0.0844915i	$-0.0269266\pi$
$193$	0.433360	+	2.45771i	0.0311939	+	0.176910i	−0.965230	+	0.261401i	$0.915815\pi$
$194$	7.38678	−	2.40607i	0.530340	−	0.172746i
$195$	5.42788	+	1.17876i	0.388698	+	0.0844127i
$196$	7.66448	+	3.39905i	0.547463	+	0.242789i
$197$	−0.904830	−	0.522404i	−0.0644664	−	0.0372197i	0.467420	−	0.884035i	$-0.345183\pi$
$197$	−0.904830	−	0.522404i	−0.0644664	−	0.0372197i	−0.531887	+	0.846815i	$0.678517\pi$
$198$	−10.2531	−	10.7906i	−0.728653	−	0.766854i
$199$	−4.50825	+	2.60284i	−0.319581	+	0.184510i	−0.651206	−	0.758901i	$-0.725737\pi$
$199$	−4.50825	+	2.60284i	−0.319581	+	0.184510i	0.331625	+	0.943411i	$0.392403\pi$
$200$	−1.96924	−	2.03029i	−0.139246	−	0.143563i
$201$	4.38236	−	0.596216i	0.309108	−	0.0420538i
$202$	−27.5024	−	5.82484i	−1.93506	−	0.409835i
$203$	−13.0009	+	10.9091i	−0.912485	+	0.765666i
$204$	0.855592	−	7.91586i	0.0599034	−	0.554221i
$205$	2.13319	−	0.776417i	0.148988	−	0.0542273i
$206$	0.877689	−	2.17693i	0.0611515	−	0.151674i
$207$	16.8513	−	12.0176i	1.17124	−	0.835284i
$208$	−10.8583	+	6.82917i	−0.752888	+	0.473518i
$209$	−24.7759	−	4.36865i	−1.71378	−	0.302186i
$210$	−3.56521	−	7.37851i	−0.246023	−	0.509166i
$211$	−8.81073	+	24.2073i	−0.606556	+	1.66650i	0.131140	+	0.991364i	$0.458136\pi$
$211$	−8.81073	+	24.2073i	−0.606556	+	1.66650i	−0.737695	+	0.675134i	$0.764086\pi$
$212$	1.78872	−	26.1278i	0.122850	−	1.79446i
$213$	7.11971	+	0.280050i	0.487835	+	0.0191887i
$214$	11.2449	+	0.384466i	0.768688	+	0.0262816i
$215$	11.7375			0.800494
$216$	14.3412	+	3.21409i	0.975794	+	0.218691i
$217$	34.6776			2.35407
$218$	11.7089	+	0.400330i	0.793030	+	0.0271138i
$219$	2.12084	+	4.03148i	0.143313	+	0.272422i
$220$	−0.479253	+	7.00045i	−0.0323112	+	0.471970i
$221$	2.52091	−	6.92615i	0.169575	−	0.465903i
$222$	7.01856	+	0.516732i	0.471055	+	0.0346808i
$223$	−22.2984	−	3.93181i	−1.49321	−	0.263294i	−0.633368	−	0.773851i	$-0.718328\pi$
$223$	−22.2984	−	3.93181i	−1.49321	−	0.263294i	−0.859844	+	0.510557i	$0.829439\pi$
$224$	17.8070	+	6.40775i	1.18978	+	0.428136i
$225$	−0.751397	+	2.90438i	−0.0500931	+	0.193625i
$226$	0.594739	−	1.47513i	0.0395615	−	0.0981241i
$227$	−18.6663	+	6.79397i	−1.23892	+	0.450932i	−0.876645	−	0.481138i	$-0.840224\pi$
$227$	−18.6663	+	6.79397i	−1.23892	+	0.450932i	−0.362280	+	0.932069i	$0.618001\pi$
$228$	22.7224	−	10.0365i	1.50483	−	0.664684i
$229$	−5.92513	+	4.97178i	−0.391544	+	0.328544i	−0.817214	−	0.576334i	$-0.804483\pi$
$229$	−5.92513	+	4.97178i	−0.391544	+	0.328544i	0.425670	+	0.904878i	$0.360038\pi$
$230$	−9.54519	−	2.02161i	−0.629391	−	0.133301i
$231$	−7.69862	+	18.8156i	−0.506532	+	1.23797i
$232$	−10.2996	+	9.98989i	−0.676203	+	0.655869i
$233$	5.62257	−	3.24619i	0.368347	−	0.212665i	−0.304389	−	0.952548i	$-0.598452\pi$
$233$	5.62257	−	3.24619i	0.368347	−	0.212665i	0.672736	+	0.739883i	$0.265119\pi$
$234$	12.1799	+	6.06291i	0.796223	+	0.396345i
$235$	−7.07915	−	4.08715i	−0.461793	−	0.266616i
$236$	−11.0195	−	4.88692i	−0.717306	−	0.318111i
$237$	3.59085	+	11.2195i	0.233251	+	0.728786i
$238$	−10.3396	+	3.36790i	−0.670219	+	0.218308i
$239$	1.62223	+	9.20012i	0.104933	+	0.595106i	0.991247	+	0.132021i	$0.0421466\pi$
$239$	1.62223	+	9.20012i	0.104933	+	0.595106i	−0.886314	+	0.463086i	$0.846742\pi$
$240$	−3.45517	−	6.00515i	−0.223030	−	0.387631i
$241$	−14.1729	−	11.8925i	−0.912959	−	0.766064i	0.0597204	−	0.998215i	$-0.480979\pi$
$241$	−14.1729	−	11.8925i	−0.912959	−	0.766064i	−0.972680	+	0.232151i	$0.925424\pi$
$242$	1.45794	−	1.14079i	0.0937202	−	0.0733325i
$243$	−5.00748	−	14.7623i	−0.321230	−	0.947001i
$244$	2.73610	−	11.0425i	0.175161	−	0.706926i
$245$	−2.69469	+	3.21140i	−0.172157	+	0.205169i
$246$	5.53220	−	0.560895i	0.352720	−	0.0357614i
$247$	22.6461	−	3.99312i	1.44094	−	0.254076i
$248$	29.2422	−	2.10916i	1.85688	−	0.133932i
$249$	−24.3747	+	7.80121i	−1.54468	+	0.494381i
$250$	1.24819	−	0.664844i	0.0789426	−	0.0420484i
$251$	2.34514	−	4.06191i	0.148024	−	0.256385i	−0.782473	−	0.622685i	$-0.786042\pi$
$251$	2.34514	−	4.06191i	0.148024	−	0.256385i	0.930497	+	0.366299i	$0.119375\pi$
$252$	−4.02884	−	19.6644i	−0.253793	−	1.23874i
$253$	12.1026	+	20.9624i	0.760885	+	1.31789i
$254$	12.2672	+	7.65296i	0.769713	+	0.480190i
$255$	3.68449	+	1.50756i	0.230732	+	0.0944069i
$256$	15.4057	+	4.32033i	0.962855	+	0.270021i
$257$	−1.34330	−	1.60088i	−0.0837928	−	0.0998604i	0.722519	−	0.691351i	$-0.242984\pi$
$257$	−1.34330	−	1.60088i	−0.0837928	−	0.0998604i	−0.806312	+	0.591491i	$0.798540\pi$
$258$	27.8712	+	7.05805i	1.73518	+	0.439415i
$259$	−3.28742	−	9.03212i	−0.204271	−	0.561229i
$260$	−1.77684	−	6.16262i	−0.110195	−	0.382190i
$261$	14.7338	+	3.81181i	0.912000	+	0.235945i
$262$	1.04367	+	7.38697i	0.0644781	+	0.456368i
$263$	1.56850	−	8.89543i	0.0967181	−	0.548516i	−0.897489	−	0.441036i	$-0.854611\pi$
$263$	1.56850	−	8.89543i	0.0967181	−	0.548516i	0.994207	−	0.107479i	$-0.0342780\pi$
$264$	−5.34753	+	16.3346i	−0.329118	+	1.00533i
$265$	12.3048	+	4.47857i	0.755877	+	0.275117i
$266$	−25.2288	−	22.6828i	−1.54688	−	1.39077i
$267$	6.51404	−	3.42683i	0.398653	−	0.209719i
$268$	−3.00781	−	4.12721i	−0.183731	−	0.252110i
$269$			8.69730i			0.530284i	0.964209	+	0.265142i	$0.0854188\pi$
$269$			8.69730i			0.530284i	−0.964209	+	0.265142i	$0.914581\pi$
$270$	−3.53068	+	6.44471i	−0.214871	+	0.392212i
$271$		−	19.7163i		−	1.19768i	−0.800868	−	0.598841i	$-0.795628\pi$
$271$		−	19.7163i		−	1.19768i	0.800868	−	0.598841i	$-0.204372\pi$
$272$	−8.51415	+	3.46888i	−0.516246	+	0.210332i
$273$	0.730351	−	18.5677i	0.0442028	−	1.12377i
$274$	−0.277696	+	0.308866i	−0.0167763	+	0.0186593i
$275$	−3.29684	−	1.19995i	−0.198807	−	0.0723597i
$276$	−21.4497	−	10.5401i	−1.29112	−	0.634441i
$277$	0.122862	−	0.696782i	0.00738203	−	0.0418656i	−0.980894	−	0.194542i	$-0.937678\pi$
$277$	0.122862	−	0.696782i	0.00738203	−	0.0418656i	0.988276	+	0.152676i	$0.0487891\pi$
$278$	1.02461	−	0.144763i	0.0614523	−	0.00868230i
$279$	−18.0556	−	25.3178i	−1.08096	−	1.51574i
$280$	−5.54510	+	7.66742i	−0.331383	+	0.458216i
$281$	9.36884	+	25.7407i	0.558898	+	1.53556i	0.821239	+	0.570585i	$0.193283\pi$
$281$	9.36884	+	25.7407i	0.558898	+	1.53556i	−0.262341	+	0.964975i	$0.584494\pi$
$282$	−14.3520	−	13.9619i	−0.854648	−	0.831420i
$283$	3.74805	+	4.46675i	0.222799	+	0.265521i	0.865852	−	0.500300i	$-0.166777\pi$
$283$	3.74805	+	4.46675i	0.222799	+	0.265521i	−0.643053	+	0.765821i	$0.722333\pi$
$284$	−3.61748	−	7.38955i	−0.214658	−	0.438489i
$285$	1.67432	+	12.3068i	0.0991783	+	0.728990i
$286$	−8.42180	+	13.4996i	−0.497991	+	0.798248i
$287$	−3.79727	−	6.57706i	−0.224145	−	0.388231i
$288$	−4.59338	−	16.3371i	−0.270668	−	0.962673i
$289$	−5.85863	+	10.1474i	−0.344625	+	0.596908i
$290$	−3.37273	−	6.33204i	−0.198054	−	0.371830i
$291$	−2.01923	+	9.29803i	−0.118369	+	0.545060i
$292$	2.93499	−	4.36504i	0.171757	−	0.255444i
$293$	19.0196	−	3.35367i	1.11114	−	0.195924i	0.412191	−	0.911097i	$-0.364764\pi$
$293$	19.0196	−	3.35367i	1.11114	−	0.195924i	0.698947	+	0.715174i	$0.253652\pi$
$294$	−8.32972	+	6.00521i	−0.485799	+	0.350231i
$295$	3.87424	−	4.61713i	0.225567	−	0.268820i
$296$	−3.32150	−	7.41646i	−0.193058	−	0.431073i
$297$	17.7455	−	4.17603i	1.02970	−	0.242318i
$298$	−1.72280	−	2.20178i	−0.0997994	−	0.127545i
$299$	−16.9484	−	14.2214i	−0.980150	−	0.822443i
$300$	3.36366	−	0.828129i	0.194201	−	0.0478121i
$301$	−6.81875	−	38.6711i	−0.393026	−	2.22896i
$302$	−6.42148	−	19.7143i	−0.369515	−	1.13443i
$303$	23.1511	−	25.4851i	1.33000	−	1.46408i
$304$	−22.6540	−	17.5930i	−1.29930	−	1.00903i
$305$	4.92615	+	2.84412i	0.282071	+	0.162854i
$306$	7.84243	+	5.79531i	0.448322	+	0.331296i
$307$	−4.60382	+	2.65802i	−0.262754	+	0.151701i	−0.625590	−	0.780152i	$-0.715142\pi$
$307$	−4.60382	+	2.65802i	−0.262754	+	0.151701i	0.362836	+	0.931853i	$0.381808\pi$
$308$	23.3424	−	2.48784i	1.33006	−	0.141758i
$309$	1.75985	+	2.27309i	0.100115	+	0.129312i
$310$	−3.03733	+	14.3410i	−0.172509	+	0.814512i
$311$	5.65210	−	4.74268i	0.320501	−	0.268933i	−0.468315	−	0.883562i	$-0.655139\pi$
$311$	5.65210	−	4.74268i	0.320501	−	0.268933i	0.788816	+	0.614629i	$0.210694\pi$
$312$	−0.513449	−	15.7018i	−0.0290683	−	0.888940i
$313$	−18.4368	+	6.71044i	−1.04211	+	0.379296i	−0.805679	−	0.592353i	$-0.798199\pi$
$313$	−18.4368	+	6.71044i	−1.04211	+	0.379296i	−0.236429	+	0.971649i	$0.575977\pi$
$314$	−9.59503	−	3.86850i	−0.541479	−	0.218312i
$315$	10.0054	+	0.788334i	0.563741	+	0.0444176i
$316$	9.43482	−	9.79862i	0.530750	−	0.551216i
$317$	−21.3647	−	3.76718i	−1.19996	−	0.211586i	−0.462280	−	0.886734i	$-0.652969\pi$
$317$	−21.3647	−	3.76718i	−1.19996	−	0.211586i	−0.737682	+	0.675148i	$0.764080\pi$
$318$	26.5251	+	18.0337i	1.48745	+	1.01128i
$319$	−6.08731	+	16.7247i	−0.340824	+	0.936406i
$320$	−4.20961	+	6.80288i	−0.235324	+	0.380293i
$321$	−7.35385	+	11.6540i	−0.410452	+	0.650463i
$322$	−1.11537	+	32.6225i	−0.0621569	+	1.81798i
$323$	16.4815			0.917053
$324$	−12.2591	+	13.1801i	−0.681060	+	0.732228i
$325$	3.20683			0.177883
$326$	0.242156	−	7.08262i	0.0134118	−	0.392270i
$327$	−7.65729	+	12.1349i	−0.423449	+	0.671061i
$328$	−3.60210	−	5.31520i	−0.198893	−	0.293483i
$329$	−9.35318	+	25.6977i	−0.515658	+	1.41676i
$330$	−7.10689	−	4.83178i	−0.391222	−	0.265981i
$331$	2.81290	+	0.495990i	0.154611	+	0.0272621i	0.250418	−	0.968138i	$-0.419432\pi$
$331$	2.81290	+	0.495990i	0.154611	+	0.0272621i	−0.0958069	+	0.995400i	$0.530543\pi$
$332$	21.2878	+	20.4974i	1.16832	+	1.12494i
$333$	−4.88260	+	7.10289i	−0.267565	+	0.389236i
$334$	−0.0824022	−	0.0332227i	−0.00450885	−	0.00181787i
$335$	2.39947	−	0.873337i	0.131097	−	0.0477155i
$336$	−17.7776	+	14.8722i	−0.969849	+	0.811343i
$337$	7.54649	−	6.33225i	0.411083	−	0.344940i	−0.413676	−	0.910424i	$-0.635755\pi$
$337$	7.54649	−	6.33225i	0.411083	−	0.344940i	0.824759	+	0.565485i	$0.191311\pi$
$338$	−0.795914	+	3.75796i	−0.0432920	+	0.204406i
$339$	1.19251	+	1.54029i	0.0647683	+	0.0836571i
$340$	−0.487173	−	4.57095i	−0.0264207	−	0.247895i
$341$	31.4944	−	18.1833i	1.70552	−	0.984682i
$342$	−3.42460	+	30.2296i	−0.185181	+	1.63463i
$343$	−8.13497	−	4.69673i	−0.439247	−	0.253599i
$344$	−8.10202	−	32.1950i	−0.436831	−	1.73584i
$345$	8.03500	−	8.84506i	0.432590	−	0.476202i
$346$	9.52058	+	29.2287i	0.511829	+	1.57135i
$347$	3.80102	+	21.5566i	0.204049	+	1.15722i	0.898929	+	0.438094i	$0.144346\pi$
$347$	3.80102	+	21.5566i	0.204049	+	1.15722i	−0.694880	+	0.719126i	$0.744542\pi$
$348$	−4.20107	−	17.0637i	−0.225201	−	0.914712i
$349$	23.1742	+	19.4455i	1.24049	+	1.04089i	0.997486	+	0.0708662i	$0.0225763\pi$
$349$	23.1742	+	19.4455i	1.24049	+	1.04089i	0.243001	+	0.970026i	$0.421868\pi$
$350$	−2.91555	−	3.72612i	−0.155842	−	0.199170i
$351$	−13.9364	+	9.13446i	−0.743870	+	0.487562i
$352$	19.5324	−	3.51762i	1.04108	−	0.187490i
$353$	−9.39079	+	11.1915i	−0.499822	+	0.595664i	−0.955687	−	0.294385i	$-0.904885\pi$
$353$	−9.39079	+	11.1915i	−0.499822	+	0.595664i	0.455866	+	0.890049i	$0.349330\pi$
$354$	11.9759	−	8.63388i	0.636511	−	0.458885i
$355$	4.05125	−	0.714345i	0.215018	−	0.0379135i
$356$	−7.05299	−	4.74234i	−0.373808	−	0.251344i
$357$	2.82642	−	13.0149i	0.149590	−	0.688822i
$358$	−1.14100	−	2.14214i	−0.0603039	−	0.113216i
$359$	1.97722	−	3.42464i	0.104354	−	0.180746i	−0.809120	−	0.587643i	$-0.800056\pi$
$359$	1.97722	−	3.42464i	0.104354	−	0.180746i	0.913474	+	0.406897i	$0.133389\pi$
$360$	8.48510	+	0.0562218i	0.447204	+	0.00296315i
$361$	16.2100	+	28.0765i	0.853157	+	1.47771i
$362$	3.34540	−	5.36247i	0.175830	−	0.281845i
$363$	0.305643	+	2.24657i	0.0160421	+	0.117914i
$364$	−19.2714	+	9.43415i	−1.01010	+	0.494484i
$365$	1.69054	+	2.01470i	0.0884867	+	0.105454i
$366$	9.98709	+	9.71566i	0.522034	+	0.507846i
$367$	13.0304	+	35.8008i	0.680182	+	1.86879i	0.439751	+	0.898120i	$0.355067\pi$
$367$	13.0304	+	35.8008i	0.680182	+	1.86879i	0.240431	+	0.970666i	$0.422711\pi$
$368$	1.04362	+	27.5770i	0.0544022	+	1.43755i
$369$	−2.82472	+	6.19684i	−0.147049	+	0.322594i
$370$	4.02318	−	0.568415i	0.209155	−	0.0295505i
$371$	7.60704	−	43.1417i	0.394938	−	2.23980i
$372$	−15.8358	+	32.2267i	−0.821047	+	1.67088i
$373$	18.4754	+	6.72448i	0.956618	+	0.348181i	0.772707	−	0.634762i	$-0.218902\pi$
$373$	18.4754	+	6.72448i	0.956618	+	0.348181i	0.183911	+	0.982943i	$0.441124\pi$
$374$	−7.62456	+	8.48037i	−0.394257	+	0.438509i
$375$	−0.0680766	+	1.73071i	−0.00351546	+	0.0893736i
$376$	−6.32417	+	22.2386i	−0.326144	+	1.14687i
$377$		−	16.2682i		−	0.837853i
$378$	23.2841	+	7.88840i	1.19761	+	0.405736i
$379$			27.2900i			1.40179i	0.713262	+	0.700897i	$0.247217\pi$
$379$			27.2900i			1.40179i	−0.713262	+	0.700897i	$0.752783\pi$
$380$	11.5902	−	8.44667i	0.594567	−	0.433305i
$381$	−15.6719	+	8.24448i	−0.802893	+	0.422377i
$382$	−6.84180	−	6.15135i	−0.350057	−	0.314730i
$383$	13.2067	+	4.80685i	0.674832	+	0.245619i	0.656627	−	0.754216i	$-0.271983\pi$
$383$	13.2067	+	4.80685i	0.674832	+	0.245619i	0.0182048	+	0.999834i	$0.494205\pi$
$384$	−14.0866	+	13.6223i	−0.718853	+	0.695162i
$385$	−2.03816	+	11.5590i	−0.103874	+	0.589102i
$386$	0.493740	+	3.49463i	0.0251307	+	0.177872i
$387$	−24.6831	+	25.1132i	−1.25471	+	1.27658i
$388$	10.5567	−	3.04376i	0.535933	−	0.154523i
$389$	−7.86582	−	21.6112i	−0.398813	−	1.09573i	−0.962863	−	0.269990i	$-0.912980\pi$
$389$	−7.86582	−	21.6112i	−0.398813	−	1.09573i	0.564050	−	0.825741i	$-0.309242\pi$
$390$	7.61473	+	1.92834i	0.385587	+	0.0976453i
$391$	−10.1928	−	12.1473i	−0.515474	−	0.614318i
$392$	10.6686	+	5.17456i	0.538847	+	0.261355i
$393$	−8.45651	−	3.46009i	−0.426575	−	0.174538i
$394$	−1.25363	−	0.782084i	−0.0631570	−	0.0394008i
$395$	3.40063	+	5.89007i	0.171104	+	0.296362i
$396$	−13.9701	−	15.7468i	−0.702024	−	0.791305i
$397$	−12.3689	+	21.4236i	−0.620779	+	1.07522i	0.368562	+	0.929603i	$0.379850\pi$
$397$	−12.3689	+	21.4236i	−0.620779	+	1.07522i	−0.989341	+	0.145618i	$0.953483\pi$
$398$	−6.49768	+	3.46096i	−0.325699	+	0.173482i
$399$	39.5738	−	12.6657i	1.98117	−	0.634080i
$400$	−2.68519	−	2.96475i	−0.134259	−	0.148238i
$401$	6.23935	−	1.10017i	0.311579	−	0.0549397i	−0.0156724	−	0.999877i	$-0.504989\pi$
$401$	6.23935	−	1.10017i	0.311579	−	0.0549397i	0.327251	+	0.944937i	$0.393878\pi$
$402$	6.22279	−	0.630912i	0.310365	−	0.0314670i
$403$	−21.3666	+	25.4637i	−1.06435	+	1.26844i
$404$	−38.5901	−	9.56179i	−1.91993	−	0.475717i
$405$	−4.63398	−	7.71533i	−0.230264	−	0.383378i
$406$	−18.9025	+	14.7905i	−0.938115	+	0.734039i
$407$	−7.72168	−	6.47926i	−0.382749	−	0.321165i
$408$	1.59181	−	11.1468i	0.0788063	−	0.551851i
$409$	1.08096	+	6.13044i	0.0534502	+	0.303131i	0.999800	−	0.0200138i	$-0.00637103\pi$
$409$	1.08096	+	6.13044i	0.0534502	+	0.303131i	−0.946350	+	0.323145i	$0.895260\pi$
$410$	3.05254	−	0.994294i	0.150754	−	0.0491047i
$411$	−0.155061	−	0.484486i	−0.00764862	−	0.0238979i
$412$	1.34571	−	3.03443i	0.0662985	−	0.149496i
$413$	−17.4625	−	10.0820i	−0.859274	−	0.496102i
$414$	24.3981	−	16.1713i	1.19910	−	0.794775i
$415$	−12.7963	+	7.38796i	−0.628147	+	0.362661i
$416$	−15.6770	+	9.12756i	−0.768628	+	0.447515i
$417$	−0.479934	+	1.17297i	−0.0235025	+	0.0574404i
$418$	−34.8068	−	7.37187i	−1.70246	−	0.360570i
$419$	−2.94140	+	2.46813i	−0.143697	+	0.120576i	−0.711803	−	0.702380i	$-0.752121\pi$
$419$	−2.94140	+	2.46813i	−0.143697	+	0.120576i	0.568106	+	0.822956i	$0.307677\pi$
$420$	−4.68246	−	10.6010i	−0.228481	−	0.517275i
$421$	−11.8996	+	4.33109i	−0.579950	+	0.211084i	−0.615303	−	0.788290i	$-0.710966\pi$
$421$	−11.8996	+	4.33109i	−0.579950	+	0.211084i	0.0353537	+	0.999375i	$0.488744\pi$
$422$	−13.6228	+	33.7885i	−0.663146	+	1.64480i
$423$	23.6316	−	6.55136i	1.14901	−	0.318538i
$424$	3.79075	−	36.8423i	0.184095	−	1.78922i
$425$	2.26350	+	0.399117i	0.109796	+	0.0193600i
$426$	10.0494	+	0.739871i	0.486894	+	0.0358469i
$427$	6.50859	−	17.8822i	0.314973	−	0.865380i
$428$	15.8749	+	1.08680i	0.767341	+	0.0525324i
$429$	−9.07274	−	17.2463i	−0.438036	−	0.832659i
$430$	16.5897	+	0.567204i	0.800026	+	0.0273530i
$431$	6.22399			0.299799			0.149899	−	0.988701i	$-0.452105\pi$
$431$	6.22399			0.299799			0.149899	+	0.988701i	$0.452105\pi$
$432$	20.1143	+	5.23578i	0.967752	+	0.251906i
$433$	−15.0813			−0.724760			−0.362380	−	0.932030i	$-0.618036\pi$
$433$	−15.0813			−0.724760			−0.362380	+	0.932030i	$0.618036\pi$
$434$	49.0129	+	1.67576i	2.35269	+	0.0804389i
$435$	8.77985	+	0.345350i	0.420962	+	0.0165583i
$436$	16.5299	+	1.13164i	0.791640	+	0.0541959i
$437$	16.9206	−	46.4889i	0.809422	−	2.22387i
$438$	2.80275	+	5.80053i	0.133920	+	0.277160i
$439$	16.8683	+	2.97433i	0.805078	+	0.141957i	0.561018	−	0.827803i	$-0.310410\pi$
$439$	16.8683	+	2.97433i	0.805078	+	0.141957i	0.244060	+	0.969760i	$0.421521\pi$
$440$	−1.01566	+	9.87119i	−0.0484197	+	0.470591i
$441$	−1.20430	−	12.5188i	−0.0573478	−	0.596132i
$442$	3.89772	−	9.66751i	0.185396	−	0.459837i
$443$	−16.6015	+	6.04245i	−0.788761	+	0.287086i	−0.704821	−	0.709385i	$-0.748973\pi$
$443$	−16.6015	+	6.04245i	−0.788761	+	0.287086i	−0.0839403	+	0.996471i	$0.526750\pi$
$444$	9.89498	+	1.06951i	0.469595	+	0.0507565i
$445$	3.25534	−	2.73155i	0.154318	−	0.129488i
$446$	−31.3263	−	6.63472i	−1.48334	−	0.314163i
$447$	3.39275	−	0.461580i	0.160472	−	0.0218320i
$448$	24.8586	+	9.91714i	1.17446	+	0.468541i
$449$	2.47053	−	1.42636i	0.116592	−	0.0673142i	−0.440570	−	0.897718i	$-0.645224\pi$
$449$	2.47053	−	1.42636i	0.116592	−	0.0673142i	0.557162	+	0.830404i	$0.311890\pi$
$450$	−1.20237	+	4.06870i	−0.0566801	+	0.191800i
$451$	−6.89740	−	3.98222i	−0.324786	−	0.187515i
$452$	0.911881	−	2.05619i	0.0428913	−	0.0967150i
$453$	24.8152	+	5.38905i	1.16592	+	0.253200i
$454$	−26.7110	+	8.70049i	−1.25361	+	0.408334i
$455$	−1.86296	−	10.5654i	−0.0873370	−	0.495313i
$456$	32.6006	−	13.0874i	1.52666	−	0.612876i
$457$	−28.6557	−	24.0450i	−1.34046	−	1.12478i	−0.981508	−	0.191420i	$-0.938691\pi$
$457$	−28.6557	−	24.0450i	−1.34046	−	1.12478i	−0.358949	−	0.933357i	$-0.616865\pi$
$458$	−8.61477	+	6.74072i	−0.402542	+	0.314973i
$459$	−10.9737	+	4.71295i	−0.512208	+	0.219982i
$460$	−13.3934	−	3.31858i	−0.624469	−	0.154730i
$461$	5.34367	−	6.36834i	0.248879	−	0.296603i	−0.627112	−	0.778929i	$-0.715763\pi$
$461$	5.34367	−	6.36834i	0.248879	−	0.296603i	0.875992	+	0.482326i	$0.160208\pi$
$462$	−11.7904	+	26.2217i	−0.548538	+	1.21994i
$463$	−13.0649	+	2.30369i	−0.607177	+	0.107062i	−0.468780	−	0.883315i	$-0.655306\pi$
$463$	−13.0649	+	2.30369i	−0.607177	+	0.107062i	−0.138397	+	0.990377i	$0.544195\pi$
$464$	−15.0401	+	13.6219i	−0.698219	+	0.632380i
$465$	−13.2891	−	12.0720i	−0.616266	−	0.559826i
$466$	8.10375	−	4.31643i	0.375399	−	0.199955i
$467$	10.6761	−	18.4916i	0.494031	−	0.855687i	−0.505945	−	0.862566i	$-0.668856\pi$
$467$	10.6761	−	18.4916i	0.494031	−	0.855687i	0.999976	+	0.00687850i	$0.00218951\pi$
$468$	16.9219	+	9.15782i	0.782214	+	0.423320i
$469$	−4.27128	−	7.39807i	−0.197229	−	0.341611i
$470$	−9.80807	−	6.11882i	−0.452413	−	0.282240i
$471$	10.0189	−	7.75673i	0.461645	−	0.357411i
$472$	−15.3386	−	7.43962i	−0.706017	−	0.342436i
$473$	−26.4701	−	31.5459i	−1.21710	−	1.45048i
$474$	4.53309	+	16.0310i	0.208212	+	0.736330i
$475$	2.45255	+	6.73832i	0.112531	+	0.309175i
$476$	−14.7767	+	4.26049i	−0.677288	+	0.195279i
$477$	−35.4581	+	16.9088i	−1.62352	+	0.774201i
$478$	1.84825	+	13.0817i	0.0845372	+	0.598344i
$479$	4.22728	−	23.9741i	0.193149	−	1.09540i	−0.721880	−	0.692018i	$-0.756722\pi$
$479$	4.22728	−	23.9741i	0.193149	−	1.09540i	0.915030	−	0.403386i	$-0.132167\pi$
$480$	−4.59330	−	8.65457i	−0.209654	−	0.395025i
$481$	8.65782	+	3.15119i	0.394762	+	0.143682i
$482$	−19.4572	−	17.4936i	−0.886250	−	0.796812i
$483$	−33.8092	−	21.3341i	−1.53837	−	0.970735i
$484$	2.11577	−	1.54192i	0.0961713	−	0.0700872i
$485$			5.49335i			0.249440i
$486$	−6.36414	−	21.1068i	−0.288683	−	0.957425i
$487$			4.18429i			0.189608i	0.995496	+	0.0948041i	$0.0302225\pi$
$487$			4.18429i			0.189608i	−0.995496	+	0.0948041i	$0.969778\pi$
$488$	4.40079	−	15.4752i	0.199215	−	0.700528i
$489$	7.34027	+	4.63182i	0.331938	+	0.209458i
$490$	−3.96383	+	4.40874i	−0.179067	+	0.199167i
$491$	−8.76679	−	3.19085i	−0.395640	−	0.144001i	0.136536	−	0.990635i	$-0.456403\pi$
$491$	−8.76679	−	3.19085i	−0.395640	−	0.144001i	−0.532176	+	0.846634i	$0.678625\pi$
$492$	7.84625	−	0.525424i	0.353736	−	0.0236879i
$493$	2.02471	−	11.4827i	0.0911882	−	0.517154i
$494$	32.2007	−	4.54948i	1.44878	−	0.204691i
$495$	9.50034	−	4.53040i	0.427009	−	0.203626i
$496$	41.4325	−	1.56796i	1.86037	−	0.0704034i
$497$	−4.70703	−	12.9325i	−0.211139	−	0.580100i
$498$	−34.8279	+	9.84825i	−1.56067	+	0.441311i
$499$	−17.2143	−	20.5152i	−0.770619	−	0.918388i	0.227850	−	0.973696i	$-0.426830\pi$
$499$	−17.2143	−	20.5152i	−0.770619	−	0.918388i	−0.998469	+	0.0553079i	$0.982386\pi$
$500$	1.79631	−	0.879365i	0.0803333	−	0.0393264i
$501$	0.0860422	−	0.0666149i	0.00384408	−	0.00297614i
$502$	3.51089	−	5.62773i	0.156699	−	0.251178i
$503$	−0.270145	−	0.467904i	−0.0120452	−	0.0208628i	0.859940	−	0.510395i	$-0.170501\pi$
$503$	−0.270145	−	0.467904i	−0.0120452	−	0.0208628i	−0.871985	+	0.489532i	$0.837168\pi$
$504$	−4.74406	−	27.9881i	−0.211317	−	1.24669i
$505$	9.93926	−	17.2153i	0.442291	−	0.766071i
$506$	16.0927	+	30.2128i	0.715408	+	1.34312i
$507$	−3.48232	−	3.16340i	−0.154655	−	0.140491i
$508$	16.9685	+	11.4094i	0.752856	+	0.506210i
$509$	8.54203	−	1.50619i	0.378619	−	0.0667607i	0.0188998	−	0.999821i	$-0.493984\pi$
$509$	8.54203	−	1.50619i	0.378619	−	0.0667607i	0.359719	+	0.933061i	$0.382873\pi$
$510$	5.13477	+	2.30881i	0.227371	+	0.102236i
$511$	5.65564	−	6.74013i	0.250191	−	0.298166i
$512$	21.5654	+	6.85077i	0.953066	+	0.302764i
$513$	−29.8521	−	22.2978i	−1.31800	−	0.984471i
$514$	−1.82124	−	2.32758i	−0.0803317	−	0.102665i
$515$	1.27142	+	1.06685i	0.0560255	+	0.0470110i
$516$	39.0517	+	11.3226i	1.71916	+	0.498450i
$517$	4.98003	+	28.2432i	0.219021	+	1.24213i
$518$	−4.20994	−	12.9247i	−0.184974	−	0.567881i
$519$	−36.7913	−	7.98988i	−1.61496	−	0.350717i
$520$	−2.21356	−	8.79604i	−0.0970712	−	0.385732i
$521$	−32.7994	−	18.9367i	−1.43697	−	0.829634i	−0.439330	−	0.898326i	$-0.644784\pi$
$521$	−32.7994	−	18.9367i	−1.43697	−	0.829634i	−0.997638	+	0.0686916i	$0.978118\pi$
$522$	20.6404	+	6.09957i	0.903405	+	0.266971i
$523$	19.5110	−	11.2647i	0.853155	−	0.492569i	−0.00855929	−	0.999963i	$-0.502725\pi$
$523$	19.5110	−	11.2647i	0.853155	−	0.492569i	0.861714	+	0.507394i	$0.169391\pi$
$524$	1.11814	+	10.4911i	0.0488462	+	0.458305i
$525$	5.74164	−	0.781144i	0.250586	−	0.0340919i
$526$	2.64677	−	12.4969i	0.115405	−	0.544891i
$527$	−18.2505	+	15.3140i	−0.795005	+	0.667088i
$528$	−8.34749	+	22.8287i	−0.363278	+	0.993494i
$529$	−23.1153	+	8.41328i	−1.00501	+	0.365795i
$530$	17.1750	+	6.92458i	0.746034	+	0.300784i
$531$	1.73146	+	17.9986i	0.0751391	+	0.781074i
$532$	−34.5620	−	33.2788i	−1.49845	−	1.44282i
$533$	7.16921	+	1.26412i	0.310533	+	0.0547553i
$534$	9.37246	−	4.52866i	0.405586	−	0.195974i
$535$	−2.72112	+	7.47621i	−0.117644	+	0.323225i
$536$	−4.05176	−	5.97870i	−0.175009	−	0.258240i
$537$	2.97025	+	0.116833i	0.128176	+	0.00504171i
$538$	−0.420288	+	12.2927i	−0.0181199	+	0.529974i
$539$	14.7080			0.633517
$540$	−5.30166	+	8.93826i	−0.228147	+	0.384641i
$541$	24.3954			1.04884			0.524421	−	0.851459i	$-0.324282\pi$
$541$	24.3954			1.04884			0.524421	+	0.851459i	$0.324282\pi$
$542$	0.952770	−	27.8668i	0.0409250	−	1.19698i
$543$	3.60398	+	6.85077i	0.154661	+	0.293995i
$544$	−12.2014	+	4.49144i	−0.523132	+	0.192569i
$545$	−2.83340	+	7.78471i	−0.121370	+	0.333460i
$546$	1.92953	−	26.2081i	0.0825764	−	1.12160i
$547$	24.8094	+	4.37457i	1.06077	+	0.187043i	0.676700	−	0.736259i	$-0.263410\pi$
$547$	24.8094	+	4.37457i	1.06077	+	0.187043i	0.384074	+	0.923302i	$0.374521\pi$
$548$	−0.407418	+	0.423128i	−0.0174040	+	0.0180751i
$549$	−16.4445	+	4.55889i	−0.701833	+	0.194569i
$550$	−4.60172	−	1.85531i	−0.196218	−	0.0791107i
$551$	34.1833	−	12.4417i	1.45626	−	0.530034i
$552$	−29.8074	−	15.9338i	−1.26869	−	0.678188i
$553$	17.4302	−	14.6256i	0.741206	−	0.621945i
$554$	0.207322	−	0.978886i	0.00880828	−	0.0415889i
$555$	−1.88447	+	4.60569i	−0.0799915	+	0.195501i
$556$	1.45517	−	0.155093i	0.0617131	−	0.00657739i
$557$	−3.79549	+	2.19132i	−0.160820	+	0.0928494i	−0.578250	−	0.815860i	$-0.696264\pi$
$557$	−3.79549	+	2.19132i	−0.160820	+	0.0928494i	0.417430	+	0.908709i	$0.362931\pi$
$558$	−24.2962	−	36.6564i	−1.02854	−	1.55179i
$559$	32.5975	+	18.8202i	1.37873	+	0.796008i
$560$	−8.20790	+	10.5691i	−0.346847	+	0.446625i
$561$	−4.25744	−	13.3023i	−0.179749	−	0.561622i
$562$	11.9979	+	36.8343i	0.506101	+	1.55376i
$563$	−3.80378	−	21.5723i	−0.160310	−	0.909164i	−0.953769	−	0.300540i	$-0.902833\pi$
$563$	−3.80378	−	21.5723i	−0.160310	−	0.909164i	0.793459	−	0.608624i	$-0.208278\pi$
$564$	−19.6102	−	20.4271i	−0.825739	−	0.860138i
$565$	0.861540	+	0.722918i	0.0362452	+	0.0304134i
$566$	5.08160	+	6.49437i	0.213596	+	0.272979i
$567$	−22.7272	+	19.7494i	−0.954454	+	0.829398i
$568$	−4.75582	−	10.6191i	−0.199550	−	0.445568i
$569$	−7.22498	+	8.61040i	−0.302887	+	0.360967i	−0.895923	−	0.444209i	$-0.853485\pi$
$569$	−7.22498	+	8.61040i	−0.302887	+	0.360967i	0.593036	+	0.805176i	$0.297929\pi$
$570$	1.77176	+	17.4751i	0.0742107	+	0.731953i
$571$	27.8556	−	4.91170i	1.16572	−	0.205548i	0.442893	−	0.896575i	$-0.353952\pi$
$571$	27.8556	−	4.91170i	1.16572	−	0.205548i	0.722829	+	0.691026i	$0.242841\pi$
$572$	−12.5556	+	18.6732i	−0.524977	+	0.780766i
$573$	10.7320	−	3.43482i	0.448336	−	0.143492i
$574$	−5.04918	−	9.47943i	−0.210749	−	0.395664i
$575$	3.44959	−	5.97487i	0.143858	−	0.249169i
$576$	−5.70275	−	23.3126i	−0.237615	−	0.971359i
$577$	−0.731900	−	1.26769i	−0.0304694	−	0.0527745i	0.850389	−	0.526155i	$-0.176367\pi$
$577$	−0.731900	−	1.26769i	−0.0304694	−	0.0527745i	−0.880858	+	0.473381i	$0.843034\pi$
$578$	−8.77088	+	14.0592i	−0.364820	+	0.584784i
$579$	−4.00061	−	1.63690i	−0.166260	−	0.0680273i
$580$	−4.46099	−	9.11261i	−0.185233	−	0.378380i
$581$	31.7746	+	37.8675i	1.31823	+	1.57101i
$582$	−3.30327	+	13.0441i	−0.136925	+	0.540697i
$583$	−15.7127	−	43.1703i	−0.650754	−	1.78793i
$584$	4.35922	−	6.02766i	0.180386	−	0.249426i
$585$	−6.74370	+	6.86123i	−0.278818	+	0.283677i
$586$	27.0442	−	3.82094i	1.11718	−	0.157841i
$587$	−1.66130	+	9.42170i	−0.0685692	+	0.388875i	0.931138	+	0.364668i	$0.118817\pi$
$587$	−1.66130	+	9.42170i	−0.0685692	+	0.388875i	−0.999707	+	0.0242075i	$0.992294\pi$
$588$	−12.0633	+	8.08517i	−0.497483	+	0.333427i
$589$	−69.8463	−	25.4220i	−2.87797	−	1.04749i
$590$	5.69891	−	6.33858i	0.234621	−	0.260955i
$591$	1.60156	−	0.842533i	0.0658795	−	0.0346572i
$592$	−4.33617	−	10.6428i	−0.178216	−	0.437418i
$593$		−	9.16389i		−	0.376316i	−0.982139	−	0.188158i	$-0.939748\pi$
$593$		−	9.16389i		−	0.376316i	0.982139	−	0.188158i	$-0.0602517\pi$
$594$	25.2831	−	5.04482i	1.03738	−	0.206991i
$595$		−	7.68931i		−	0.315231i
$596$	−2.32859	−	3.19521i	−0.0953829	−	0.130881i
$597$	0.354385	−	9.00953i	0.0145040	−	0.368735i
$598$	−23.2674	−	20.9193i	−0.951475	−	0.855455i
$599$	30.5902	+	11.1339i	1.24988	+	0.454920i	0.880362	−	0.474303i	$-0.157300\pi$
$599$	30.5902	+	11.1339i	1.24988	+	0.454920i	0.369520	+	0.929223i	$0.379522\pi$
$600$	4.79417	−	1.00792i	0.195721	−	0.0411483i
$601$	5.89242	−	33.4176i	0.240357	−	1.36313i	−0.590676	−	0.806909i	$-0.701139\pi$
$601$	5.89242	−	33.4176i	0.240357	−	1.36313i	0.831033	−	0.556223i	$-0.187750\pi$
$602$	−7.76880	−	54.9867i	−0.316633	−	2.24109i
$603$	−3.17733	+	6.97039i	−0.129391	+	0.283856i
$604$	−8.12337	−	28.1743i	−0.330535	−	1.14640i
$605$	0.447707	+	1.23006i	0.0182019	+	0.0500092i
$606$	33.9531	−	34.9016i	1.37925	−	1.41778i
$607$	20.5781	+	24.5241i	0.835241	+	0.995402i	0.999959	+	0.00906087i	$0.00288420\pi$
$607$	20.5781	+	24.5241i	0.835241	+	0.995402i	−0.164718	+	0.986341i	$0.552671\pi$
$608$	−31.1688	−	25.9605i	−1.26406	−	1.05284i
$609$	−3.96272	−	29.1271i	−0.160577	−	1.18029i
$610$	6.82513	+	4.25789i	0.276341	+	0.172397i
$611$	−13.1068	−	22.7016i	−0.530244	−	0.918410i
$612$	10.8043	+	8.57000i	0.436740	+	0.346422i
$613$	−9.67422	+	16.7562i	−0.390738	+	0.676778i	−0.992547	−	0.121862i	$-0.961114\pi$
$613$	−9.67422	+	16.7562i	−0.390738	+	0.676778i	0.601809	+	0.798640i	$0.294447\pi$
$614$	−6.63543	+	3.53434i	−0.267784	+	0.142634i
$615$	−0.834434	+	3.84235i	−0.0336476	+	0.154939i
$616$	33.1121	−	2.38828i	1.33413	−	0.0962267i
$617$	−18.4821	+	3.25889i	−0.744062	+	0.131198i	−0.532812	−	0.846234i	$-0.678865\pi$
$617$	−18.4821	+	3.25889i	−0.744062	+	0.131198i	−0.211250	+	0.977432i	$0.567753\pi$
$618$	2.37751	+	3.29780i	0.0956376	+	0.132657i
$619$	18.3423	−	21.8595i	0.737238	−	0.878606i	−0.258946	−	0.965892i	$-0.583375\pi$
$619$	18.3423	−	21.8595i	0.737238	−	0.878606i	0.996183	+	0.0872863i	$0.0278195\pi$
$620$	−4.98593	+	20.1226i	−0.200240	+	0.808141i
$621$	2.02764	+	35.7918i	0.0813665	+	1.43628i
$622$	8.21780	−	6.43011i	0.329504	−	0.257824i
$623$	−10.8907	−	9.13834i	−0.436325	−	0.366120i
$624$	0.0330711	−	22.2176i	0.00132390	−	0.889414i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	−26.3826	+	8.59351i	−1.05446	+	0.343466i
$627$	29.2999	−	32.2538i	1.17012	−	1.28809i
$628$	−13.3746	−	5.93136i	−0.533703	−	0.236687i
$629$	5.71882	+	3.30176i	0.228024	+	0.131650i
$630$	14.1034	+	1.59772i	0.561894	+	0.0636548i
$631$	−21.3908	+	12.3500i	−0.851553	+	0.491645i	−0.861175	−	0.508309i	$-0.830271\pi$
$631$	−21.3908	+	12.3500i	−0.851553	+	0.491645i	0.00962134	+	0.999954i	$0.496937\pi$
$632$	13.8086	−	13.3933i	0.549275	−	0.532758i
$633$	−27.3150	−	35.2811i	−1.08567	−	1.40230i
$634$	−30.0146	−	6.35691i	−1.19203	−	0.252465i
$635$	−7.83189	+	6.57173i	−0.310799	+	0.260791i
$636$	36.6187	+	26.7704i	1.45203	+	1.06151i
$637$	−12.6329	+	4.59800i	−0.500534	+	0.182179i
$638$	−9.41193	+	23.3444i	−0.372622	+	0.924213i
$639$	−6.99105	+	10.1701i	−0.276562	+	0.402324i
$640$	−6.27855	+	9.41169i	−0.248181	+	0.372030i
$641$	34.0788	+	6.00902i	1.34603	+	0.237342i	0.799788	−	0.600283i	$-0.204945\pi$
$641$	34.0788	+	6.00902i	1.34603	+	0.237342i	0.546246	+	0.837625i	$0.316057\pi$
$642$	−10.9570	+	16.1163i	−0.432438	+	0.636058i
$643$	−14.8492	+	40.7979i	−0.585595	+	1.60891i	0.192871	+	0.981224i	$0.438220\pi$
$643$	−14.8492	+	40.7979i	−0.585595	+	1.60891i	−0.778467	+	0.627686i	$0.784002\pi$
$644$	−3.15289	+	46.0543i	−0.124241	+	1.81479i
$645$	−10.8492	+	17.1932i	−0.427185	+	0.676981i
$646$	23.2947	+	0.796448i	0.916517	+	0.0313358i
$647$	21.8300			0.858227			0.429114	−	0.903251i	$-0.358826\pi$
$647$	21.8300			0.858227			0.429114	+	0.903251i	$0.358826\pi$
$648$	−17.9637	+	18.0362i	−0.705682	+	0.708528i
$649$	−21.1461			−0.830057
$650$	4.53250	+	0.154967i	0.177779	+	0.00607829i
$651$	−32.0529	+	50.7959i	−1.25625	+	1.99085i
$652$	0.684520	−	9.99879i	0.0268079	−	0.391583i
$653$	−8.08482	+	22.2129i	−0.316384	+	0.869257i	0.674947	+	0.737866i	$0.264166\pi$
$653$	−8.08482	+	22.2129i	−0.316384	+	0.869257i	−0.991331	+	0.131391i	$0.958056\pi$
$654$	−11.4091	+	16.7813i	−0.446132	+	0.656199i
$655$	−5.19511	−	0.916038i	−0.202990	−	0.0357926i
$656$	−4.83432	−	7.68651i	−0.188748	−	0.300108i
$657$	−7.86564	−	0.619740i	−0.306868	−	0.0241783i
$658$	−14.4615	+	35.8688i	−0.563767	+	1.39831i
$659$	−23.9853	+	8.72992i	−0.934333	+	0.340069i	−0.763926	−	0.645304i	$-0.776731\pi$
$659$	−23.9853	+	8.72992i	−0.934333	+	0.340069i	−0.170407	+	0.985374i	$0.554508\pi$
$660$	−9.81130	−	7.17262i	−0.381904	−	0.279194i
$661$	−4.15845	+	3.48935i	−0.161745	+	0.135720i	−0.720068	−	0.693904i	$-0.755889\pi$
$661$	−4.15845	+	3.48935i	−0.161745	+	0.135720i	0.558323	+	0.829624i	$0.311445\pi$
$662$	3.95175	+	0.836957i	0.153589	+	0.0325292i
$663$	7.81533	+	10.0946i	0.303522	+	0.392040i
$664$	29.0973	+	29.9995i	1.12920	+	1.16420i
$665$	20.7756	−	11.9948i	0.805644	−	0.465139i
$666$	−7.24425	+	9.80319i	−0.280709	+	0.379866i
$667$	−30.3103	−	17.4997i	−1.17362	−	0.677590i
$668$	−0.114861	−	0.0509386i	−0.00444410	−	0.00197087i
$669$	26.3700	−	29.0285i	1.01952	−	1.12231i
$670$	3.43359	−	1.11841i	0.132651	−	0.0432080i
$671$	−3.46545	−	19.6535i	−0.133782	−	0.758716i
$672$	−25.8454	+	20.1610i	−0.997006	+	0.777729i
$673$	31.3838	+	26.3342i	1.20976	+	1.01511i	0.999296	+	0.0375058i	$0.0119413\pi$
$673$	31.3838	+	26.3342i	1.20976	+	1.01511i	0.210462	+	0.977602i	$0.432503\pi$
$674$	10.9721	−	8.58525i	0.422630	−	0.330692i
$675$	−3.55981	−	3.78520i	−0.137017	−	0.145692i
$676$	−1.30653	+	5.27300i	−0.0502513	+	0.202808i
$677$	−8.96862	+	10.6884i	−0.344692	+	0.410788i	−0.910342	−	0.413858i	$-0.864181\pi$
$677$	−8.96862	+	10.6884i	−0.344692	+	0.410788i	0.565649	+	0.824646i	$0.308626\pi$
$678$	1.61105	+	2.23466i	0.0618719	+	0.0858214i
$679$	18.0986	−	3.19128i	0.694562	−	0.122470i
$680$	−0.467678	−	6.48407i	−0.0179346	−	0.248653i
$681$	7.30165	−	33.6222i	0.279800	−	1.28840i
$682$	45.3925	−	24.1781i	1.73817	−	0.925829i
$683$	−10.4379	+	18.0789i	−0.399394	+	0.691771i	−0.993651	−	0.112504i	$-0.964113\pi$
$683$	−10.4379	+	18.0789i	−0.399394	+	0.691771i	0.594257	+	0.804275i	$0.297446\pi$
$684$	−6.30110	+	42.5607i	−0.240929	+	1.62735i
$685$	−0.146848	−	0.254347i	−0.00561075	−	0.00971811i
$686$	−11.2709	−	7.03141i	−0.430325	−	0.268460i
$687$	−1.80600	−	13.2746i	−0.0689032	−	0.506459i
$688$	−9.89550	−	45.8955i	−0.377262	−	1.74975i
$689$	26.9918	+	32.1676i	1.02831	+	1.22549i
$690$	11.7840	−	12.1132i	0.448609	−	0.461142i
$691$	4.04094	+	11.1024i	0.153724	+	0.422354i	0.992518	−	0.122094i	$-0.0389611\pi$
$691$	4.04094	+	11.1024i	0.153724	+	0.422354i	−0.838794	+	0.544449i	$0.816739\pi$
$692$	12.0438	+	41.7716i	0.457837	+	1.58792i
$693$	−20.4452	−	28.6684i	−0.776647	−	1.08902i
$694$	4.33061	+	30.6516i	0.164388	+	1.16352i
$695$	−0.127060	+	0.720591i	−0.00481965	+	0.0273336i
$696$	−5.11316	−	24.3207i	−0.193814	−	0.921873i
$697$	4.90297	+	1.78453i	0.185713	+	0.0675940i
$698$	31.8145	+	28.6039i	1.20420	+	1.08267i
$699$	−0.441980	+	11.2365i	−0.0167172	+	0.425002i
$700$	−3.94074	−	5.40734i	−0.148946	−	0.204378i
$701$			33.7134i			1.27334i	0.771137	+	0.636669i	$0.219688\pi$
$701$			33.7134i			1.27334i	−0.771137	+	0.636669i	$0.780312\pi$
$702$	−20.1390	+	12.2371i	−0.760096	+	0.461859i
$703$			20.6021i			0.777024i
$704$	27.7768	−	4.02788i	1.04688	−	0.151807i
$705$	12.5302	−	6.59175i	0.471915	−	0.248260i
$706$	−13.8137	+	15.3641i	−0.519884	+	0.578237i
$707$	−62.4924	−	22.7454i	−2.35027	−	0.855428i
$708$	17.3438	−	11.6243i	0.651820	−	0.436868i
$709$	0.162738	−	0.922932i	0.00611175	−	0.0346614i	−0.981599	−	0.190952i	$-0.938843\pi$
$709$	0.162738	−	0.922932i	0.00611175	−	0.0346614i	0.987711	+	0.156291i	$0.0499536\pi$
$710$	5.76051	−	0.813874i	0.216188	−	0.0305441i
$711$	−19.7534	−	5.11045i	−0.740812	−	0.191657i
$712$	−9.73944	−	7.04359i	−0.365001	−	0.263970i
$713$	24.4591	+	67.2009i	0.916002	+	2.51669i
$714$	4.62375	−	18.2585i	0.173040	−	0.683308i
$715$	−7.23195	−	8.61870i	−0.270459	−	0.322321i
$716$	−1.50916	−	3.08282i	−0.0564001	−	0.115210i
$717$	−14.9758	−	6.12754i	−0.559282	−	0.228837i
$718$	2.96007	−	4.74480i	0.110469	−	0.177074i
$719$	−11.5378	−	19.9841i	−0.430289	−	0.745282i	0.566609	−	0.823987i	$-0.308255\pi$
$719$	−11.5378	−	19.9841i	−0.430289	−	0.745282i	−0.996898	+	0.0787049i	$0.974922\pi$
$720$	11.9900	+	0.489496i	0.446841	+	0.0182424i
$721$	2.77628	−	4.80866i	0.103394	−	0.179084i
$722$	21.5542	+	40.4663i	0.802165	+	1.50600i
$723$	30.5204	−	9.76817i	1.13507	−	0.363282i
$724$	4.98749	−	7.41758i	0.185358	−	0.275672i
$725$	4.99590	−	0.880912i	0.185543	−	0.0327162i
$726$	0.323430	+	3.19004i	0.0120036	+	0.118394i
$727$	28.5327	−	34.0040i	1.05822	−	1.26114i	0.0941300	−	0.995560i	$-0.469993\pi$
$727$	28.5327	−	34.0040i	1.05822	−	1.26114i	0.964090	−	0.265577i	$-0.0855625\pi$
$728$	−27.6939	+	12.4028i	−1.02640	+	0.459680i
$729$	26.2523	+	6.30999i	0.972308	+	0.233704i
$730$	2.29202	+	2.92925i	0.0848316	+	0.108416i
$731$	20.6662	+	17.3410i	0.764367	+	0.641380i
$732$	13.6461	+	14.2146i	0.504376	+	0.525387i
$733$	−7.35750	−	41.7265i	−0.271756	−	1.54120i	−0.749083	−	0.662477i	$-0.769505\pi$
$733$	−7.35750	−	41.7265i	−0.271756	−	1.54120i	0.477327	−	0.878726i	$-0.341606\pi$
$734$	16.6870	+	51.2301i	0.615928	+	1.89094i
$735$	−2.21334	−	6.91553i	−0.0816403	−	0.255083i
$736$	0.142405	+	39.0274i	0.00524911	+	1.43857i
$737$	−7.75841	−	4.47932i	−0.285785	−	0.164998i
$738$	−4.29188	+	8.62203i	−0.157986	+	0.317381i
$739$	24.5287	−	14.1616i	0.902301	−	0.520944i	0.0243552	−	0.999703i	$-0.492247\pi$
$739$	24.5287	−	14.1616i	0.902301	−	0.520944i	0.877946	+	0.478759i	$0.158913\pi$
$740$	5.71378	−	0.608975i	0.210043	−	0.0223864i
$741$	−15.0829	+	36.8630i	−0.554086	+	1.35420i
$742$	12.8365	−	60.6083i	0.471242	−	2.22500i
$743$	−16.4461	+	13.7999i	−0.603349	+	0.506270i	−0.892520	−	0.451007i	$-0.851065\pi$
$743$	−16.4461	+	13.7999i	−0.603349	+	0.506270i	0.289171	+	0.957277i	$0.406620\pi$
$744$	−23.9394	+	44.7836i	−0.877662	+	1.64184i
$745$	1.85763	−	0.676122i	0.0680583	−	0.0247712i
$746$	25.7879	+	10.3971i	0.944162	+	0.380665i
$747$	11.1026	−	42.9148i	0.406222	−	1.57017i
$748$	−11.1863	+	11.6176i	−0.409010	+	0.424782i
$749$	26.2123	+	4.62193i	0.957776	+	0.168882i
$750$	−0.179853	+	2.44288i	−0.00656732	+	0.0892013i
$751$	13.7122	−	37.6740i	0.500366	−	1.37474i	−0.390553	−	0.920580i	$-0.627716\pi$
$751$	13.7122	−	37.6740i	0.500366	−	1.37474i	0.890919	−	0.454163i	$-0.150062\pi$
$752$	−10.0132	+	31.1262i	−0.365143	+	1.13506i
$753$	3.78225	+	7.18965i	0.137833	+	0.262005i
$754$	0.786141	−	22.9932i	0.0286296	−	0.837364i
$755$	14.6610			0.533568
$756$	32.5283	+	12.2746i	1.18304	+	0.446421i
$757$	−33.4950			−1.21739			−0.608697	−	0.793402i	$-0.708308\pi$
$757$	−33.4950			−1.21739			−0.608697	+	0.793402i	$0.708308\pi$
$758$	−1.31876	+	38.5714i	−0.0478996	+	1.40098i
$759$	−41.8923	−	1.64781i	−1.52059	−	0.0598117i
$760$	16.7897	−	11.3783i	0.609025	−	0.412736i
$761$	9.33508	−	25.6479i	0.338396	−	0.929736i	−0.647453	−	0.762105i	$-0.724166\pi$
$761$	9.33508	−	25.6479i	0.338396	−	0.929736i	0.985850	−	0.167631i	$-0.0536118\pi$
$762$	−22.5488	+	10.8953i	−0.816857	+	0.394696i
$763$	27.2939	+	4.81265i	0.988105	+	0.174230i
$764$	−9.37285	−	9.02486i	−0.339098	−	0.326508i
$765$	−5.61390	+	4.00360i	−0.202971	+	0.144751i
$766$	18.4339	+	7.43214i	0.666045	+	0.268534i
$767$	18.1627	−	6.61069i	0.655817	−	0.238698i
$768$	−20.5681	+	18.5729i	−0.742187	+	0.670193i
$769$	6.92881	−	5.81397i	0.249859	−	0.209657i	−0.509252	−	0.860617i	$-0.670078\pi$
$769$	6.92881	−	5.81397i	0.249859	−	0.209657i	0.759112	+	0.650960i	$0.225634\pi$
$770$	−3.43929	+	16.2389i	−0.123944	+	0.585208i
$771$	3.58661	−	0.487954i	0.129169	−	0.0175733i
$772$	0.528971	+	4.96313i	0.0190381	+	0.178627i
$773$	−12.1103	+	6.99190i	−0.435578	+	0.251481i	−0.701720	−	0.712453i	$-0.747584\pi$
$773$	−12.1103	+	6.99190i	−0.435578	+	0.251481i	0.266142	+	0.963934i	$0.414251\pi$
$774$	−36.1003	+	34.3020i	−1.29760	+	1.23296i
$775$	−8.97681	−	5.18277i	−0.322457	−	0.186170i
$776$	15.0677	−	3.79187i	0.540900	−	0.136120i
$777$	16.2689	+	3.53307i	0.583643	+	0.126748i
$778$	−10.0731	−	30.9251i	−0.361139	−	1.10872i
$779$	2.82670	+	16.0310i	0.101277	+	0.574370i
$780$	10.6694	+	3.09347i	0.382025	+	0.110764i
$781$	−11.0561	−	9.27719i	−0.395619	−	0.331964i
$782$	−13.8194	−	17.6615i	−0.494181	−	0.631573i
$783$	−19.2022	+	18.0588i	−0.686231	+	0.645370i
$784$	14.8289	+	7.82920i	0.529602	+	0.279614i
$785$	4.70224	−	5.60391i	0.167830	−	0.200012i
$786$	−11.7851	−	5.29910i	−0.420362	−	0.189013i
$787$	46.6396	−	8.22382i	1.66252	−	0.293148i	0.738149	−	0.674637i	$-0.235700\pi$
$787$	46.6396	−	8.22382i	1.66252	−	0.293148i	0.924373	+	0.381490i	$0.124589\pi$
$788$	−1.73407	−	1.16597i	−0.0617738	−	0.0415359i
$789$	11.5803	+	10.5197i	0.412268	+	0.374511i
$790$	4.52178	+	8.48928i	0.160878	+	0.302035i
$791$	1.88126	−	3.25844i	0.0668899	−	0.115857i
$792$	−18.9842	−	22.9314i	−0.674575	−	0.814831i
$793$	9.12061	+	15.7974i	0.323882	+	0.560980i
$794$	−18.5174	+	29.6822i	−0.657157	+	1.05338i
$795$	−17.9337	+	13.8845i	−0.636042	+	0.492432i
$796$	−9.35099	+	4.57769i	−0.331437	+	0.162252i
$797$	20.3965	+	24.3076i	0.722480	+	0.861019i	0.994869	−	0.101169i	$-0.0322582\pi$
$797$	20.3965	+	24.3076i	0.722480	+	0.861019i	−0.272389	+	0.962187i	$0.587814\pi$
$798$	56.5452	−	15.9892i	2.00168	−	0.566013i
$799$	−6.42586	−	17.6549i	−0.227331	−	0.624586i
$800$	−3.65194	−	4.32011i	−0.129116	−	0.152739i
$801$	−1.00137	+	12.7092i	−0.0353817	+	0.449059i
$802$	8.87179	−	1.25345i	0.313274	−	0.0442609i
$803$	1.60228	−	9.08698i	0.0565432	−	0.320673i
$804$	8.82570	−	0.591013i	0.311259	−	0.0208434i
$805$	−21.6891	−	7.89418i	−0.764440	−	0.278233i
$806$	−31.4298	+	34.9576i	−1.10707	+	1.23133i
$807$	−12.7398	−	8.03902i	−0.448463	−	0.282987i
$808$	−54.0807	−	15.3793i	−1.90255	−	0.541043i
$809$		−	50.8650i		−	1.78832i	−0.447749	−	0.894159i	$-0.647774\pi$
$809$		−	50.8650i		−	1.78832i	0.447749	−	0.894159i	$-0.352226\pi$
$810$	−6.17677	−	11.1287i	−0.217030	−	0.391022i
$811$			21.7980i			0.765433i	0.923866	+	0.382716i	$0.125011\pi$
$811$			21.7980i			0.765433i	−0.923866	+	0.382716i	$0.874989\pi$
$812$	−27.4313	+	19.9912i	−0.962649	+	0.701555i
$813$	28.8805	+	18.2240i	1.01288	+	0.639145i
$814$	−10.6006	−	9.53085i	−0.371552	−	0.334056i
$815$	4.70889	+	1.71390i	0.164945	+	0.0600352i
$816$	2.78850	−	15.6779i	0.0976171	−	0.548835i
$817$	−14.6155	+	82.8885i	−0.511331	+	2.89990i
$818$	1.23157	+	8.71693i	0.0430609	+	0.304780i
$819$	26.5230	+	18.2322i	0.926788	+	0.637085i
$820$	4.36247	−	1.25781i	0.152344	−	0.0439247i
$821$	−4.77717	−	13.1252i	−0.166724	−	0.458072i	0.827991	−	0.560741i	$-0.189484\pi$
$821$	−4.77717	−	13.1252i	−0.166724	−	0.458072i	−0.994716	+	0.102670i	$0.967262\pi$
$822$	−0.195750	−	0.692259i	−0.00682755	−	0.0241453i
$823$	11.9241	+	14.2106i	0.415648	+	0.495350i	0.932725	−	0.360589i	$-0.117424\pi$
$823$	11.9241	+	14.2106i	0.415648	+	0.495350i	−0.517077	+	0.855939i	$0.672980\pi$
$824$	2.04865	−	4.22380i	0.0713681	−	0.147143i
$825$	4.80500	−	3.72009i	0.167288	−	0.129517i
$826$	−24.1941	−	15.0936i	−0.841820	−	0.525174i
$827$	7.54660	+	13.0711i	0.262421	+	0.454527i	0.966885	−	0.255213i	$-0.0821457\pi$
$827$	7.54660	+	13.0711i	0.262421	+	0.454527i	−0.704464	+	0.709740i	$0.748812\pi$
$828$	35.2655	−	21.6773i	1.22556	−	0.753337i
$829$	15.5011	−	26.8486i	0.538374	−	0.932491i	−0.460618	−	0.887598i	$-0.652372\pi$
$829$	15.5011	−	26.8486i	0.538374	−	0.932491i	0.998992	−	0.0448923i	$-0.0142945\pi$
$830$	−18.4432	+	9.82368i	−0.640172	+	0.340985i
$831$	0.907086	+	0.824012i	0.0314665	+	0.0285847i
$832$	−22.5988	+	12.1432i	−0.783471	+	0.420990i
$833$	−9.48904	+	1.67317i	−0.328776	+	0.0579720i
$834$	−0.735015	+	1.63466i	−0.0254515	+	0.0566038i
$835$	0.0403829	−	0.0481265i	0.00139751	−	0.00166549i
$836$	−48.8393	−	12.1013i	−1.68914	−	0.418533i
$837$	53.7747	−	3.04639i	1.85872	−	0.105298i
$838$	−4.27662	+	3.34629i	−0.147733	+	0.115596i
$839$	21.1753	+	17.7682i	0.731052	+	0.613425i	0.930418	−	0.366500i	$-0.119444\pi$
$839$	21.1753	+	17.7682i	0.731052	+	0.613425i	−0.199366	+	0.979925i	$0.563888\pi$
$840$	−6.10585	−	15.2096i	−0.210672	−	0.524780i
$841$	0.566959	+	3.21538i	0.0195503	+	0.110875i
$842$	−17.0280	+	5.54647i	−0.586824	+	0.191144i
$843$	−46.3647	−	10.0689i	−1.59689	−	0.346792i
$844$	−20.8870	+	47.0979i	−0.718962	+	1.62118i
$845$	−2.35232	−	1.35811i	−0.0809223	−	0.0467205i
$846$	33.7172	−	8.11765i	1.15922	−	0.279090i
$847$	3.79254	−	2.18962i	0.130313	−	0.0752363i
$848$	7.13816	−	51.8892i	0.245125	−	1.78188i
$849$	−10.0073	+	1.36148i	−0.343449	+	0.0467259i
$850$	3.17992	+	0.673488i	0.109070	+	0.0231004i
$851$	15.1844	−	12.7412i	0.520515	−	0.436764i
$852$	14.1679	+	1.53135i	0.485385	+	0.0524632i
$853$	−49.0082	+	17.8375i	−1.67801	+	0.610745i	−0.993034	−	0.117824i	$-0.962408\pi$
$853$	−49.0082	+	17.8375i	−1.67801	+	0.610745i	−0.684973	+	0.728569i	$0.740186\pi$
$854$	10.0633	−	24.9600i	0.344359	−	0.854112i
$855$	−19.5746	−	8.92274i	−0.669437	−	0.305151i
$856$	22.3848	+	2.30320i	0.765098	+	0.0787219i
$857$	−15.4560	−	2.72531i	−0.527966	−	0.0930947i	−0.0966899	−	0.995315i	$-0.530826\pi$
$857$	−15.4560	−	2.72531i	−0.527966	−	0.0930947i	−0.431276	+	0.902220i	$0.641937\pi$
$858$	−11.9899	−	24.8141i	−0.409328	−	0.847140i
$859$	−9.45006	+	25.9638i	−0.322432	+	0.885874i	0.667535	+	0.744578i	$0.267349\pi$
$859$	−9.45006	+	25.9638i	−0.322432	+	0.885874i	−0.989967	+	0.141296i	$0.954873\pi$
$860$	23.4203	+	1.60336i	0.798624	+	0.0546741i
$861$	13.1439	+	0.517010i	0.447945	+	0.0176196i
$862$	8.79691	+	0.300767i	0.299624	+	0.0102442i
$863$	25.0822			0.853807			0.426904	−	0.904297i	$-0.359604\pi$
$863$	25.0822			0.853807			0.426904	+	0.904297i	$0.359604\pi$
$864$	28.1763	+	8.37219i	0.958579	+	0.284828i
$865$	−21.7366			−0.739067
$866$	−21.3157	−	0.728787i	−0.724337	−	0.0247652i
$867$	−9.44880	−	17.9611i	−0.320898	−	0.609992i
$868$	69.1933	+	4.73699i	2.34857	+	0.160784i
$869$	8.16118	−	22.4227i	0.276849	−	0.760637i
$870$	12.3926	+	0.912391i	0.420150	+	0.0309329i
$871$	8.06414	+	1.42193i	0.273243	+	0.0481801i
$872$	23.3085	+	2.39824i	0.789326	+	0.0812148i
$873$	−11.7534	−	11.5521i	−0.397792	−	0.390978i
$874$	26.1619	−	64.8892i	0.884939	−	2.19491i
$875$	3.14372	−	1.14422i	0.106277	−	0.0386817i
$876$	3.68107	+	8.33384i	0.124372	+	0.281574i
$877$	−18.9398	+	15.8924i	−0.639552	+	0.536648i	−0.903881	−	0.427785i	$-0.859294\pi$
$877$	−18.9398	+	15.8924i	−0.639552	+	0.536648i	0.264329	+	0.964433i	$0.414850\pi$
$878$	23.6977	+	5.01902i	0.799757	+	0.169384i
$879$	−12.6676	+	30.9598i	−0.427267	+	1.04425i
$880$	−1.91254	+	13.9027i	−0.0644716	+	0.468661i
$881$	−44.7128	+	25.8149i	−1.50641	+	0.869727i	−0.506439	+	0.862276i	$0.669038\pi$
$881$	−44.7128	+	25.8149i	−1.50641	+	0.869727i	−0.999972	+	0.00745086i	$0.997628\pi$
$882$	−1.09719	−	17.7521i	−0.0369443	−	0.597744i
$883$	17.5357	+	10.1242i	0.590123	+	0.340708i	0.765146	−	0.643857i	$-0.222667\pi$
$883$	17.5357	+	10.1242i	0.590123	+	0.340708i	−0.175023	+	0.984564i	$0.556000\pi$
$884$	5.97617	−	13.4756i	0.201000	−	0.453233i
$885$	3.18219	+	9.94266i	0.106968	+	0.334219i
$886$	−23.7564	+	7.73808i	−0.798110	+	0.259966i
$887$	−2.55743	−	14.5039i	−0.0858701	−	0.486994i	−0.997165	−	0.0752402i	$-0.976028\pi$
$887$	−2.55743	−	14.5039i	−0.0858701	−	0.486994i	0.911295	−	0.411753i	$-0.135083\pi$
$888$	13.9338	+	1.98979i	0.467586	+	0.0667730i
$889$	26.2014	+	21.9856i	0.878766	+	0.737372i
$890$	4.73306	−	3.70343i	0.158652	−	0.124139i
$891$	−10.2854	+	29.8537i	−0.344572	+	1.00014i
$892$	−43.9556	−	10.8912i	−1.47174	−	0.364666i
$893$	37.6776	−	44.9025i	1.26083	−	1.50260i
$894$	4.81758	−	0.488441i	0.161124	−	0.0163359i
$895$	1.69013	−	0.298015i	0.0564946	−	0.00996153i
$896$	34.6556	+	15.2180i	1.15776	+	0.508399i
$897$	36.4971	−	11.6810i	1.21860	−	0.390018i
$898$	3.56075	−	1.89662i	0.118824	−	0.0632910i
$899$	−26.2920	+	45.5391i	−0.876888	+	1.51881i
$900$	−1.89603	+	5.69255i	−0.0632008	+	0.189752i
$901$	15.0483	+	26.0644i	0.501332	+	0.868332i
$902$	−9.55627	−	5.96173i	−0.318189	−	0.198504i
$903$	62.9481	+	25.7560i	2.09478	+	0.857107i
$904$	1.38820	−	2.86213i	0.0461710	−	0.0951929i
$905$	2.87276	+	3.42362i	0.0954937	+	0.113805i
$906$	34.8130	+	8.81598i	1.15659	+	0.292891i
$907$	10.9877	+	30.1885i	0.364841	+	1.00239i	0.977294	+	0.211886i	$0.0679604\pi$
$907$	10.9877	+	30.1885i	0.364841	+	1.00239i	−0.612453	+	0.790507i	$0.709817\pi$
$908$	−38.1734	+	11.0064i	−1.26683	+	0.365260i
$909$	15.9318	+	57.4681i	0.528425	+	1.90610i
$910$	−2.12253	−	15.0230i	−0.0703611	−	0.498008i
$911$	2.71224	−	15.3819i	0.0898606	−	0.509625i	−0.906341	−	0.422547i	$-0.861136\pi$
$911$	2.71224	−	15.3819i	0.0898606	−	0.509625i	0.996202	−	0.0870775i	$-0.0277528\pi$
$912$	46.7097	−	16.9222i	1.54671	−	0.560352i
$913$	48.7138	+	17.7304i	1.61219	+	0.586790i
$914$	−39.3397	−	35.3697i	−1.30124	−	1.16992i
$915$	−8.71938	+	4.58699i	−0.288254	+	0.151641i
$916$	−12.5017	+	9.11096i	−0.413069	+	0.301034i
$917$			17.6482i			0.582795i
$918$	−15.7378	+	6.13093i	−0.519426	+	0.202351i
$919$		−	8.98488i		−	0.296384i	−0.988959	−	0.148192i	$-0.952655\pi$
$919$		−	8.98488i		−	0.296384i	0.988959	−	0.148192i	$-0.0473454\pi$
$920$	−18.7696	−	5.33767i	−0.618817	−	0.175978i
$921$	0.361897	−	9.20053i	0.0119249	−	0.303168i
$922$	7.86042	−	8.74270i	0.258869	−	0.287926i
$923$	12.3965	+	4.51196i	0.408036	+	0.148513i
$924$	−17.9315	+	36.4916i	−0.589903	+	1.20049i
$925$	−0.498904	+	2.82942i	−0.0164038	+	0.0930308i
$926$	−18.5771	+	2.62466i	−0.610481	+	0.0862518i
$927$	−4.95629	+	0.476793i	−0.162786	+	0.0156600i
$928$	−21.9158	+	18.5262i	−0.719420	+	0.608152i
$929$	−12.3543	−	33.9433i	−0.405333	−	1.11364i	−0.959616	−	0.281314i	$-0.909230\pi$
$929$	−12.3543	−	33.9433i	−0.405333	−	1.11364i	0.554283	−	0.832328i	$-0.312993\pi$
$930$	−18.1992	−	17.7046i	−0.596776	−	0.580557i
$931$	−19.3230	−	23.0282i	−0.633285	−	0.754720i
$932$	11.6623	−	5.70918i	0.382012	−	0.187010i
$933$	1.72278	+	12.6629i	0.0564012	+	0.414566i
$934$	15.9831	−	25.6198i	0.522982	−	0.838306i
$935$	−4.03191	−	6.98348i	−0.131858	−	0.228384i
$936$	23.4746	+	13.7613i	0.767293	+	0.449801i
$937$	−9.20827	+	15.9492i	−0.300821	+	0.521038i	−0.976322	−	0.216321i	$-0.930594\pi$
$937$	−9.20827	+	15.9492i	−0.300821	+	0.521038i	0.675501	+	0.737359i	$0.263927\pi$
$938$	−5.67947	−	10.6627i	−0.185441	−	0.348151i
$939$	7.21187	−	33.2088i	0.235350	−	1.08373i
$940$	−13.5669	−	9.12222i	−0.442504	−	0.297534i
$941$	32.9621	−	5.81211i	1.07453	−	0.189469i	0.391737	−	0.920077i	$-0.371874\pi$
$941$	32.9621	−	5.81211i	1.07453	−	0.189469i	0.682797	+	0.730608i	$0.260763\pi$
$942$	14.5354	−	10.4791i	0.473589	−	0.341428i
$943$	10.0672	−	11.9976i	0.327833	−	0.390696i
$944$	−21.3199	−	11.2563i	−0.693904	−	0.366361i
$945$	−10.4029	+	13.9273i	−0.338406	+	0.453055i
$946$	−35.8881	−	45.8657i	−1.16682	−	1.49122i
$947$	−34.6344	−	29.0617i	−1.12547	−	0.944378i	−0.126598	−	0.991954i	$-0.540406\pi$
$947$	−34.6344	−	29.0617i	−1.12547	−	0.944378i	−0.998868	+	0.0475763i	$0.984850\pi$
$948$	5.63233	+	22.8771i	0.182930	+	0.743015i
$949$	1.46455	+	8.30586i	0.0475412	+	0.269620i
$950$	3.14078	+	9.64238i	0.101900	+	0.312840i
$951$	25.2658	−	27.8131i	0.819301	−	0.901900i
$952$	−21.0910	+	5.30766i	−0.683565	+	0.172022i
$953$	−29.7405	−	17.1707i	−0.963389	−	0.556213i	−0.0661748	−	0.997808i	$-0.521079\pi$
$953$	−29.7405	−	17.1707i	−0.963389	−	0.556213i	−0.897215	+	0.441595i	$0.854413\pi$
$954$	−50.9332	+	22.1852i	−1.64902	+	0.718273i
$955$	5.63413	−	3.25287i	0.182316	−	0.105260i
$956$	1.98014	+	18.5789i	0.0640423	+	0.600884i
$957$	−18.8719	−	24.3756i	−0.610041	−	0.787951i
$958$	7.13331	−	33.6804i	0.230467	−	1.08816i
$959$	−0.752676	+	0.631570i	−0.0243052	+	0.0203945i
$960$	−6.07389	−	12.4542i	−0.196034	−	0.401959i
$961$	71.8341	−	26.1455i	2.31723	−	0.843402i
$962$	12.0846	+	4.87223i	0.389622	+	0.157087i
$963$	−10.2736	−	21.5439i	−0.331061	−	0.694241i
$964$	−26.6552	−	25.6655i	−0.858505	−	0.826630i
$965$	−2.45771	−	0.433360i	−0.0791164	−	0.0139503i
$966$	−46.7545	−	31.7871i	−1.50430	−	1.02273i
$967$	−5.68196	+	15.6111i	−0.182719	+	0.502018i	−0.996908	−	0.0785837i	$-0.974960\pi$
$967$	−5.68196	+	15.6111i	−0.182719	+	0.502018i	0.814188	+	0.580601i	$0.197182\pi$
$968$	3.06491	−	2.07709i	0.0985100	−	0.0667601i
$969$	−15.2340	+	24.1421i	−0.489387	+	0.775555i
$970$	−0.265460	+	7.76423i	−0.00852341	+	0.249294i
$971$	47.3923			1.52089			0.760445	−	0.649402i	$-0.224981\pi$
$971$	47.3923			1.52089			0.760445	+	0.649402i	$0.224981\pi$
$972$	−7.97503	−	30.1397i	−0.255799	−	0.966730i
$973$	2.44791			0.0784763
$974$	−0.202201	+	5.91402i	−0.00647895	+	0.189498i
$975$	−2.96411	+	4.69738i	−0.0949276	+	0.150436i
$976$	6.96785	−	21.6598i	0.223035	−	0.693312i
$977$	−10.2925	+	28.2785i	−0.329287	+	0.904708i	0.659006	+	0.752138i	$0.270977\pi$
$977$	−10.2925	+	28.2785i	−0.329287	+	0.904708i	−0.988293	+	0.152570i	$0.951245\pi$
$978$	10.1508	+	6.90127i	0.324587	+	0.220678i
$979$	−14.6827	−	2.58895i	−0.469260	−	0.0827433i
$980$	−5.81547	+	6.03971i	−0.185768	+	0.192932i
$981$	−10.6975	−	22.4328i	−0.341544	−	0.716226i
$982$	−12.2367	−	4.93356i	−0.390488	−	0.157436i
$983$	−18.3494	+	6.67863i	−0.585254	+	0.213015i	−0.617641	−	0.786460i	$-0.711911\pi$
$983$	−18.3494	+	6.67863i	−0.585254	+	0.213015i	0.0323866	+	0.999475i	$0.489689\pi$
$984$	11.1152	−	0.363466i	0.354339	−	0.0115869i
$985$	0.800369	−	0.671589i	0.0255019	−	0.0213986i
$986$	3.41658	−	16.1316i	0.108806	−	0.513736i
$987$	−28.9967	−	37.4532i	−0.922976	−	1.19215i
$988$	45.7319	−	4.87411i	1.45493	−	0.155066i
$989$	70.1303	−	40.4897i	2.23001	−	1.28750i
$990$	13.6466	−	5.94412i	0.433717	−	0.188916i
$991$	23.2834	+	13.4427i	0.739622	+	0.427021i	0.821932	−	0.569586i	$-0.192896\pi$
$991$	23.2834	+	13.4427i	0.739622	+	0.427021i	−0.0823100	+	0.996607i	$0.526230\pi$
$992$	58.6359	−	0.213953i	1.86169	−	0.00679301i
$993$	−3.32652	+	3.66189i	−0.105564	+	0.116207i
$994$	−6.02791	−	18.5060i	−0.191194	−	0.586976i
$995$	−0.903956	−	5.12659i	−0.0286573	−	0.162524i
$996$	−49.7012	+	12.2364i	−1.57484	+	0.387724i
$997$	−18.9498	−	15.9008i	−0.600147	−	0.503583i	0.291346	−	0.956618i	$-0.405897\pi$
$997$	−18.9498	−	15.9008i	−0.600147	−	0.503583i	−0.891493	+	0.453035i	$0.850341\pi$
$998$	−23.3391	−	29.8279i	−0.738788	−	0.944184i
$999$	−5.89128	−	13.7173i	−0.186392	−	0.433997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.71	yes	432
4.3	odd	2	inner	540.2.be.a.11.32	✓	432
27.5	odd	18	inner	540.2.be.a.491.32	yes	432
108.59	even	18	inner	540.2.be.a.491.71	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.32	✓	432	4.3	odd	2	inner
540.2.be.a.11.71	yes	432	1.1	even	1	trivial
540.2.be.a.491.32	yes	432	27.5	odd	18	inner
540.2.be.a.491.71	yes	432	108.59	even	18	inner

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:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41339 + 0.0483239i) q^{2} +(-0.924312 + 1.46480i) q^{3} +(1.99533 + 0.136601i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-1.37720 + 2.02567i) q^{6} +(3.29465 + 0.580935i) q^{7} +(2.81357 + 0.289492i) q^{8} +(-1.29129 - 2.70787i) q^{9} +(-0.528817 + 1.31162i) q^{10} +(3.29684 - 1.19995i) q^{11} +(-2.04440 + 2.79650i) q^{12} +(-2.45658 + 2.06131i) q^{13} +(4.62854 + 0.980297i) q^{14} +(-1.06033 - 1.36956i) q^{15} +(3.96268 + 0.545127i) q^{16} +(-1.99049 + 1.14921i) q^{17} +(-1.69424 - 3.88967i) q^{18} +(-6.21007 - 3.58539i) q^{19} +(-0.810806 + 1.82828i) q^{20} +(-3.89624 + 4.28904i) q^{21} +(4.71769 - 1.53668i) q^{22} +(1.19803 + 6.79437i) q^{23} +(-3.02467 + 3.85375i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(-3.57171 + 2.79472i) q^{26} +(5.16005 + 0.611427i) q^{27} +(6.49455 + 1.60921i) q^{28} +(-3.26084 + 3.88612i) q^{29} +(-1.43248 - 1.98696i) q^{30} +(10.2081 - 1.79996i) q^{31} +(5.57446 + 0.961969i) q^{32} +(-1.28962 + 5.93834i) q^{33} +(-2.86887 + 1.52809i) q^{34} +(-1.67274 + 2.89726i) q^{35} +(-2.20666 - 5.57949i) q^{36} +(-1.43654 - 2.48815i) q^{37} +(-8.60398 - 5.36764i) q^{38} +(-0.748772 - 5.50370i) q^{39} +(-1.23433 + 2.54488i) q^{40} +(-1.45919 - 1.73899i) q^{41} +(-5.71416 + 5.87380i) q^{42} +(-4.01448 - 11.0297i) q^{43} +(6.74219 - 1.94395i) q^{44} +(2.98621 - 0.287273i) q^{45} +(1.36495 + 9.66098i) q^{46} +(-1.41945 + 8.05011i) q^{47} +(-4.46126 + 5.30068i) q^{48} +(3.93937 + 1.43381i) q^{49} +(-1.05166 - 0.945526i) q^{50} +(0.156469 - 3.97791i) q^{51} +(-5.18326 + 3.77743i) q^{52} -13.0945i q^{53} +(7.26361 + 1.11354i) q^{54} +3.50842i q^{55} +(9.10156 + 2.58828i) q^{56} +(10.9919 - 5.78251i) q^{57} +(-4.79663 + 5.33502i) q^{58} +(-5.66375 - 2.06144i) q^{59} +(-1.92863 - 2.87757i) q^{60} +(0.987751 - 5.60182i) q^{61} +(14.5149 - 2.05074i) q^{62} +(-2.68126 - 9.67164i) q^{63} +(7.83239 + 1.62901i) q^{64} +(-1.09680 - 3.01344i) q^{65} +(-2.10969 + 8.33086i) q^{66} +(-1.64134 - 1.95607i) q^{67} +(-4.12867 + 2.02115i) q^{68} +(-11.0598 - 4.52524i) q^{69} +(-2.50423 + 4.01413i) q^{70} +(-2.05687 - 3.56261i) q^{71} +(-2.84924 - 7.99261i) q^{72} +(1.31500 - 2.27765i) q^{73} +(-1.91014 - 3.58614i) q^{74} +(1.64962 - 0.527967i) q^{75} +(-11.9014 - 8.00233i) q^{76} +(11.5590 - 2.03816i) q^{77} +(-0.792345 - 7.81504i) q^{78} +(4.37177 - 5.21007i) q^{79} +(-1.86757 + 3.53726i) q^{80} +(-5.66512 + 6.99331i) q^{81} +(-1.97836 - 2.52838i) q^{82} +(11.3190 + 9.49778i) q^{83} +(-8.36017 + 8.02583i) q^{84} +(-0.399117 - 2.26350i) q^{85} +(-5.14101 - 15.7832i) q^{86} +(-2.67836 - 8.36848i) q^{87} +(9.62326 - 2.42174i) q^{88} +(-3.68021 - 2.12477i) q^{89} +(4.23456 - 0.261723i) q^{90} +(-9.29104 + 5.36419i) q^{91} +(1.46235 + 13.7207i) q^{92} +(-6.79885 + 16.6165i) q^{93} +(-2.39525 + 11.3093i) q^{94} +(5.49313 - 4.60928i) q^{95} +(-6.56164 + 7.27633i) q^{96} +(5.16206 - 1.87884i) q^{97} +(5.49857 + 2.21690i) q^{98} +(-7.50649 - 7.37792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more