LMFDB - Embedded newform 768.2.z.a.13.30

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [768,2,Mod(13,768)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(768, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 47, 0]))

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

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

chi := DirichletCharacter("768.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 768 = 2^{8} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	768.z (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.13251087523$
Analytic rank:	$0$
Dimension:	$2048$
Relative dimension:	$64$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			13.30
Character	$\chi$	$=$	768.13
Dual form			768.2.z.a.709.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.192503 - 1.40105i) q^{2} +(-0.595699 + 0.803208i) q^{3} +(-1.92589 + 0.539412i) q^{4} +(0.765784 - 0.844912i) q^{5} +(1.24001 + 0.679985i) q^{6} +(-0.628656 - 1.17613i) q^{7} +(1.12648 + 2.59442i) q^{8} +(-0.290285 - 0.956940i) q^{9} +O(q^{10})$	\(q+(-0.192503 - 1.40105i) q^{2} +(-0.595699 + 0.803208i) q^{3} +(-1.92589 + 0.539412i) q^{4} +(0.765784 - 0.844912i) q^{5} +(1.24001 + 0.679985i) q^{6} +(-0.628656 - 1.17613i) q^{7} +(1.12648 + 2.59442i) q^{8} +(-0.290285 - 0.956940i) q^{9} +(-1.33118 - 0.910254i) q^{10} +(1.32690 + 5.29729i) q^{11} +(0.713989 - 1.86821i) q^{12} +(-0.0360610 + 0.734039i) q^{13} +(-1.52680 + 1.10719i) q^{14} +(0.222463 + 1.11840i) q^{15} +(3.41807 - 2.07769i) q^{16} +(1.25325 - 6.30053i) q^{17} +(-1.28484 + 0.590917i) q^{18} +(-1.31106 + 0.469105i) q^{19} +(-1.01906 + 2.04028i) q^{20} +(1.31917 + 0.195680i) q^{21} +(7.16634 - 2.87880i) q^{22} +(4.72760 + 5.76060i) q^{23} +(-2.75491 - 0.640699i) q^{24} +(0.362634 + 3.68188i) q^{25} +(1.03537 - 0.0907811i) q^{26} +(0.941544 + 0.336890i) q^{27} +(1.84514 + 1.92599i) q^{28} +(-1.68235 - 2.80684i) q^{29} +(1.52411 - 0.526976i) q^{30} +(8.44839 - 3.49944i) q^{31} +(-3.56894 - 4.38893i) q^{32} +(-5.04526 - 2.08981i) q^{33} +(-9.06862 - 0.543003i) q^{34} +(-1.47514 - 0.369504i) q^{35} +(1.07524 + 1.68637i) q^{36} +(4.40818 + 9.32031i) q^{37} +(0.909622 + 1.74656i) q^{38} +(-0.568104 - 0.466231i) q^{39} +(3.05470 + 1.03499i) q^{40} +(0.336149 - 3.41297i) q^{41} +(0.0202144 - 1.88589i) q^{42} +(8.07591 - 5.98950i) q^{43} +(-5.41288 - 9.48623i) q^{44} +(-1.03083 - 0.487544i) q^{45} +(7.16082 - 7.73254i) q^{46} +(-0.533445 - 0.798357i) q^{47} +(-0.367325 + 3.98310i) q^{48} +(2.90091 - 4.34152i) q^{49} +(5.08870 - 1.21684i) q^{50} +(4.31407 + 4.75984i) q^{51} +(-0.326500 - 1.43313i) q^{52} +(-2.10703 + 3.51537i) q^{53} +(0.290750 - 1.38400i) q^{54} +(5.49187 + 2.93546i) q^{55} +(2.34322 - 2.95589i) q^{56} +(0.404209 - 1.33250i) q^{57} +(-3.60866 + 2.89739i) q^{58} +(-0.507860 - 10.3377i) q^{59} +(-1.03171 - 2.03391i) q^{60} +(7.02457 - 1.04200i) q^{61} +(-6.52923 - 11.1630i) q^{62} +(-0.943000 + 0.943000i) q^{63} +(-5.46208 + 5.84514i) q^{64} +(0.592583 + 0.592583i) q^{65} +(-1.95671 + 7.47096i) q^{66} +(1.79345 + 12.0904i) q^{67} +(0.984958 + 12.8101i) q^{68} +(-7.44319 + 0.365660i) q^{69} +(-0.233725 + 2.13788i) q^{70} +(-0.450886 - 0.136775i) q^{71} +(2.15571 - 1.83110i) q^{72} +(3.22240 - 6.02869i) q^{73} +(12.2096 - 7.97026i) q^{74} +(-3.17334 - 1.90203i) q^{75} +(2.27191 - 1.61064i) q^{76} +(5.39615 - 4.89079i) q^{77} +(-0.543852 + 0.885693i) q^{78} +(14.2265 + 9.50584i) q^{79} +(0.862036 - 4.47903i) q^{80} +(-0.831470 + 0.555570i) q^{81} +(-4.84646 + 0.186045i) q^{82} +(-0.446640 + 0.944341i) q^{83} +(-2.64612 + 0.334718i) q^{84} +(-4.36367 - 5.88373i) q^{85} +(-9.94623 - 10.1618i) q^{86} +(3.25665 + 0.320752i) q^{87} +(-12.2487 + 9.40985i) q^{88} +(-3.73167 + 4.54706i) q^{89} +(-0.484638 + 1.53809i) q^{90} +(0.885997 - 0.419046i) q^{91} +(-12.2122 - 8.54413i) q^{92} +(-2.22193 + 8.87042i) q^{93} +(-1.01585 + 0.901070i) q^{94} +(-0.607636 + 1.46696i) q^{95} +(5.65123 - 0.252116i) q^{96} +(-4.14680 - 10.0113i) q^{97} +(-6.64112 - 3.22857i) q^{98} +(4.68401 - 2.80749i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2048 q+O(q^{10}) $ 2048 * q	$ 2048 q+O(q^{100}) $ 2048 * q

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/768\mathbb{Z}\right)^\times$.

$n$	$257$	$511$	$517$
$\chi(n)$	$1$	$1$	$e\left(\frac{47}{64}\right)$

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 $

$2$	−0.192503	−	1.40105i	−0.136120	−	0.990692i
$2$	−0.192503	−	1.40105i	−0.136120	−	0.990692i
$3$	−0.595699	+	0.803208i	−0.343927	+	0.463732i
$3$	−0.595699	+	0.803208i	−0.343927	+	0.463732i
$4$	−1.92589	+	0.539412i	−0.962943	+	0.269706i
$5$	0.765784	−	0.844912i	0.342469	−	0.377856i	−0.545225	−	0.838289i	$-0.683556\pi$
$5$	0.765784	−	0.844912i	0.342469	−	0.377856i	0.887694	+	0.460433i	$0.152306\pi$
$6$	1.24001	+	0.679985i	0.506231	+	0.277603i
$7$	−0.628656	−	1.17613i	−0.237610	−	0.444536i	0.734648	−	0.678448i	$-0.237347\pi$
$7$	−0.628656	−	1.17613i	−0.237610	−	0.444536i	−0.972258	+	0.233912i	$0.924847\pi$
$8$	1.12648	+	2.59442i	0.398271	+	0.917268i
$9$	−0.290285	−	0.956940i	−0.0967616	−	0.318980i
$10$	−1.33118	−	0.910254i	−0.420956	−	0.287848i
$11$	1.32690	+	5.29729i	0.400076	+	1.59719i	0.750678	+	0.660669i	$0.229727\pi$
$11$	1.32690	+	5.29729i	0.400076	+	1.59719i	−0.350602	+	0.936525i	$0.614023\pi$
$12$	0.713989	−	1.86821i	0.206111	−	0.539307i
$13$	−0.0360610	+	0.734039i	−0.0100015	+	0.203586i	0.988594	+	0.150605i	$0.0481222\pi$
$13$	−0.0360610	+	0.734039i	−0.0100015	+	0.203586i	−0.998596	+	0.0529807i	$0.983128\pi$
$14$	−1.52680	+	1.10719i	−0.408055	+	0.295908i
$15$	0.222463	+	1.11840i	0.0574397	+	0.288769i
$16$	3.41807	−	2.07769i	0.854517	−	0.519423i
$17$	1.25325	−	6.30053i	0.303959	−	1.52810i	−0.462972	−	0.886373i	$-0.653217\pi$
$17$	1.25325	−	6.30053i	0.303959	−	1.52810i	0.766930	−	0.641730i	$-0.221783\pi$
$18$	−1.28484	+	0.590917i	−0.302840	+	0.139280i
$19$	−1.31106	+	0.469105i	−0.300778	+	0.107620i	−0.482954	−	0.875646i	$-0.660436\pi$
$19$	−1.31106	+	0.469105i	−0.300778	+	0.107620i	0.182176	+	0.983266i	$0.441686\pi$
$20$	−1.01906	+	2.04028i	−0.227868	+	0.456220i
$21$	1.31917	+	0.195680i	0.287866	+	0.0427009i
$22$	7.16634	−	2.87880i	1.52787	−	0.613762i
$23$	4.72760	+	5.76060i	0.985773	+	1.20117i	0.979553	+	0.201187i	$0.0644800\pi$
$23$	4.72760	+	5.76060i	0.985773	+	1.20117i	0.00622025	+	0.999981i	$0.498020\pi$
$24$	−2.75491	−	0.640699i	−0.562343	−	0.130782i
$25$	0.362634	+	3.68188i	0.0725268	+	0.736377i
$26$	1.03537	−	0.0907811i	0.203052	−	0.0178036i
$27$	0.941544	+	0.336890i	0.181200	+	0.0648345i
$28$	1.84514	+	1.92599i	0.348699	+	0.363978i
$29$	−1.68235	−	2.80684i	−0.312405	−	0.521217i	0.660977	−	0.750407i	$-0.270142\pi$
$29$	−1.68235	−	2.80684i	−0.312405	−	0.521217i	−0.973382	+	0.229190i	$0.926392\pi$
$30$	1.52411	−	0.526976i	0.278262	−	0.0962122i
$31$	8.44839	−	3.49944i	1.51738	−	0.628518i	0.540312	−	0.841465i	$-0.318306\pi$
$31$	8.44839	−	3.49944i	1.51738	−	0.628518i	0.977064	+	0.212947i	$0.0683062\pi$
$32$	−3.56894	−	4.38893i	−0.630905	−	0.775860i
$33$	−5.04526	−	2.08981i	−0.878267	−	0.363790i
$34$	−9.06862	−	0.543003i	−1.55525	−	0.0931242i
$35$	−1.47514	−	0.369504i	−0.249345	−	0.0624576i
$36$	1.07524	+	1.68637i	0.179207	+	0.281062i
$37$	4.40818	+	9.32031i	0.724700	+	1.53225i	0.842193	+	0.539176i	$0.181264\pi$
$37$	4.40818	+	9.32031i	0.724700	+	1.53225i	−0.117493	+	0.993074i	$0.537486\pi$
$38$	0.909622	+	1.74656i	0.147560	+	0.283329i
$39$	−0.568104	−	0.466231i	−0.0909695	−	0.0746567i
$40$	3.05470	+	1.03499i	0.482991	+	0.163646i
$41$	0.336149	−	3.41297i	0.0524976	−	0.533017i	−0.932587	−	0.360946i	$-0.882454\pi$
$41$	0.336149	−	3.41297i	0.0524976	−	0.533017i	0.985084	−	0.172071i	$-0.0550460\pi$
$42$	0.0202144	−	1.88589i	0.00311916	−	0.290999i
$43$	8.07591	−	5.98950i	1.23156	−	0.913391i	0.233308	−	0.972403i	$-0.425045\pi$
$43$	8.07591	−	5.98950i	1.23156	−	0.913391i	0.998257	+	0.0590121i	$0.0187951\pi$
$44$	−5.41288	−	9.48623i	−0.816023	−	1.43010i
$45$	−1.03083	−	0.487544i	−0.153666	−	0.0726788i
$46$	7.16082	−	7.73254i	1.05580	−	1.14010i
$47$	−0.533445	−	0.798357i	−0.0778110	−	0.116452i	0.790523	−	0.612433i	$-0.209809\pi$
$47$	−0.533445	−	0.798357i	−0.0778110	−	0.116452i	−0.868334	+	0.495980i	$0.834809\pi$
$48$	−0.367325	+	3.98310i	−0.0530188	+	0.574911i
$49$	2.90091	−	4.34152i	0.414416	−	0.620217i
$50$	5.08870	−	1.21684i	0.719650	−	0.172087i
$51$	4.31407	+	4.75984i	0.604091	+	0.666512i
$52$	−0.326500	−	1.43313i	−0.0452774	−	0.198739i
$53$	−2.10703	+	3.51537i	−0.289423	+	0.482873i	−0.967759	−	0.251879i	$-0.918952\pi$
$53$	−2.10703	+	3.51537i	−0.289423	+	0.482873i	0.678336	+	0.734752i	$0.262702\pi$
$54$	0.290750	−	1.38400i	0.0395661	−	0.188339i
$55$	5.49187	+	2.93546i	0.740523	+	0.395818i
$56$	2.34322	−	2.95589i	0.313126	−	0.394998i
$57$	0.404209	−	1.33250i	0.0535388	−	0.176494i
$58$	−3.60866	+	2.89739i	−0.473841	+	0.380445i
$59$	−0.507860	−	10.3377i	−0.0661177	−	1.34586i	−0.771137	−	0.636669i	$-0.780312\pi$
$59$	−0.507860	−	10.3377i	−0.0661177	−	1.34586i	0.705019	−	0.709188i	$-0.250938\pi$
$60$	−1.03171	−	2.03391i	−0.133194	−	0.262576i
$61$	7.02457	−	1.04200i	0.899404	−	0.133414i	0.319012	−	0.947751i	$-0.396649\pi$
$61$	7.02457	−	1.04200i	0.899404	−	0.133414i	0.580393	+	0.814337i	$0.302899\pi$
$62$	−6.52923	−	11.1630i	−0.829213	−	1.41770i
$63$	−0.943000	+	0.943000i	−0.118807	+	0.118807i
$64$	−5.46208	+	5.84514i	−0.682760	+	0.730643i
$65$	0.592583	+	0.592583i	0.0735009	+	0.0735009i
$66$	−1.95671	+	7.47096i	−0.240854	+	0.919611i
$67$	1.79345	+	12.0904i	0.219104	+	1.47708i	0.767601	+	0.640928i	$0.221450\pi$
$67$	1.79345	+	12.0904i	0.219104	+	1.47708i	−0.548497	+	0.836153i	$0.684800\pi$
$68$	0.984958	+	12.8101i	0.119444	+	1.55346i
$69$	−7.44319	+	0.365660i	−0.896054	+	0.0440203i
$70$	−0.233725	+	2.13788i	−0.0279355	+	0.255526i
$71$	−0.450886	−	0.136775i	−0.0535104	−	0.0162322i	0.263416	−	0.964682i	$-0.415151\pi$
$71$	−0.450886	−	0.136775i	−0.0535104	−	0.0162322i	−0.316926	+	0.948450i	$0.602651\pi$
$72$	2.15571	−	1.83110i	0.254053	−	0.215797i
$73$	3.22240	−	6.02869i	0.377153	−	0.705604i	−0.619703	−	0.784837i	$-0.712747\pi$
$73$	3.22240	−	6.02869i	0.377153	−	0.705604i	0.996856	+	0.0792322i	$0.0252468\pi$
$74$	12.2096	−	7.97026i	1.41934	−	0.926524i
$75$	−3.17334	−	1.90203i	−0.366425	−	0.219627i
$76$	2.27191	−	1.61064i	0.260606	−	0.184753i
$77$	5.39615	−	4.89079i	0.614949	−	0.557357i
$78$	−0.543852	+	0.885693i	−0.0615791	+	0.100285i
$79$	14.2265	+	9.50584i	1.60061	+	1.06949i	0.950988	+	0.309229i	$0.100071\pi$
$79$	14.2265	+	9.50584i	1.60061	+	1.06949i	0.649617	+	0.760261i	$0.274929\pi$
$80$	0.862036	−	4.47903i	0.0963786	−	0.500771i
$81$	−0.831470	+	0.555570i	−0.0923855	+	0.0617300i
$82$	−4.84646	+	0.186045i	−0.535202	+	0.0205453i
$83$	−0.446640	+	0.944341i	−0.0490251	+	0.103655i	−0.927015	−	0.375024i	$-0.877634\pi$
$83$	−0.446640	+	0.944341i	−0.0490251	+	0.103655i	0.877990	+	0.478679i	$0.158884\pi$
$84$	−2.64612	+	0.334718i	−0.288715	+	0.0365207i
$85$	−4.36367	−	5.88373i	−0.473307	−	0.638180i
$86$	−9.94623	−	10.1618i	−1.07253	−	1.09577i
$87$	3.25665	+	0.320752i	0.349149	+	0.0343882i
$88$	−12.2487	+	9.40985i	−1.30572	+	1.00309i
$89$	−3.73167	+	4.54706i	−0.395557	+	0.481987i	−0.932263	−	0.361782i	$-0.882168\pi$
$89$	−3.73167	+	4.54706i	−0.395557	+	0.481987i	0.536706	+	0.843769i	$0.319668\pi$
$90$	−0.484638	+	1.53809i	−0.0510853	+	0.162129i
$91$	0.885997	−	0.419046i	0.0928778	−	0.0439279i
$92$	−12.2122	−	8.54413i	−1.27321	−	0.890787i
$93$	−2.22193	+	8.87042i	−0.230403	+	0.919820i
$94$	−1.01585	+	0.901070i	−0.104777	+	0.0929382i
$95$	−0.607636	+	1.46696i	−0.0623422	+	0.150507i
$96$	5.65123	−	0.252116i	0.576777	−	0.0257315i
$97$	−4.14680	−	10.0113i	−0.421044	−	1.01649i	−0.982040	−	0.188671i	$-0.939582\pi$
$97$	−4.14680	−	10.0113i	−0.421044	−	1.01649i	0.560997	−	0.827818i	$-0.310418\pi$
$98$	−6.64112	−	3.22857i	−0.670855	−	0.326135i
$99$	4.68401	−	2.80749i	0.470761	−	0.282163i
$100$	−2.68444	−	6.89528i	−0.268444	−	0.689528i
$101$	5.41322	−	15.1289i	0.538635	−	1.50538i	−0.296332	−	0.955085i	$-0.595763\pi$
$101$	5.41322	−	15.1289i	0.538635	−	1.50538i	0.834967	−	0.550300i	$-0.185487\pi$
$102$	5.83831	−	6.96051i	0.578079	−	0.689194i
$103$	−16.4701	+	1.62216i	−1.62285	+	0.159836i	−0.868172	−	0.496264i	$-0.834705\pi$
$103$	−16.4701	+	1.62216i	−1.62285	+	0.159836i	−0.754674	+	0.656100i	$0.772205\pi$
$104$	−1.94503	+	0.733323i	−0.190726	+	0.0719083i
$105$	1.17553	−	0.964733i	0.114720	−	0.0941483i
$106$	5.33082	+	2.27534i	0.517775	+	0.221001i
$107$	−1.88432	+	12.7031i	−0.182164	+	1.22805i	0.684445	+	0.729065i	$0.260045\pi$
$107$	−1.88432	+	12.7031i	−0.182164	+	1.22805i	−0.866609	+	0.498988i	$0.833705\pi$
$108$	−1.99503	−	0.140931i	−0.191972	−	0.0135611i
$109$	2.77851	+	7.76543i	0.266133	+	0.743793i	0.998051	+	0.0624002i	$0.0198755\pi$
$109$	2.77851	+	7.76543i	0.266133	+	0.743793i	−0.731918	+	0.681393i	$0.761374\pi$
$110$	3.05553	−	8.25947i	0.291334	−	0.787509i
$111$	−10.1121	−	2.01142i	−0.959797	−	0.190916i
$112$	−4.59243	−	2.71395i	−0.433944	−	0.256444i
$113$	−19.6438	+	3.90740i	−1.84794	+	0.367578i	−0.989405	−	0.145181i	$-0.953623\pi$
$113$	−19.6438	+	3.90740i	−1.84794	+	0.367578i	−0.858533	+	0.512759i	$0.828623\pi$
$114$	−1.94471	−	0.309808i	−0.182139	−	0.0290162i
$115$	8.48752	+	0.416965i	0.791465	+	0.0388822i
$116$	4.75406	+	4.49817i	0.441403	+	0.417644i
$117$	0.712899	−	0.178572i	0.0659076	−	0.0165090i
$118$	−14.3859	+	2.70158i	−1.32433	+	0.248700i
$119$	−8.19813	+	2.48687i	−0.751521	+	0.227971i
$120$	−2.65100	+	1.83702i	−0.242002	+	0.167696i
$121$	−16.5995	+	8.87261i	−1.50904	+	0.806601i
$122$	−2.81214	−	9.64119i	−0.254599	−	0.872873i
$123$	2.54108	+	2.30310i	0.229122	+	0.207664i
$124$	−14.3830	+	11.2967i	−1.29163	+	1.01447i
$125$	7.96809	+	5.90953i	0.712687	+	0.528565i
$126$	1.50272	+	1.13966i	0.133873	+	0.101529i
$127$			5.84891i			0.519007i	0.965742	+	0.259503i	$0.0835588\pi$
$127$			5.84891i			0.519007i	−0.965742	+	0.259503i	$0.916441\pi$
$128$	9.24080	+	6.52745i	0.816779	+	0.576950i
$129$			10.0546i			0.885256i
$130$	0.716166	−	0.944313i	0.0628119	−	0.0828218i
$131$	9.81063	+	7.27606i	0.857159	+	0.635712i	0.932390	−	0.361454i	$-0.117720\pi$
$131$	9.81063	+	7.27606i	0.857159	+	0.635712i	−0.0752313	+	0.997166i	$0.523970\pi$
$132$	10.8439	+	1.30327i	0.943837	+	0.113435i
$133$	1.37594	+	1.24708i	0.119309	+	0.108135i
$134$	16.5941	−	4.84015i	1.43351	−	0.418125i
$135$	1.00566	−	0.537537i	0.0865536	−	0.0462638i
$136$	17.7580	−	3.84596i	1.52274	−	0.329788i
$137$	−4.32336	+	1.31148i	−0.369370	+	0.112047i	−0.469512	−	0.882926i	$-0.655570\pi$
$137$	−4.32336	+	1.31148i	−0.369370	+	0.112047i	0.100142	+	0.994973i	$0.468070\pi$
$138$	1.94514	+	10.3579i	0.165581	+	0.881722i
$139$	−15.5032	+	3.88334i	−1.31496	+	0.329381i	−0.836133	−	0.548527i	$-0.815189\pi$
$139$	−15.5032	+	3.88334i	−1.31496	+	0.329381i	−0.478830	+	0.877908i	$0.658939\pi$
$140$	3.04027	−	0.0840870i	0.256950	−	0.00710665i
$141$	0.959019	+	0.0471136i	0.0807640	+	0.00396768i
$142$	−0.104832	+	0.658044i	−0.00879728	+	0.0552218i
$143$	−3.93627	+	0.782972i	−0.329167	+	0.0654754i
$144$	−2.98044	−	2.66777i	−0.248370	−	0.222314i
$145$	−3.65985	−	0.727989i	−0.303934	−	0.0604562i
$146$	−9.06682	−	3.35421i	−0.750375	−	0.277596i
$147$	1.75907	+	4.91627i	0.145086	+	0.405488i
$148$	−13.5171	−	15.5720i	−1.11110	−	1.28001i
$149$	0.259608	−	1.75014i	0.0212679	−	0.143377i	−0.975941	−	0.218033i	$-0.930036\pi$
$149$	0.259608	−	1.75014i	0.0212679	−	0.143377i	0.997209	+	0.0746563i	$0.0237860\pi$
$150$	−2.05396	+	4.81215i	−0.167705	+	0.392911i
$151$	−5.30155	+	4.35087i	−0.431434	+	0.354069i	−0.824908	−	0.565267i	$-0.808773\pi$
$151$	−5.30155	+	4.35087i	−0.431434	+	0.354069i	0.393474	+	0.919336i	$0.371273\pi$
$152$	−2.69394	−	2.87301i	−0.218508	−	0.233032i
$153$	−6.39303	+	0.629659i	−0.516846	+	0.0509049i
$154$	−7.89102	−	6.61879i	−0.635876	−	0.533358i
$155$	3.51292	−	9.81796i	0.282165	−	0.788597i
$156$	1.34559	+	0.591465i	0.107734	+	0.0473551i
$157$	−10.9172	+	6.54350i	−0.871285	+	0.522228i	−0.878498	−	0.477746i	$-0.841454\pi$
$157$	−10.9172	+	6.54350i	−0.871285	+	0.522228i	0.00721318	+	0.999974i	$0.497704\pi$
$158$	10.5795	−	21.7619i	0.841661	−	1.73129i
$159$	−1.56841	−	3.78649i	−0.124383	−	0.300288i
$160$	−6.44129	−	0.345531i	−0.509229	−	0.0273167i
$161$	3.80319	−	9.18172i	0.299734	−	0.723621i
$162$	0.938442	+	1.05798i	0.0737310	+	0.0831229i
$163$	2.38107	−	9.50575i	0.186500	−	0.744548i	−0.802503	−	0.596648i	$-0.796499\pi$
$163$	2.38107	−	9.50575i	0.186500	−	0.744548i	0.989002	−	0.147900i	$-0.0472512\pi$
$164$	1.19361	+	6.75432i	0.0932057	+	0.527424i
$165$	−5.62929	+	2.66245i	−0.438239	+	0.207272i
$166$	1.40905	+	0.443977i	0.109363	+	0.0344593i
$167$	−8.02844	+	9.78269i	−0.621260	+	0.757007i	−0.984633	−	0.174637i	$-0.944125\pi$
$167$	−8.02844	+	9.78269i	−0.621260	+	0.757007i	0.363373	+	0.931644i	$0.381625\pi$
$168$	0.978341	+	3.64291i	0.0754807	+	0.281057i
$169$	12.3999	+	1.22128i	0.953838	+	0.0939448i
$170$	−7.40339	+	7.24636i	−0.567814	+	0.555771i
$171$	0.829486	+	1.11843i	0.0634324	+	0.0855287i
$172$	−12.3225	+	15.8913i	−0.939580	+	1.21170i
$173$	−4.67166	+	9.87740i	−0.355180	+	0.750965i	−0.999910	−	0.0134459i	$-0.995720\pi$
$173$	−4.67166	+	9.87740i	−0.355180	+	0.750965i	0.644730	+	0.764411i	$0.276970\pi$
$174$	−0.177524	−	4.62448i	−0.0134580	−	0.350581i
$175$	4.10241	−	2.74114i	0.310113	−	0.207211i
$176$	15.5416	+	15.3496i	1.17149	+	1.15702i
$177$	8.60587	+	5.75026i	0.646857	+	0.432216i
$178$	7.08901	+	4.35294i	0.531344	+	0.326267i
$179$	5.72083	−	5.18506i	0.427595	−	0.387549i	−0.429198	−	0.903211i	$-0.641204\pi$
$179$	5.72083	−	5.18506i	0.427595	−	0.387549i	0.856793	+	0.515661i	$0.172454\pi$
$180$	2.24824	+	0.382915i	0.167574	+	0.0285408i
$181$	7.77914	+	4.66263i	0.578219	+	0.346571i	0.773128	−	0.634250i	$-0.218691\pi$
$181$	7.77914	+	4.66263i	0.578219	+	0.346571i	−0.194909	+	0.980821i	$0.562441\pi$
$182$	−0.757661	−	1.16066i	−0.0561616	−	0.0860338i
$183$	−3.34759	+	6.26291i	−0.247461	+	0.462967i
$184$	−9.61989	+	18.7546i	−0.709188	+	1.38261i
$185$	11.2506	+	3.41282i	0.827157	+	0.250915i
$186$	12.8556	+	1.40545i	0.942621	+	0.103053i
$187$	35.0387	−	1.72134i	2.56228	−	0.125877i
$188$	1.45800	+	1.24980i	0.106335	+	0.0911509i
$189$	−0.195680	−	1.31917i	−0.0142336	−	0.0959554i
$190$	2.17226	+	0.568935i	0.157592	+	0.0412749i
$191$	−14.6177	−	14.6177i	−1.05770	−	1.05770i	−0.998230	−	0.0594711i	$-0.981059\pi$
$191$	−14.6177	−	14.6177i	−1.05770	−	1.05770i	−0.0594711	−	0.998230i	$-0.518941\pi$
$192$	−1.44110	−	7.86913i	−0.104003	−	0.567906i
$193$	18.5919	−	18.5919i	1.33827	−	1.33827i	0.440543	−	0.897732i	$-0.354786\pi$
$193$	18.5919	−	18.5919i	1.33827	−	1.33827i	0.897732	−	0.440543i	$-0.145214\pi$
$194$	−13.2280	+	7.73707i	−0.949716	+	0.555489i
$195$	−0.828969	+	0.122966i	−0.0593637	+	0.00880577i
$196$	−3.24496	+	9.92606i	−0.231783	+	0.709004i
$197$	0.111277	+	2.26510i	0.00792819	+	0.161382i	0.999495	+	0.0317837i	$0.0101188\pi$
$197$	0.111277	+	2.26510i	0.00792819	+	0.161382i	−0.991567	+	0.129598i	$0.958631\pi$
$198$	−4.83512	−	6.02209i	−0.343617	−	0.427971i
$199$	0.158740	−	0.523296i	0.0112528	−	0.0370955i	−0.951134	−	0.308778i	$-0.900080\pi$
$199$	0.158740	−	0.523296i	0.0112528	−	0.0370955i	0.962387	+	0.271682i	$0.0875800\pi$
$200$	−9.14387	+	5.08840i	−0.646569	+	0.359804i
$201$	−10.7795	−	5.76175i	−0.760326	−	0.406402i
$202$	−22.2385	−	4.67183i	−1.56469	−	0.328709i
$203$	−2.24359	+	3.74321i	−0.157469	+	0.262722i
$204$	−10.8759	−	6.83985i	−0.761467	−	0.478886i
$205$	−2.62625	−	2.89762i	−0.183425	−	0.202378i
$206$	5.44326	+	22.7631i	0.379250	+	1.58598i
$207$	4.14020	−	6.19625i	0.287764	−	0.430669i
$208$	1.40185	+	2.58392i	0.0972006	+	0.179163i
$209$	−4.22463	−	6.32261i	−0.292224	−	0.437344i
$210$	−1.57793	−	1.46126i	−0.108888	−	0.100837i
$211$	12.3355	+	5.83424i	0.849208	+	0.401646i	0.802061	−	0.597242i	$-0.203737\pi$
$211$	12.3355	+	5.83424i	0.849208	+	0.401646i	0.0471476	+	0.998888i	$0.484987\pi$
$212$	2.16167	−	7.90676i	0.148464	−	0.543038i
$213$	0.378451	−	0.280679i	0.0259311	−	0.0192318i
$214$	18.1604	+	0.194657i	1.24142	+	0.0133065i
$215$	1.12380	−	11.4101i	0.0766423	−	0.778162i
$216$	0.186596	+	2.82227i	0.0126963	+	0.192031i
$217$	−9.42694	−	7.73649i	−0.639942	−	0.525187i
$218$	10.3449	−	5.38771i	0.700644	−	0.364901i
$219$	2.92271	+	6.17954i	0.197498	+	0.417575i
$220$	−12.1601	−	2.69099i	−0.819836	−	0.181426i
$221$	4.57964	+	1.14714i	0.308060	+	0.0771650i
$222$	−0.871497	+	14.5548i	−0.0584911	+	0.976851i
$223$	17.4325	+	7.22079i	1.16737	+	0.483540i	0.880322	−	0.474377i	$-0.157327\pi$
$223$	17.4325	+	7.22079i	1.16737	+	0.483540i	0.287046	+	0.957917i	$0.407327\pi$
$224$	−2.91833	+	6.95667i	−0.194989	+	0.464812i
$225$	3.41808	−	1.41581i	0.227872	−	0.0943876i
$226$	9.25596	+	26.7698i	0.615697	+	1.78070i
$227$	1.71600	+	2.86297i	0.113895	+	0.190022i	0.909398	−	0.415928i	$-0.136543\pi$
$227$	1.71600	+	2.86297i	0.113895	+	0.190022i	−0.795503	+	0.605950i	$0.792793\pi$
$228$	−0.0596949	+	2.78428i	−0.00395339	+	0.184393i
$229$	−9.54862	−	3.41655i	−0.630991	−	0.225772i	0.00191851	−	0.999998i	$-0.499389\pi$
$229$	−9.54862	−	3.41655i	−0.630991	−	0.225772i	−0.632909	+	0.774226i	$0.718139\pi$
$230$	−1.04968	−	11.9717i	−0.0692139	−	0.789391i
$231$	0.713833	+	7.24767i	0.0469668	+	0.476862i
$232$	5.38699	−	7.52659i	0.353673	−	0.494145i
$233$	−4.06829	−	4.95723i	−0.266523	−	0.324759i	0.622502	−	0.782618i	$-0.286116\pi$
$233$	−4.06829	−	4.95723i	−0.266523	−	0.324759i	−0.889025	+	0.457859i	$0.848616\pi$
$234$	−0.387423	−	0.964433i	−0.0253267	−	0.0630469i
$235$	−1.08305	−	0.160655i	−0.0706501	−	0.0104800i
$236$	6.55437	+	19.6353i	0.426653	+	1.27815i
$237$	−16.1099	+	5.76420i	−1.04645	+	0.374425i
$238$	5.06240	+	11.0073i	0.328147	+	0.713495i
$239$	−0.0818795	+	0.411636i	−0.00529634	+	0.0266265i	−0.983343	−	0.181759i	$-0.941821\pi$
$239$	−0.0818795	+	0.411636i	−0.00529634	+	0.0266265i	0.978047	+	0.208386i	$0.0668209\pi$
$240$	3.08408	+	3.36055i	0.199076	+	0.216923i
$241$	−0.693118	−	3.48454i	−0.0446476	−	0.224459i	0.952019	−	0.306038i	$-0.0990036\pi$
$241$	−0.693118	−	3.48454i	−0.0446476	−	0.224459i	−0.996667	+	0.0815794i	$0.974004\pi$
$242$	15.6264	+	21.5487i	1.00450	+	1.38520i
$243$	0.0490677	−	0.998795i	0.00314769	−	0.0640728i
$244$	−12.9665	+	5.79590i	−0.830092	+	0.371045i
$245$	−1.44673	−	5.77568i	−0.0924284	−	0.368995i
$246$	2.73760	−	4.00354i	0.174543	−	0.255256i
$247$	−0.297063	−	0.979286i	−0.0189017	−	0.0623105i
$248$	18.5960	+	17.9767i	1.18085	+	1.14152i
$249$	−0.492438	−	0.921287i	−0.0312070	−	0.0583842i
$250$	6.74568	−	12.3013i	0.426634	−	0.778002i
$251$	−3.40757	+	3.75968i	−0.215084	+	0.237309i	−0.838931	−	0.544238i	$-0.816819\pi$
$251$	−3.40757	+	3.75968i	−0.215084	+	0.237309i	0.623847	+	0.781547i	$0.285569\pi$
$252$	1.30744	−	2.32477i	0.0823613	−	0.146447i
$253$	−24.2425	+	32.6872i	−1.52411	+	2.05503i
$254$	8.19461	−	1.12593i	0.514176	−	0.0706471i
$255$	7.32530			0.458728
$256$	7.36640	−	14.2034i	0.460400	−	0.887711i
$257$	−9.63582			−0.601066			−0.300533	−	0.953771i	$-0.597165\pi$
$257$	−9.63582			−0.601066			−0.300533	+	0.953771i	$0.597165\pi$
$258$	14.0870	−	1.93553i	0.877016	−	0.120501i
$259$	8.19069	−	11.0439i	0.508945	−	0.686233i
$260$	−1.46089	−	0.821601i	−0.0906008	−	0.0509536i
$261$	−2.19761	+	2.42469i	−0.136029	+	0.150085i
$262$	8.30555	−	15.1458i	0.513119	−	0.935714i
$263$	−12.3373	−	23.0814i	−0.760750	−	1.42326i	−0.901303	−	0.433189i	$-0.857388\pi$
$263$	−12.3373	−	23.0814i	−0.760750	−	1.42326i	0.140554	−	0.990073i	$-0.455112\pi$
$264$	−0.261522	−	15.4437i	−0.0160956	−	0.950493i
$265$	1.35665	+	4.47227i	0.0833382	+	0.274729i
$266$	1.48234	−	2.16782i	0.0908884	−	0.132918i
$267$	−1.42928	−	5.70599i	−0.0874702	−	0.349201i
$268$	−9.97569	−	22.3174i	−0.609362	−	1.36325i
$269$	−0.462164	+	9.40757i	−0.0281786	+	0.573589i	0.942645	+	0.333796i	$0.108330\pi$
$269$	−0.462164	+	9.40757i	−0.0281786	+	0.573589i	−0.970824	+	0.239793i	$0.922920\pi$
$270$	−0.946709	−	1.30551i	−0.0576149	−	0.0794505i
$271$	3.67868	+	18.4940i	0.223464	+	1.12343i	0.915733	+	0.401788i	$0.131611\pi$
$271$	3.67868	+	18.4940i	0.223464	+	1.12343i	−0.692269	+	0.721640i	$0.743389\pi$
$272$	−8.80685	−	24.1395i	−0.533993	−	1.46367i
$273$	−0.191207	+	0.961265i	−0.0115724	+	0.0581784i
$274$	2.66971	+	5.80479i	0.161283	+	0.350680i
$275$	−19.0228	+	6.80648i	−1.14712	+	0.410446i
$276$	14.1375	−	4.71916i	0.850976	−	0.284060i
$277$	12.8503	+	1.90617i	0.772101	+	0.114530i	0.521145	−	0.853468i	$-0.325505\pi$
$277$	12.8503	+	1.90617i	0.772101	+	0.114530i	0.250956	+	0.967998i	$0.419255\pi$
$278$	8.42516	+	20.9732i	0.505308	+	1.25789i
$279$	−5.80119	−	7.06877i	−0.347308	−	0.423196i
$280$	−0.703071	−	4.24339i	−0.0420165	−	0.253591i
$281$	−1.81477	−	18.4257i	−0.108260	−	1.09919i	−0.883793	−	0.467878i	$-0.845019\pi$
$281$	−1.81477	−	18.4257i	−0.108260	−	1.09919i	0.775533	−	0.631307i	$-0.217481\pi$
$282$	−0.118605	−	1.35270i	−0.00706284	−	0.0805524i
$283$	−11.0077	−	3.93863i	−0.654342	−	0.234127i	−0.0112743	−	0.999936i	$-0.503589\pi$
$283$	−11.0077	−	3.93863i	−0.654342	−	0.234127i	−0.643068	+	0.765809i	$0.722339\pi$
$284$	0.942134	+	0.0201994i	0.0559053	+	0.00119861i
$285$	−0.816308	−	1.36193i	−0.0483539	−	0.0806736i
$286$	1.85473	+	5.36419i	0.109672	+	0.317191i
$287$	−4.22543	+	1.75023i	−0.249419	+	0.103313i
$288$	−3.16393	+	4.68930i	−0.186437	+	0.276320i
$289$	−22.4201	−	9.28671i	−1.31883	−	0.546277i
$290$	−0.315419	+	5.26777i	−0.0185221	+	0.309334i
$291$	10.5114	+	2.63296i	0.616187	+	0.154347i
$292$	−2.95403	+	13.3488i	−0.172871	+	0.781177i
$293$	−3.90968	−	8.26632i	−0.228406	−	0.482924i	0.756942	−	0.653482i	$-0.226693\pi$
$293$	−3.90968	−	8.26632i	−0.228406	−	0.482924i	−0.985347	+	0.170559i	$0.945443\pi$
$294$	6.54932	−	3.41094i	0.381964	−	0.198930i
$295$	−9.12338	−	7.48737i	−0.531184	−	0.435931i
$296$	−19.2151	+	21.9358i	−1.11686	+	1.27499i
$297$	−0.535267	+	5.43465i	−0.0310593	+	0.315351i
$298$	−2.50200	−	0.0268184i	−0.144937	−	0.00155355i
$299$	−4.39899	+	3.26251i	−0.254400	+	0.188676i
$300$	7.13746	+	1.95135i	0.412081	+	0.112661i
$301$	−12.1214	−	5.73301i	−0.698667	−	0.330445i
$302$	7.11635	+	6.59018i	0.409500	+	0.379223i
$303$	8.92702	+	13.3602i	0.512844	+	0.767525i
$304$	−3.50664	+	4.32741i	−0.201120	+	0.248194i
$305$	4.49891	−	6.73309i	0.257607	−	0.385536i
$306$	2.11286	+	8.83575i	0.120784	+	0.505106i
$307$	−21.5457	−	23.7720i	−1.22968	−	1.35674i	−0.912868	−	0.408254i	$-0.866138\pi$
$307$	−21.5457	−	23.7720i	−1.22968	−	1.35674i	−0.316811	−	0.948489i	$-0.602612\pi$
$308$	−7.75422	+	12.3298i	−0.441838	+	0.702558i
$309$	8.50828	−	14.1952i	0.484019	−	0.807537i
$310$	−14.4317	−	3.03180i	−0.819666	−	0.172195i
$311$	−11.9429	−	6.38360i	−0.677219	−	0.361981i	0.0966576	−	0.995318i	$-0.469185\pi$
$311$	−11.9429	−	6.38360i	−0.677219	−	0.361981i	−0.773876	+	0.633337i	$0.781685\pi$
$312$	0.569643	−	1.99910i	0.0322497	−	0.113177i
$313$	7.62492	−	25.1360i	0.430986	−	1.42077i	−0.425668	−	0.904879i	$-0.639961\pi$
$313$	7.62492	−	25.1360i	0.430986	−	1.42077i	0.856654	−	0.515891i	$-0.172539\pi$
$314$	11.2694	+	14.0359i	0.635967	+	0.792090i
$315$	0.0746181	+	1.51889i	0.00420425	+	0.0855795i
$316$	−32.5261	−	10.6332i	−1.82974	−	0.598165i
$317$	5.54762	−	0.822911i	0.311585	−	0.0462193i	0.0108934	−	0.999941i	$-0.496532\pi$
$317$	5.54762	−	0.822911i	0.311585	−	0.0462193i	0.300692	+	0.953721i	$0.402782\pi$
$318$	−5.00314	+	2.92634i	−0.280562	+	0.164101i
$319$	12.6363	−	12.6363i	0.707498	−	0.707498i
$320$	0.755859	+	9.09109i	0.0422538	+	0.508207i
$321$	−9.08071	−	9.08071i	−0.506836	−	0.506836i
$322$	−13.5962	−	3.56096i	−0.757686	−	0.198445i
$323$	1.31252	+	8.84828i	0.0730305	+	0.492332i
$324$	1.30163	−	1.51847i	0.0723130	−	0.0843594i
$325$	−2.71572	+	0.133415i	−0.150641	+	0.00740053i
$326$	−13.7764	−	1.50611i	−0.763004	−	0.0834159i
$327$	−7.89241	−	2.39414i	−0.436451	−	0.132396i
$328$	9.23337	−	2.97254i	0.509828	−	0.164131i
$329$	−0.603621	+	1.12929i	−0.0332787	+	0.0622600i
$330$	4.81389	+	7.37439i	0.264996	+	0.405947i
$331$	−7.67792	−	4.60197i	−0.422016	−	0.252947i	0.287295	−	0.957842i	$-0.407244\pi$
$331$	−7.67792	−	4.60197i	−0.422016	−	0.252947i	−0.709311	+	0.704895i	$0.750994\pi$
$332$	0.350789	−	2.05961i	0.0192520	−	0.113036i
$333$	7.63935	−	6.92391i	0.418634	−	0.379428i
$334$	15.2515	+	9.36506i	0.834527	+	0.512433i
$335$	11.5887	+	7.74335i	0.633160	+	0.423064i
$336$	4.91557	−	2.07198i	0.268167	−	0.113036i
$337$	5.49350	−	3.67064i	0.299250	−	0.199953i	−0.396876	−	0.917872i	$-0.629906\pi$
$337$	5.49350	−	3.67064i	0.299250	−	0.199953i	0.696126	+	0.717920i	$0.254906\pi$
$338$	−0.675932	−	17.6080i	−0.0367659	−	0.957747i
$339$	8.56337	−	18.1057i	0.465098	−	0.983368i
$340$	11.5777	+	8.97758i	0.627888	+	0.486878i
$341$	29.7477	+	40.1102i	1.61093	+	2.17209i
$342$	1.40730	−	1.37745i	0.0760982	−	0.0744841i
$343$	−16.2202	−	1.59755i	−0.875806	−	0.0862594i
$344$	24.6367	+	14.2053i	1.32832	+	0.765897i
$345$	−5.39092	+	6.56885i	−0.290237	+	0.353655i
$346$	14.7380	+	4.64381i	0.792322	+	0.249653i
$347$	30.7625	−	14.5496i	1.65142	−	0.781062i	0.651672	−	0.758501i	$-0.274068\pi$
$347$	30.7625	−	14.5496i	1.65142	−	0.781062i	0.999745	−	0.0225612i	$-0.00718207\pi$
$348$	−6.44495	+	1.13894i	−0.345486	+	0.0610538i
$349$	3.11960	−	12.4541i	0.166988	−	0.666654i	−0.827469	−	0.561511i	$-0.810220\pi$
$349$	3.11960	−	12.4541i	0.166988	−	0.666654i	0.994457	−	0.105143i	$-0.0335299\pi$
$350$	−4.63021	−	5.22001i	−0.247495	−	0.279021i
$351$	−0.281243	+	0.678981i	−0.0150117	+	0.0362413i
$352$	18.5138	−	24.7294i	0.986789	−	1.31808i
$353$	−4.07579	−	9.83982i	−0.216932	−	0.523721i	0.777526	−	0.628850i	$-0.216474\pi$
$353$	−4.07579	−	9.83982i	−0.216932	−	0.523721i	−0.994459	+	0.105130i	$0.966474\pi$
$354$	6.39975	−	13.1642i	0.340143	−	0.699669i
$355$	−0.460844	+	0.276219i	−0.0244591	+	0.0146602i
$356$	4.73404	−	10.7700i	0.250904	−	0.570810i
$357$	2.88614	−	8.06623i	0.152751	−	0.426910i
$358$	−8.36580	−	7.01703i	−0.442146	−	0.370862i
$359$	−27.4641	+	2.70498i	−1.44950	+	0.142763i	−0.791921	−	0.610623i	$-0.790919\pi$
$359$	−27.4641	+	2.70498i	−1.44950	+	0.142763i	−0.657578	+	0.753386i	$0.728419\pi$
$360$	0.103691	−	3.22361i	0.00546501	−	0.169899i
$361$	−13.1884	+	10.8234i	−0.694125	+	0.569654i
$362$	5.03508	−	11.7965i	0.264638	−	0.620012i
$363$	2.76176	−	18.6182i	0.144955	−	0.977204i
$364$	−1.48029	+	1.28495i	−0.0775884	+	0.0673497i
$365$	−2.62605	−	7.33932i	−0.137454	−	0.384157i
$366$	9.41907	+	3.48452i	0.492343	+	0.182139i
$367$	−0.813523	−	0.161820i	−0.0424656	−	0.00844693i	0.173812	−	0.984779i	$-0.444392\pi$
$367$	−0.813523	−	0.161820i	−0.0424656	−	0.00844693i	−0.216277	+	0.976332i	$0.569392\pi$
$368$	28.1280	+	9.86764i	1.46627	+	0.514386i
$369$	−3.36359	+	0.669060i	−0.175102	+	0.0348299i
$370$	2.61577	−	16.4196i	0.135987	−	0.853613i
$371$	5.45914	+	0.268190i	0.283424	+	0.0139237i
$372$	−0.505637	−	18.2820i	−0.0262161	−	0.947875i
$373$	9.91386	−	2.48329i	0.513320	−	0.128580i	0.0223395	−	0.999750i	$-0.492889\pi$
$373$	9.91386	−	2.48329i	0.513320	−	0.128580i	0.490981	+	0.871170i	$0.336639\pi$
$374$	−9.15672	−	48.7596i	−0.473483	−	2.52130i
$375$	−9.49317	+	2.87972i	−0.490225	+	0.148708i
$376$	1.47036	−	2.28332i	0.0758281	−	0.117753i
$377$	2.12100	−	1.13370i	0.109237	−	0.0583883i
$378$	−1.81055	+	0.528101i	−0.0931248	+	0.0271626i
$379$	−14.5961	−	13.2291i	−0.749751	−	0.679535i	0.204391	−	0.978889i	$-0.434479\pi$
$379$	−14.5961	−	13.2291i	−0.749751	−	0.679535i	−0.954142	+	0.299355i	$0.903229\pi$
$380$	0.378940	−	3.15297i	0.0194392	−	0.161744i
$381$	−4.69789	−	3.48419i	−0.240680	−	0.178500i
$382$	−17.6662	+	23.2941i	−0.903882	+	1.19183i
$383$			7.64298i			0.390538i	0.980750	+	0.195269i	$0.0625580\pi$
$383$			7.64298i			0.390538i	−0.980750	+	0.195269i	$0.937442\pi$
$384$	−10.7476	+	3.53389i	−0.548463	+	0.180338i
$385$		−	8.30456i		−	0.423240i
$386$	−29.6272	−	22.4692i	−1.50798	−	1.14365i
$387$	−8.07591	−	5.98950i	−0.410522	−	0.304464i
$388$	13.3865	+	17.0437i	0.679594	+	0.865263i
$389$	−11.9473	−	10.8284i	−0.605755	−	0.549024i	0.310013	−	0.950732i	$-0.399667\pi$
$389$	−11.9473	−	10.8284i	−0.605755	−	0.549024i	−0.915768	+	0.401708i	$0.868417\pi$
$390$	0.331860	+	1.13776i	0.0168044	+	0.0576125i
$391$	42.2197	−	22.5669i	2.13514	−	1.14126i
$392$	14.5316	+	2.63556i	0.733955	+	0.133116i
$393$	−11.6884	+	3.54563i	−0.589600	+	0.178853i
$394$	3.15211	−	0.591944i	0.158801	−	0.0298217i
$395$	18.9260	−	4.74072i	0.952271	−	0.238531i
$396$	−7.50648	+	7.93351i	−0.377215	+	0.398674i
$397$	−1.80611	−	0.0887287i	−0.0906463	−	0.00445317i	0.00369399	−	0.999993i	$-0.498824\pi$
$397$	−1.80611	−	0.0887287i	−0.0906463	−	0.00445317i	−0.0943403	+	0.995540i	$0.530074\pi$
$398$	−0.763723	−	0.121667i	−0.0382820	−	0.00609863i
$399$	−1.82130	+	0.362280i	−0.0911793	+	0.0181367i
$400$	8.88932	+	11.8315i	0.444466	+	0.591575i
$401$	0.155102	+	0.0308517i	0.00774542	+	0.00154066i	0.198962	−	0.980007i	$-0.436243\pi$
$401$	0.155102	+	0.0308517i	0.00774542	+	0.00154066i	−0.191216	+	0.981548i	$0.561243\pi$
$402$	−5.99743	+	16.2117i	−0.299124	+	0.808568i
$403$	2.26407	+	6.32764i	0.112781	+	0.315202i
$404$	−2.26451	+	32.0565i	−0.112664	+	1.59487i
$405$	−0.167318	+	1.12797i	−0.00831409	+	0.0560491i
$406$	5.67632	+	2.42281i	0.281711	+	0.120242i
$407$	−43.5232	+	35.7185i	−2.15736	+	1.77050i
$408$	−7.48934	+	16.5544i	−0.370777	+	0.819565i
$409$	30.4327	−	2.99736i	1.50480	−	0.148210i	0.688245	−	0.725478i	$-0.258381\pi$
$409$	30.4327	−	2.99736i	1.50480	−	0.148210i	0.816555	+	0.577268i	$0.195881\pi$
$410$	−3.55415	+	4.23730i	−0.175527	+	0.209265i
$411$	1.52204	−	4.25381i	0.0750765	−	0.209825i
$412$	30.8445	−	12.0083i	1.51960	−	0.591604i
$413$	−11.8393	+	7.09619i	−0.582572	+	0.349180i
$414$	−9.47825	−	4.60784i	−0.465831	−	0.226463i
$415$	0.455855	+	1.10053i	0.0223771	+	0.0540230i
$416$	3.35034	−	2.46147i	0.164264	−	0.120683i
$417$	6.11610	−	14.7656i	0.299507	−	0.723073i
$418$	−8.04504	+	7.13604i	−0.393496	+	0.349035i
$419$	−4.85447	+	19.3801i	−0.237157	+	0.946782i	0.728098	+	0.685473i	$0.240404\pi$
$419$	−4.85447	+	19.3801i	−0.237157	+	0.946782i	−0.965255	+	0.261310i	$0.915846\pi$
$420$	−1.74355	+	2.49206i	−0.0850765	+	0.121600i
$421$	7.11745	−	3.36630i	0.346883	−	0.164064i	−0.246170	−	0.969227i	$-0.579172\pi$
$421$	7.11745	−	3.36630i	0.346883	−	0.164064i	0.593054	+	0.805163i	$0.297922\pi$
$422$	5.79946	−	18.4057i	0.282313	−	0.895976i
$423$	−0.609129	+	0.742226i	−0.0296169	+	0.0360883i
$424$	−11.4939	−	1.50654i	−0.558193	−	0.0731639i
$425$	23.6523	+	2.32955i	1.14730	+	0.113000i
$426$	−0.466098	−	0.476198i	−0.0225825	−	0.0230719i
$427$	−5.64157	−	7.60677i	−0.273015	−	0.368118i
$428$	−3.22320	−	25.4811i	−0.155799	−	1.23167i
$429$	1.71594	−	3.62806i	0.0828465	−	0.175164i
$430$	−16.2025	+	0.621978i	−0.781352	+	0.0299944i
$431$	−2.24354	+	1.49909i	−0.108068	+	0.0722085i	−0.608430	−	0.793608i	$-0.708200\pi$
$431$	−2.24354	+	1.49909i	−0.108068	+	0.0722085i	0.500362	+	0.865816i	$0.333200\pi$
$432$	3.91822	−	0.804724i	0.188515	−	0.0387173i
$433$	−17.7509	−	11.8608i	−0.853052	−	0.569991i	0.0503761	−	0.998730i	$-0.483958\pi$
$433$	−17.7509	−	11.8608i	−0.853052	−	0.569991i	−0.903428	+	0.428739i	$0.858958\pi$
$434$	−9.02450	+	14.6969i	−0.433190	+	0.705474i
$435$	2.76490	−	2.50596i	0.132567	−	0.120151i
$436$	−9.53987	−	13.4566i	−0.456877	−	0.644452i
$437$	−8.90050	−	5.33475i	−0.425768	−	0.255196i
$438$	8.09522	−	5.28444i	0.386805	−	0.252500i
$439$	4.03948	−	7.55734i	0.192794	−	0.360692i	−0.766888	−	0.641781i	$-0.778196\pi$
$439$	4.03948	−	7.55734i	0.192794	−	0.360692i	0.959682	+	0.281089i	$0.0906957\pi$
$440$	−1.42936	+	17.5550i	−0.0681419	+	0.836901i
$441$	−4.99667	−	1.51572i	−0.237937	−	0.0721772i
$442$	0.725609	−	6.63714i	0.0345137	−	0.315696i
$443$	−8.00264	+	0.393145i	−0.380217	+	0.0186789i	−0.238279	−	0.971197i	$-0.576583\pi$
$443$	−8.00264	+	0.393145i	−0.380217	+	0.0186789i	−0.141938	+	0.989876i	$0.545333\pi$
$444$	20.5597	−	1.58082i	0.975721	−	0.0750222i
$445$	0.984209	+	6.63500i	0.0466560	+	0.314529i
$446$	6.76088	−	25.8139i	0.320137	−	1.22232i
$447$	1.25107	+	1.25107i	0.0591738	+	0.0591738i
$448$	10.3084	+	2.74955i	0.487028	+	0.129904i
$449$	24.6839	−	24.6839i	1.16490	−	1.16490i	0.181516	−	0.983388i	$-0.441900\pi$
$449$	24.6839	−	24.6839i	1.16490	−	1.16490i	0.983388	−	0.181516i	$-0.0581004\pi$
$450$	−2.64161	−	4.51635i	−0.124527	−	0.212903i
$451$	18.5256	−	2.74801i	0.872334	−	0.129399i
$452$	35.7241	−	18.1213i	1.68032	−	0.852356i
$453$	−0.336522	−	6.85005i	−0.0158112	−	0.321844i
$454$	3.68083	−	2.95533i	0.172750	−	0.138701i
$455$	0.324426	−	1.06949i	0.0152093	−	0.0501384i
$456$	3.91240	−	0.452345i	0.183215	−	0.0211830i
$457$	16.7860	+	8.97232i	0.785217	+	0.419707i	0.814718	−	0.579857i	$-0.196892\pi$
$457$	16.7860	+	8.97232i	0.785217	+	0.419707i	−0.0295006	+	0.999565i	$0.509392\pi$
$458$	−2.94863	+	14.0358i	−0.137780	+	0.655850i
$459$	3.30258	−	5.51002i	0.154151	−	0.257186i
$460$	−16.5709	+	3.77524i	−0.772623	+	0.176022i
$461$	21.6623	+	23.9006i	1.00891	+	1.11316i	0.993563	+	0.113281i	$0.0361360\pi$
$461$	21.6623	+	23.9006i	1.00891	+	1.11316i	0.0153491	+	0.999882i	$0.495114\pi$
$462$	10.0169	−	2.39531i	0.466030	−	0.111440i
$463$	−10.2398	+	15.3249i	−0.475882	+	0.712208i	−0.989294	−	0.145934i	$-0.953381\pi$
$463$	−10.2398	+	15.3249i	−0.475882	+	0.712208i	0.513412	+	0.858142i	$0.328381\pi$
$464$	−11.5821	−	6.09856i	−0.537687	−	0.283118i
$465$	5.79321	+	8.67016i	0.268654	+	0.402069i
$466$	−6.16217	+	6.65416i	−0.285457	+	0.308248i
$467$	−16.4690	−	7.78924i	−0.762093	−	0.360443i	0.00666955	−	0.999978i	$-0.497877\pi$
$467$	−16.4690	−	7.78924i	−0.762093	−	0.360443i	−0.768762	+	0.639535i	$0.779127\pi$
$468$	−1.27664	+	0.728456i	−0.0590127	+	0.0336729i
$469$	13.0925	−	9.71005i	0.604555	−	0.448368i
$470$	−0.0165962	+	1.54833i	−0.000765524	+	0.0714190i
$471$	1.24756	−	12.6667i	0.0574846	−	0.583651i
$472$	26.2484	−	12.9629i	1.20818	−	0.596664i
$473$	42.4441	+	34.8330i	1.95158	+	1.60162i
$474$	11.1771	+	21.4611i	0.513383	+	0.985742i
$475$	−2.20262	−	4.65706i	−0.101063	−	0.213680i
$476$	14.4472	−	9.21160i	0.662187	−	0.422213i
$477$	3.97564	+	0.995845i	0.182032	+	0.0455966i
$478$	0.592485	+	0.0354763i	0.0270996	+	0.00162265i
$479$	−27.6215	−	11.4412i	−1.26206	−	0.522761i	−0.351516	−	0.936182i	$-0.614334\pi$
$479$	−27.6215	−	11.4412i	−1.26206	−	0.522761i	−0.910540	+	0.413421i	$0.864334\pi$
$480$	4.11461	−	4.96786i	0.187805	−	0.226751i
$481$	−7.00043	+	2.89967i	−0.319192	+	0.132214i
$482$	−4.74859	+	1.64188i	−0.216292	+	0.0747854i
$483$	5.10927	+	8.52430i	0.232480	+	0.387869i
$484$	27.1827	−	26.0416i	1.23558	−	1.18371i
$485$	−11.6342	−	4.16278i	−0.528281	−	0.189022i
$486$	−1.40881	+	0.123524i	−0.0639049	+	0.00560318i
$487$	0.470143	+	4.77345i	0.0213042	+	0.216305i	0.999943	+	0.0107161i	$0.00341111\pi$
$487$	0.470143	+	4.77345i	0.0213042	+	0.216305i	−0.978638	+	0.205589i	$0.934089\pi$
$488$	10.6164	+	17.0509i	0.480583	+	0.771859i
$489$	6.21669	+	7.57506i	0.281128	+	0.342556i
$490$	−7.81352	+	3.13878i	−0.352979	+	0.141796i
$491$	19.3572	+	2.87136i	0.873577	+	0.129583i	0.568439	−	0.822725i	$-0.307548\pi$
$491$	19.3572	+	2.87136i	0.873577	+	0.129583i	0.305138	+	0.952308i	$0.401298\pi$
$492$	−6.13616	−	3.06482i	−0.276639	−	0.138173i
$493$	−19.7930	+	7.08204i	−0.891431	+	0.318959i
$494$	−1.31484	+	0.604715i	−0.0591576	+	0.0272074i
$495$	1.21486	−	6.10751i	0.0546038	−	0.274512i
$496$	21.6064	−	29.5145i	0.970158	−	1.32524i
$497$	0.122587	+	0.616287i	0.00549878	+	0.0276442i
$498$	−1.19597	+	0.867281i	−0.0535929	+	0.0388638i
$499$	−1.33581	+	27.1911i	−0.0597993	+	1.21724i	0.762043	+	0.647527i	$0.224197\pi$
$499$	−1.33581	+	27.1911i	−0.0597993	+	1.21724i	−0.821842	+	0.569715i	$0.807053\pi$
$500$	−18.5333	−	7.08301i	−0.828834	−	0.316762i
$501$	−3.07499	−	12.2760i	−0.137380	−	0.548453i
$502$	5.92347	+	4.05043i	0.264377	+	0.180780i
$503$	11.7643	+	38.7818i	0.524546	+	1.72920i	0.672402	+	0.740186i	$0.265263\pi$
$503$	11.7643	+	38.7818i	0.524546	+	1.72920i	−0.147856	+	0.989009i	$0.547237\pi$
$504$	−3.50881	−	1.38427i	−0.156295	−	0.0616603i
$505$	−8.63726	−	16.1592i	−0.384353	−	0.719074i
$506$	50.4632	+	27.6726i	2.24336	+	1.23020i
$507$	−8.36755	+	9.23217i	−0.371616	+	0.410015i
$508$	−3.15497	−	11.2643i	−0.139979	−	0.499774i
$509$	17.5356	−	23.6441i	0.777254	−	1.04801i	−0.220113	−	0.975474i	$-0.570643\pi$
$509$	17.5356	−	23.6441i	0.777254	−	1.04801i	0.997366	−	0.0725306i	$-0.0231075\pi$
$510$	−1.41014	−	10.2631i	−0.0624420	−	0.454458i
$511$	−9.11632			−0.403282
$512$	−21.3177	−	7.58652i	−0.942119	−	0.335280i
$513$	−1.39246			−0.0614785
$514$	1.85492	+	13.5003i	0.0818170	+	0.595472i
$515$	−11.2419	+	15.1580i	−0.495379	+	0.667941i
$516$	−5.42356	−	19.3640i	−0.238759	−	0.852451i
$517$	3.52130	−	3.88516i	0.154867	−	0.170869i
$518$	−17.0498	−	9.34960i	−0.749123	−	0.410798i
$519$	−5.15070	−	9.63627i	−0.226090	−	0.422985i
$520$	−0.869879	+	2.20495i	−0.0381467	+	0.0966933i
$521$	5.37339	+	17.7137i	0.235412	+	0.776050i	0.992447	+	0.122676i	$0.0391474\pi$
$521$	5.37339	+	17.7137i	0.235412	+	0.776050i	−0.757035	+	0.653375i	$0.773353\pi$
$522$	3.82016	+	2.61221i	0.167204	+	0.114333i
$523$	1.73191	+	6.91418i	0.0757312	+	0.302336i	0.996046	−	0.0888437i	$-0.0283172\pi$
$523$	1.73191	+	6.91418i	0.0757312	+	0.302336i	−0.920314	+	0.391179i	$0.872067\pi$
$524$	−22.8189	−	8.72089i	−0.996850	−	0.380974i
$525$	−0.242096	+	4.92799i	−0.0105660	+	0.215075i
$526$	−29.9633	+	21.7284i	−1.30646	+	0.947403i
$527$	−11.4603	−	57.6150i	−0.499220	−	2.50975i
$528$	−21.5870	+	3.33935i	−0.939455	+	0.145327i
$529$	−6.34721	+	31.9096i	−0.275966	+	1.38737i
$530$	6.00472	−	2.76166i	0.260828	−	0.119959i
$531$	−9.74516	+	3.48688i	−0.422904	+	0.151317i
$532$	−3.32258	−	1.65953i	−0.144052	−	0.0719497i
$533$	2.49313	+	0.369822i	0.107990	+	0.0160187i
$534$	−7.71924	+	3.10090i	−0.334044	+	0.134189i
$535$	9.29000	+	11.3199i	0.401642	+	0.489402i
$536$	−29.3474	+	18.2726i	−1.26762	+	0.789256i
$537$	0.756783	+	7.68375i	0.0326576	+	0.331578i
$538$	13.2694	−	1.16347i	0.572086	−	0.0501606i
$539$	26.8475	+	9.60620i	1.15640	+	0.413768i
$540$	−1.64683	+	1.57770i	−0.0708685	+	0.0678934i
$541$	17.4881	+	29.1771i	0.751870	+	1.25442i	0.961005	+	0.276533i	$0.0891854\pi$
$541$	17.4881	+	29.1771i	0.751870	+	1.25442i	−0.209134	+	0.977887i	$0.567065\pi$
$542$	25.2028	−	8.71415i	1.08255	−	0.374305i
$543$	−8.37909	+	3.47073i	−0.359581	+	0.148943i
$544$	−32.1254	+	16.9858i	−1.37736	+	0.728258i
$545$	8.68885	+	3.59904i	0.372189	+	0.154166i
$546$	1.38359	+	0.0828454i	0.0592121	+	0.00354545i
$547$	4.12917	+	1.03430i	0.176550	+	0.0442236i	0.330247	−	0.943894i	$-0.392868\pi$
$547$	4.12917	+	1.03430i	0.176550	+	0.0442236i	−0.153697	+	0.988118i	$0.549118\pi$
$548$	7.61888	−	4.85783i	0.325462	−	0.207516i
$549$	−3.03625	−	6.41962i	−0.129584	−	0.273983i
$550$	13.1982	+	25.3417i	0.562772	+	1.08057i
$551$	3.52237	+	2.89073i	0.150058	+	0.123149i
$552$	−9.33329	−	18.8989i	−0.397251	−	0.804390i
$553$	2.23656	−	22.7081i	0.0951081	−	0.965649i
$554$	0.196914	−	18.3709i	0.00836605	−	0.780505i
$555$	−9.44315	+	7.00351i	−0.400839	+	0.297283i
$556$	27.7626	−	15.8415i	1.17740	−	0.671828i
$557$	−36.8537	−	17.4305i	−1.56154	−	0.738553i	−0.565275	−	0.824903i	$-0.691230\pi$
$557$	−36.8537	−	17.4305i	−1.56154	−	0.738553i	−0.996265	+	0.0863495i	$0.972480\pi$
$558$	−8.78696	+	9.48852i	−0.371982	+	0.401681i
$559$	4.10530	+	6.14402i	0.173636	+	0.259864i
$560$	−5.80986	+	1.80190i	−0.245511	+	0.0761442i
$561$	−19.4899	+	29.1687i	−0.822865	+	1.23151i
$562$	−25.4660	+	6.08959i	−1.07422	+	0.256874i
$563$	−11.0206	−	12.1593i	−0.464462	−	0.512455i	0.463007	−	0.886355i	$-0.346770\pi$
$563$	−11.0206	−	12.1593i	−0.464462	−	0.512455i	−0.927469	+	0.373899i	$0.878020\pi$
$564$	−1.87238	+	0.426571i	−0.0788412	+	0.0179619i
$565$	−11.7415	+	19.5896i	−0.493970	+	0.824139i
$566$	−3.39921	+	16.1806i	−0.142879	+	0.680121i
$567$	1.17613	+	0.628656i	0.0493929	+	0.0264011i
$568$	−0.153063	−	1.32387i	−0.00642237	−	0.0555482i
$569$	−2.59161	+	8.54341i	−0.108646	+	0.358158i	−0.994358	−	0.106077i	$-0.966171\pi$
$569$	−2.59161	+	8.54341i	−0.108646	+	0.358158i	0.885712	+	0.464236i	$0.153671\pi$
$570$	−1.75099	+	1.40586i	−0.0733408	+	0.0588851i
$571$	−1.26108	−	25.6699i	−0.0527747	−	1.07425i	−0.868461	−	0.495758i	$-0.834890\pi$
$571$	−1.26108	−	25.6699i	−0.0527747	−	1.07425i	0.815686	−	0.578495i	$-0.196360\pi$
$572$	7.15846	−	3.63118i	0.299310	−	0.151827i
$573$	20.4488	−	3.03330i	0.854262	−	0.126718i
$574$	3.26557	+	5.58312i	0.136302	+	0.233035i
$575$	−19.4955	+	19.4955i	−0.813017	+	0.813017i
$576$	7.17901	+	3.53013i	0.299125	+	0.147089i
$577$	−8.34643	−	8.34643i	−0.347466	−	0.347466i	0.511699	−	0.859165i	$-0.329016\pi$
$577$	−8.34643	−	8.34643i	−0.347466	−	0.347466i	−0.859165	+	0.511699i	$0.829016\pi$
$578$	−8.69522	+	33.1994i	−0.361673	+	1.38091i
$579$	3.85797	+	26.0083i	0.160332	+	1.08087i
$580$	7.44114	−	0.572142i	0.308976	−	0.0237569i
$581$	1.39145	−	0.0683577i	0.0577272	−	0.00283596i
$582$	1.66544	−	15.2338i	0.0690349	−	0.631461i
$583$	−21.4178	−	6.49701i	−0.887033	−	0.269078i
$584$	19.2709	+	1.56907i	0.797437	+	0.0649287i
$585$	0.395049	−	0.739085i	0.0163333	−	0.0305574i
$586$	−10.8289	+	7.06895i	−0.447338	+	0.292015i
$587$	−19.9243	−	11.9422i	−0.822364	−	0.492906i	0.0399969	−	0.999200i	$-0.487265\pi$
$587$	−19.9243	−	11.9422i	−0.822364	−	0.492906i	−0.862361	+	0.506294i	$0.831015\pi$
$588$	−6.03967	−	8.51932i	−0.249072	−	0.351331i
$589$	−9.43474	+	8.55115i	−0.388752	+	0.352344i
$590$	−8.73390	+	14.2237i	−0.359569	+	0.585579i
$591$	−1.88564	−	1.25994i	−0.0775647	−	0.0518271i
$592$	34.4322	+	22.6986i	1.41515	+	0.932908i
$593$	−12.2307	+	8.17230i	−0.502255	+	0.335596i	−0.780752	−	0.624841i	$-0.785164\pi$
$593$	−12.2307	+	8.17230i	−0.502255	+	0.335596i	0.278497	+	0.960437i	$0.410164\pi$
$594$	7.71726	−	0.296249i	0.316643	−	0.0121553i
$595$	−4.17680	+	8.83111i	−0.171232	+	0.362040i
$596$	0.444068	+	3.51060i	0.0181897	+	0.143800i
$597$	0.325754	+	0.439229i	0.0133322	+	0.0179764i
$598$	5.41776	+	5.53516i	0.221549	+	0.226350i
$599$	23.0333	+	2.26858i	0.941114	+	0.0926916i	0.556925	−	0.830563i	$-0.311981\pi$
$599$	23.0333	+	2.26858i	0.941114	+	0.0926916i	0.384189	+	0.923255i	$0.374481\pi$
$600$	1.35996	−	10.3756i	0.0555200	−	0.423581i
$601$	−2.89432	+	3.52673i	−0.118062	+	0.143858i	−0.828687	−	0.559712i	$-0.810912\pi$
$601$	−2.89432	+	3.52673i	−0.118062	+	0.143858i	0.710626	+	0.703570i	$0.248412\pi$
$602$	−5.69883	+	18.0863i	−0.232267	+	0.737145i
$603$	11.0492	−	5.22589i	0.449958	−	0.212814i
$604$	7.86327	−	11.2390i	0.319952	−	0.457308i
$605$	−5.21504	+	20.8196i	−0.212022	+	0.846437i
$606$	16.9999	−	15.0791i	0.690573	−	0.612546i
$607$	6.52056	−	15.7420i	0.264661	−	0.638949i	−0.734554	−	0.678550i	$-0.762609\pi$
$607$	6.52056	−	15.7420i	0.264661	−	0.638949i	0.999216	+	0.0396010i	$0.0126087\pi$
$608$	6.73796	+	4.07994i	0.273260	+	0.165464i
$609$	−1.67007	−	4.03190i	−0.0676745	−	0.163381i
$610$	−10.2995	−	5.00706i	−0.417013	−	0.202730i
$611$	0.605262	−	0.362780i	0.0244863	−	0.0146765i
$612$	11.9726	−	4.66113i	0.483964	−	0.188415i
$613$	−11.7187	+	32.7516i	−0.473314	+	1.32282i	0.433447	+	0.901179i	$0.357297\pi$
$613$	−11.7187	+	32.7516i	−0.473314	+	1.32282i	−0.906761	+	0.421645i	$0.861453\pi$
$614$	−29.1582	+	34.7628i	−1.17673	+	1.40291i
$615$	3.89184	−	0.383313i	0.156934	−	0.0154567i
$616$	18.7674	+	8.49053i	0.756162	+	0.342093i
$617$	−8.14181	+	6.68181i	−0.327777	+	0.269000i	−0.783860	−	0.620938i	$-0.786752\pi$
$617$	−8.14181	+	6.68181i	−0.327777	+	0.269000i	0.456083	+	0.889937i	$0.349252\pi$
$618$	−21.5261	−	9.18792i	−0.865906	−	0.369592i
$619$	0.934260	−	6.29827i	0.0375511	−	0.253149i	−0.962269	−	0.272099i	$-0.912282\pi$
$619$	0.934260	−	6.29827i	0.0375511	−	0.253149i	0.999820	+	0.0189499i	$0.00603230\pi$
$620$	−1.46956	+	20.8032i	−0.0590191	+	0.835476i
$621$	2.51056	+	7.01654i	0.100745	+	0.281564i
$622$	−6.64472	+	17.9614i	−0.266429	+	0.720188i
$623$	7.69388	+	1.53041i	0.308249	+	0.0613145i
$624$	−2.91050	−	0.413266i	−0.116513	−	0.0165439i
$625$	−7.04818	+	1.40197i	−0.281927	+	0.0560788i
$626$	−36.6846	−	5.84416i	−1.46621	−	0.233579i
$627$	7.59498	+	0.373117i	0.303314	+	0.0149009i
$628$	17.4956	−	18.4909i	0.698149	−	0.737866i
$629$	64.2475	−	16.0931i	2.56171	−	0.641676i
$630$	2.11367	−	0.396933i	0.0842107	−	0.0158142i
$631$	16.3918	−	4.97241i	0.652549	−	0.197948i	0.0533836	−	0.998574i	$-0.482999\pi$
$631$	16.3918	−	4.97241i	0.652549	−	0.197948i	0.599165	+	0.800626i	$0.295499\pi$
$632$	−8.63631	+	47.6177i	−0.343534	+	1.89413i
$633$	−12.0343	+	6.43249i	−0.478322	+	0.255668i
$634$	−2.22087	−	7.61408i	−0.0882020	−	0.302394i
$635$	4.94181	+	4.47900i	0.196110	+	0.177744i
$636$	5.06306	+	6.44632i	0.200763	+	0.255613i
$637$	3.08224	+	2.28594i	0.122123	+	0.0905723i
$638$	−20.1366	−	15.2716i	−0.797217	−	0.604608i
$639$			0.471175i			0.0186394i
$640$	12.5916	−	2.80905i	0.497726	−	0.111038i
$641$		−	4.38445i		−	0.173175i	−0.996244	−	0.0865877i	$-0.972404\pi$
$641$		−	4.38445i		−	0.173175i	0.996244	−	0.0865877i	$-0.0275963\pi$
$642$	−10.9745	+	14.4706i	−0.433128	+	0.571109i
$643$	5.15256	+	3.82140i	0.203197	+	0.150701i	0.692513	−	0.721405i	$-0.256504\pi$
$643$	5.15256	+	3.82140i	0.203197	+	0.150701i	−0.489316	+	0.872107i	$0.662754\pi$
$644$	−2.37179	+	19.7344i	−0.0934615	+	0.777646i
$645$	8.49523	+	7.69963i	0.334499	+	0.303173i
$646$	12.1442	−	3.54222i	0.477808	−	0.139367i
$647$	−23.5790	+	12.6032i	−0.926986	+	0.495485i	−0.864540	−	0.502564i	$-0.832390\pi$
$647$	−23.5790	+	12.6032i	−0.926986	+	0.495485i	−0.0624463	+	0.998048i	$0.519890\pi$
$648$	−2.37802	−	1.53135i	−0.0934175	−	0.0601570i
$649$	54.0881	−	16.4074i	2.12314	−	0.644048i
$650$	0.709705	+	3.77918i	0.0278369	+	0.148232i
$651$	11.8296	−	2.96317i	0.463640	−	0.116136i
$652$	0.541852	+	19.5914i	0.0212206	+	0.767257i
$653$	4.08055	+	0.200465i	0.159684	+	0.00784479i	0.128753	−	0.991677i	$-0.458903\pi$
$653$	4.08055	+	0.200465i	0.159684	+	0.00784479i	0.0309315	+	0.999522i	$0.490153\pi$
$654$	−1.83500	+	11.5185i	−0.0717541	+	0.450411i
$655$	13.6605	−	2.71723i	0.533758	−	0.106171i
$656$	−5.94213	−	12.3642i	−0.232001	−	0.482741i
$657$	−6.70451	−	1.33361i	−0.261568	−	0.0520291i
$658$	1.69840	+	0.628311i	0.0662104	+	0.0244941i
$659$	−8.38333	−	23.4298i	−0.326568	−	0.912696i	−0.986844	−	0.161674i	$-0.948311\pi$
$659$	−8.38333	−	23.4298i	−0.326568	−	0.912696i	0.660276	−	0.751023i	$-0.270439\pi$
$660$	9.40520	−	8.16409i	0.366097	−	0.317787i
$661$	−3.24488	+	21.8752i	−0.126211	+	0.850846i	0.829915	+	0.557890i	$0.188389\pi$
$661$	−3.24488	+	21.8752i	−0.126211	+	0.850846i	−0.956126	+	0.292956i	$0.905361\pi$
$662$	−4.96957	+	11.6430i	−0.193148	+	0.452520i
$663$	−3.64948	+	2.99505i	−0.141734	+	0.116318i
$664$	−2.95315	−	0.0949916i	−0.114605	−	0.00368639i
$665$	2.10734	−	0.207555i	0.0817191	−	0.00804863i
$666$	−11.1713	−	9.37025i	−0.432881	−	0.363090i
$667$	8.21557	−	22.9610i	0.318108	−	0.889052i
$668$	10.1850	−	23.1710i	0.394068	−	0.896512i
$669$	−16.1843	+	9.70051i	−0.625722	+	0.375044i
$670$	8.61796	−	17.7270i	0.332941	−	0.684855i
$671$	14.8407	+	35.8286i	0.572918	+	1.38315i
$672$	−3.84920	−	6.48811i	−0.148486	−	0.250284i
$673$	−1.73937	+	4.19921i	−0.0670478	+	0.161868i	−0.953852	−	0.300278i	$-0.902920\pi$
$673$	−1.73937	+	4.19921i	−0.0670478	+	0.161868i	0.886804	+	0.462146i	$0.152920\pi$
$674$	−6.20027	−	6.99007i	−0.238825	−	0.269247i
$675$	−0.898953	+	3.58882i	−0.0346007	+	0.138134i
$676$	−24.5395	+	4.33660i	−0.943828	+	0.166792i
$677$	−1.13881	+	0.538617i	−0.0437680	+	0.0207007i	−0.449314	−	0.893374i	$-0.648331\pi$
$677$	−1.13881	+	0.538617i	−0.0437680	+	0.0207007i	0.405546	+	0.914075i	$0.367081\pi$
$678$	−27.0155	−	8.51231i	−1.03752	−	0.326913i
$679$	−9.16766	+	11.1708i	−0.351823	+	0.428697i
$680$	10.3493	−	17.9491i	0.396878	−	0.688318i
$681$	−3.32178	−	0.327167i	−0.127291	−	0.0125371i
$682$	50.4699	−	49.3994i	1.93259	−	1.89160i
$683$	−19.0385	−	25.6704i	−0.728487	−	0.982251i	−0.999805	−	0.0197611i	$-0.993709\pi$
$683$	−19.0385	−	25.6704i	−0.728487	−	0.982251i	0.271318	−	0.962490i	$-0.412541\pi$
$684$	−2.20079	−	1.70654i	−0.0841493	−	0.0652511i
$685$	−2.20268	+	4.65717i	−0.0841600	+	0.177941i
$686$	0.884179	+	23.0328i	0.0337581	+	0.879396i
$687$	8.43231	−	5.63429i	0.321713	−	0.214961i
$688$	15.1597	−	37.2518i	0.577958	−	1.42021i
$689$	−2.50444	−	1.67341i	−0.0954114	−	0.0637519i
$690$	10.2411	+	6.28843i	0.389871	+	0.239396i
$691$	10.7490	−	9.74232i	0.408911	−	0.370615i	−0.441031	−	0.897492i	$-0.645387\pi$
$691$	10.7490	−	9.74232i	0.408911	−	0.370615i	0.849942	+	0.526877i	$0.176637\pi$
$692$	3.66910	−	21.5427i	0.139478	−	0.818930i
$693$	−6.24661	−	3.74408i	−0.237289	−	0.142226i
$694$	−26.3066	−	40.2990i	−0.998583	−	1.52973i
$695$	−8.59100	+	16.0726i	−0.325875	+	0.609669i
$696$	2.83639	+	8.81045i	0.107513	+	0.333959i
$697$	−21.0823	−	6.39524i	−0.798548	−	0.242237i
$698$	−18.0494	−	1.97326i	−0.683180	−	0.0746890i
$699$	6.40516	−	0.314665i	0.242265	−	0.0119017i
$700$	−6.42217	+	7.49202i	−0.242735	+	0.283172i
$701$	−3.92475	−	26.4585i	−0.148236	−	0.999324i	−0.927820	−	0.373027i	$-0.878320\pi$
$701$	−3.92475	−	26.4585i	−0.148236	−	0.999324i	0.779585	−	0.626297i	$-0.215430\pi$
$702$	1.00543	+	0.263330i	0.0379474	+	0.00993877i
$703$	−10.1516	−	10.1516i	−0.382874	−	0.382874i
$704$	−38.2111	−	21.1783i	−1.44013	−	0.798187i
$705$	0.774208	−	0.774208i	0.0291584	−	0.0291584i
$706$	−13.0015	+	7.60458i	−0.489317	+	0.286202i
$707$	−21.1967	+	3.14423i	−0.797183	+	0.118251i
$708$	−19.6757	−	6.43223i	−0.739457	−	0.241738i
$709$	0.339614	+	6.91300i	0.0127545	+	0.259623i	0.996701	+	0.0811601i	$0.0258625\pi$
$709$	0.339614	+	6.91300i	0.0127545	+	0.259623i	−0.983947	+	0.178463i	$0.942887\pi$
$710$	0.475711	+	0.592493i	0.0178531	+	0.0222359i
$711$	4.96679	−	16.3733i	0.186269	−	0.614047i
$712$	−16.0007	−	4.55937i	−0.599650	−	0.170870i
$713$	60.0995	+	32.1238i	2.25074	+	1.20305i
$714$	−11.8568	−	2.49086i	−0.443729	−	0.0932182i
$715$	−2.35279	+	3.92539i	−0.0879892	+	0.146801i
$716$	−8.22078	+	13.0717i	−0.307225	+	0.488513i
$717$	−0.281854	−	0.310977i	−0.0105260	−	0.0116137i
$718$	9.07672	+	37.9579i	0.338740	+	1.41657i
$719$	5.88986	−	8.81481i	0.219655	−	0.328737i	−0.705234	−	0.708975i	$-0.749158\pi$
$719$	5.88986	−	8.81481i	0.219655	−	0.328737i	0.924889	+	0.380238i	$0.124158\pi$
$720$	−4.53640	+	0.475277i	−0.169062	+	0.0177125i
$721$	12.2619	+	18.3512i	0.456657	+	0.683435i
$722$	17.7030	+	16.3940i	0.658836	+	0.610123i
$723$	3.21170	+	1.51902i	0.119444	+	0.0564930i
$724$	−17.4968	−	4.78354i	−0.650264	−	0.177779i
$725$	9.72437	−	7.21208i	0.361154	−	0.267850i
$726$	−26.6167	−	0.285299i	−0.987840	−	0.0105884i
$727$	−1.53144	+	15.5489i	−0.0567978	+	0.576678i	0.924100	+	0.382152i	$0.124817\pi$
$727$	−1.53144	+	15.5489i	−0.0567978	+	0.576678i	−0.980897	+	0.194526i	$0.937683\pi$
$728$	2.08524	+	1.82661i	0.0772842	+	0.0676986i
$729$	0.773010	+	0.634393i	0.0286300	+	0.0234960i
$730$	−9.77723	+	5.09206i	−0.361872	+	0.188466i
$731$	−27.6159	−	58.3889i	−1.02141	−	2.15959i
$732$	3.06880	−	13.8674i	0.113426	−	0.512553i
$733$	11.0691	+	2.77267i	0.408847	+	0.102411i	0.441947	−	0.897041i	$-0.354288\pi$
$733$	11.0691	+	2.77267i	0.408847	+	0.102411i	−0.0331000	+	0.999452i	$0.510538\pi$
$734$	−0.0701124	+	1.17094i	−0.00258790	+	0.0432201i
$735$	5.50089	+	2.27854i	0.202903	+	0.0840453i
$736$	8.41034	−	41.3083i	0.310009	−	1.52264i
$737$	−61.6668	+	25.5432i	−2.27152	+	0.940896i
$738$	1.58489	+	4.58377i	0.0583405	+	0.168731i
$739$	−13.7717	−	22.9766i	−0.506599	−	0.845210i	0.493094	−	0.869976i	$-0.335866\pi$
$739$	−13.7717	−	22.9766i	−0.506599	−	0.845210i	−0.999693	+	0.0247663i	$0.992116\pi$
$740$	−23.5082	−	0.504016i	−0.864178	−	0.0185280i
$741$	0.963530	+	0.344757i	0.0353962	+	0.0126649i
$742$	−0.675150	−	7.70016i	−0.0247856	−	0.282682i
$743$	−1.54403	−	15.6768i	−0.0566451	−	0.575128i	−0.981055	−	0.193728i	$-0.937942\pi$
$743$	−1.54403	−	15.6768i	−0.0566451	−	0.575128i	0.924410	−	0.381400i	$-0.124558\pi$
$744$	−25.5166	+	4.22775i	−0.935484	+	0.154997i
$745$	−1.27991	−	1.55957i	−0.0468922	−	0.0571383i
$746$	−5.38766	−	13.4118i	−0.197256	−	0.491040i
$747$	1.03333	+	0.153280i	0.0378076	+	0.00560822i
$748$	−66.5520	+	22.2154i	−2.43338	+	0.812275i
$749$	16.1251	−	5.76965i	0.589198	−	0.210818i
$750$	5.86209	+	12.7461i	0.214053	+	0.465420i
$751$	1.63652	−	8.22733i	0.0597174	−	0.300219i	−0.939371	−	0.342902i	$-0.888590\pi$
$751$	1.63652	−	8.22733i	0.0597174	−	0.300219i	0.999089	+	0.0426821i	$0.0135903\pi$
$752$	−3.48209	−	1.62051i	−0.126979	−	0.0590938i
$753$	−0.989912	−	4.97663i	−0.0360744	−	0.181358i
$754$	−1.99666	−	2.75338i	−0.0727141	−	0.100272i
$755$	−0.383738	+	7.81117i	−0.0139657	+	0.284277i
$756$	1.08843	+	2.43502i	0.0395859	+	0.0885607i
$757$	−5.81405	−	23.2110i	−0.211315	−	0.843618i	−0.979178	−	0.203003i	$-0.934930\pi$
$757$	−5.81405	−	23.2110i	−0.211315	−	0.843618i	0.767863	−	0.640614i	$-0.221320\pi$
$758$	−15.7249	+	22.9965i	−0.571154	+	0.835271i
$759$	−11.8134	−	38.9435i	−0.428799	−	1.41356i
$760$	−4.49042	+	0.0760403i	−0.162885	+	0.00275827i
$761$	2.40253	+	4.49482i	0.0870917	+	0.162937i	0.921696	−	0.387913i	$-0.126804\pi$
$761$	2.40253	+	4.49482i	0.0870917	+	0.162937i	−0.834604	+	0.550850i	$0.814304\pi$
$762$	−3.97717	+	7.25269i	−0.144078	+	0.262737i
$763$	7.38645	−	8.14969i	0.267407	−	0.295039i
$764$	36.0370	+	20.2671i	1.30377	+	0.733237i
$765$	−4.36367	+	5.88373i	−0.157769	+	0.212727i
$766$	10.7082	−	1.47129i	0.386903	−	0.0531600i
$767$	7.60661			0.274659
$768$	7.02010	+	14.3777i	0.253316	+	0.518810i
$769$	26.9804			0.972937			0.486469	−	0.873698i	$-0.338285\pi$
$769$	26.9804			0.972937			0.486469	+	0.873698i	$0.338285\pi$
$770$	−11.6351	+	1.59865i	−0.419300	+	0.0576113i
$771$	5.74005	−	7.73956i	0.206723	−	0.278734i
$772$	−25.7772	+	45.8346i	−0.927741	+	1.64962i
$773$	15.0328	−	16.5862i	0.540693	−	0.596563i	−0.407914	−	0.913021i	$-0.633744\pi$
$773$	15.0328	−	16.5862i	0.540693	−	0.596563i	0.948607	+	0.316458i	$0.102494\pi$
$774$	−6.83696	+	12.4678i	−0.245750	+	0.448144i
$775$	15.9482	+	29.8370i	0.572876	+	1.07178i
$776$	21.3022	−	22.0361i	0.764703	−	0.791048i
$777$	3.99133	+	13.1577i	0.143188	+	0.472028i
$778$	−12.8713	+	18.8233i	−0.461459	+	0.674849i
$779$	1.16033	+	4.63230i	0.0415732	+	0.165970i
$780$	1.53017	−	0.683974i	0.0547889	−	0.0244902i
$781$	0.126254	−	2.56996i	0.00451773	−	0.0919605i
$782$	−39.7448	−	54.8078i	−1.42127	−	1.95992i
$783$	−0.638415	−	3.20953i	−0.0228151	−	0.114699i
$784$	0.895181	−	20.8668i	0.0319708	−	0.745243i
$785$	−2.83151	+	14.2350i	−0.101061	+	0.508067i
$786$	7.21765	+	15.6935i	0.257445	+	0.559767i
$787$	−37.0761	+	13.2660i	−1.32162	+	0.472883i	−0.900789	−	0.434256i	$-0.857011\pi$
$787$	−37.0761	+	13.2660i	−1.32162	+	0.472883i	−0.420831	+	0.907139i	$0.638261\pi$
$788$	−1.43613	−	4.30231i	−0.0511601	−	0.153263i
$789$	25.8885	+	3.84020i	0.921655	+	0.136715i
$790$	−10.2853	−	25.6037i	−0.365934	−	0.910939i
$791$	16.9449	+	20.6474i	0.602490	+	0.734136i
$792$	12.5603	+	8.98973i	0.446310	+	0.319436i
$793$	0.511553	+	5.19388i	0.0181658	+	0.184440i
$794$	0.223368	+	2.54754i	0.00792704	+	0.0904087i
$795$	−4.40031	−	1.57446i	−0.156063	−	0.0558403i
$796$	−0.0234433	+	1.09344i	−0.000830925	+	0.0387558i
$797$	9.08637	+	15.1597i	0.321856	+	0.536984i	0.975551	−	0.219774i	$-0.0705320\pi$
$797$	9.08637	+	15.1597i	0.321856	+	0.536984i	−0.653695	+	0.756758i	$0.726782\pi$
$798$	0.858178	+	2.48200i	0.0303792	+	0.0878618i
$799$	−5.69862	+	2.36044i	−0.201603	+	0.0835065i
$800$	14.8653	−	14.7320i	0.525568	−	0.520854i
$801$	5.43451	+	2.25105i	0.192019	+	0.0795369i
$802$	0.0133673	−	0.223245i	0.000472014	−	0.00788304i
$803$	36.2115	+	9.07051i	1.27788	+	0.320091i
$804$	23.8680	+	5.28189i	0.841759	+	0.186278i
$805$	−4.84533	−	10.2446i	−0.170775	−	0.361074i
$806$	8.42951	−	4.39016i	0.296917	−	0.154637i
$807$	−7.28092	−	5.97529i	−0.256300	−	0.210340i
$808$	45.3488	−	2.99827i	1.59536	−	0.105479i
$809$	−2.59040	+	26.3007i	−0.0910735	+	0.924684i	0.835731	+	0.549139i	$0.185044\pi$
$809$	−2.59040	+	26.3007i	−0.0910735	+	0.924684i	−0.926804	+	0.375545i	$0.877456\pi$
$810$	1.61255	+	0.0172845i	0.0566591	+	0.000607316i
$811$	−41.9343	+	31.1006i	−1.47251	+	1.09209i	−0.498155	+	0.867088i	$0.665989\pi$
$811$	−41.9343	+	31.1006i	−1.47251	+	1.09209i	−0.974358	+	0.225002i	$0.927761\pi$
$812$	2.30177	−	8.41921i	0.0807763	−	0.295456i
$813$	−17.0459	−	8.06210i	−0.597825	−	0.282750i
$814$	58.4218	+	54.1022i	2.04768	+	1.89628i
$815$	−6.20814	−	9.29114i	−0.217462	−	0.325454i
$816$	24.6353	+	7.30617i	0.862407	+	0.255767i
$817$	−7.77830	+	11.6410i	−0.272128	+	0.407269i
$818$	−10.0578	−	42.0607i	−0.351664	−	1.47062i
$819$	−0.658193	−	0.726204i	−0.0229991	−	0.0253756i
$820$	6.62086	+	4.16385i	0.231210	+	0.145408i
$821$	10.1358	−	16.9105i	0.353741	−	0.590181i	−0.628499	−	0.777810i	$-0.716330\pi$
$821$	10.1358	−	16.9105i	0.353741	−	0.590181i	0.982240	+	0.187630i	$0.0600804\pi$
$822$	−6.25279	−	1.31358i	−0.218091	−	0.0458164i
$823$	−25.2930	−	13.5194i	−0.881659	−	0.471256i	−0.0325474	−	0.999470i	$-0.510362\pi$
$823$	−25.2930	−	13.5194i	−0.881659	−	0.471256i	−0.849111	+	0.528214i	$0.822862\pi$
$824$	−22.7618	−	40.9031i	−0.792945	−	1.42493i
$825$	5.86487	−	19.3339i	0.204189	−	0.673120i
$826$	12.2212	+	15.2214i	0.425230	+	0.529620i
$827$	1.98302	+	40.3654i	0.0689565	+	1.40364i	0.745140	+	0.666908i	$0.232383\pi$
$827$	1.98302	+	40.3654i	0.0689565	+	1.40364i	−0.676183	+	0.736734i	$0.736367\pi$
$828$	−4.63122	+	14.1665i	−0.160946	+	0.492321i
$829$	10.6806	−	1.58432i	0.370954	−	0.0550259i	0.0413491	−	0.999145i	$-0.486834\pi$
$829$	10.6806	−	1.58432i	0.370954	−	0.0550259i	0.329605	+	0.944119i	$0.393084\pi$
$830$	1.45415	−	0.850532i	0.0504742	−	0.0295224i
$831$	−9.18598	+	9.18598i	−0.318658	+	0.318658i
$832$	−4.09359	−	4.22016i	−0.141920	−	0.146308i
$833$	−23.7183	−	23.7183i	−0.821791	−	0.821791i
$834$	−21.8647	−	5.72656i	−0.757112	−	0.198294i
$835$	2.11746	+	14.2748i	0.0732777	+	0.493998i
$836$	11.5467	+	9.89781i	0.399349	+	0.342323i
$837$	9.13346	−	0.448698i	0.315698	−	0.0155093i
$838$	28.0871	+	3.07064i	0.970252	+	0.106073i
$839$	14.7407	+	4.47155i	0.508907	+	0.154375i	0.534288	−	0.845303i	$-0.320580\pi$
$839$	14.7407	+	4.47155i	0.508907	+	0.154375i	−0.0253810	+	0.999678i	$0.508080\pi$
$840$	3.82714	+	1.96307i	0.132049	+	0.0677324i
$841$	8.62248	−	16.1315i	0.297327	−	0.556260i
$842$	−6.08649	−	9.32388i	−0.209754	−	0.321322i
$843$	15.8807	+	9.51854i	0.546961	+	0.327836i
$844$	−26.9038	−	4.58218i	−0.926065	−	0.157725i
$845$	10.5275	−	9.54158i	0.362157	−	0.328240i
$846$	1.15716	+	0.710540i	0.0397838	+	0.0244289i
$847$	20.8707	+	13.9454i	0.717127	+	0.479169i
$848$	0.101870	+	16.3935i	0.00349822	+	0.562956i
$849$	9.72085	−	6.49526i	0.333619	−	0.222917i
$850$	−1.28931	−	33.5865i	−0.0442231	−	1.15201i
$851$	−32.8505	+	69.4564i	−1.12610	+	2.38094i
$852$	−0.577453	+	0.744696i	−0.0197832	+	0.0255129i
$853$	−29.4793	−	39.7482i	−1.00935	−	1.36095i	−0.931401	−	0.363994i	$-0.881413\pi$
$853$	−29.4793	−	39.7482i	−1.00935	−	1.36095i	−0.0779490	−	0.996957i	$-0.524837\pi$
$854$	−9.57146	+	9.36844i	−0.327529	+	0.320582i
$855$	1.58018	+	0.155635i	0.0540412	+	0.00532259i
$856$	−35.0798	+	9.42104i	−1.19900	+	0.322004i
$857$	−10.3143	+	12.5681i	−0.352331	+	0.429317i	−0.918774	−	0.394784i	$-0.870819\pi$
$857$	−10.3143	+	12.5681i	−0.352331	+	0.429317i	0.566442	+	0.824101i	$0.308319\pi$
$858$	−5.41341	−	1.70571i	−0.184811	−	0.0582321i
$859$	−22.7387	+	10.7546i	−0.775834	+	0.366942i	−0.774106	−	0.633056i	$-0.781800\pi$
$859$	−22.7387	+	10.7546i	−0.775834	+	0.366942i	−0.00172818	+	0.999999i	$0.500550\pi$
$860$	3.99044	+	22.5807i	0.136073	+	0.769997i
$861$	1.11129	−	4.43651i	0.0378726	−	0.151196i
$862$	2.53218	+	2.85474i	0.0862465	+	0.0972327i
$863$	5.48358	−	13.2385i	0.186663	−	0.450645i	−0.802650	−	0.596450i	$-0.796577\pi$
$863$	5.48358	−	13.2385i	0.186663	−	0.450645i	0.989313	+	0.145805i	$0.0465773\pi$
$864$	−1.88173	−	5.33471i	−0.0640176	−	0.181490i
$865$	4.76805	+	11.5111i	0.162119	+	0.391389i
$866$	−13.2004	+	27.1531i	−0.448569	+	0.922700i
$867$	20.8148	−	12.4759i	0.706907	−	0.423704i
$868$	22.3284	+	9.81459i	0.757874	+	0.333129i
$869$	−31.4780	+	87.9752i	−1.06782	+	2.98435i
$870$	−4.04322	−	3.39136i	−0.137078	−	0.114978i
$871$	−8.93952	+	0.880466i	−0.302904	+	0.0298334i
$872$	−17.0169	+	15.9563i	−0.576264	+	0.540347i
$873$	−8.37642	+	6.87435i	−0.283499	+	0.232662i
$874$	−5.76089	+	13.4970i	−0.194865	+	0.456543i
$875$	1.94121	−	13.0866i	0.0656250	−	0.442408i
$876$	−8.96211	−	10.3245i	−0.302802	−	0.348834i
$877$	−2.17807	−	6.08730i	−0.0735482	−	0.205553i	0.899144	−	0.437653i	$-0.144190\pi$
$877$	−2.17807	−	6.08730i	−0.0735482	−	0.205553i	−0.972692	+	0.232100i	$0.925440\pi$
$878$	−11.3658	−	4.20471i	−0.383578	−	0.141902i
$879$	8.96856	+	1.78396i	0.302502	+	0.0601714i
$880$	24.8706	−	1.37678i	0.838387	−	0.0464112i
$881$	9.73702	−	1.93681i	0.328048	−	0.0652529i	−0.0283186	−	0.999599i	$-0.509015\pi$
$881$	9.73702	−	1.93681i	0.328048	−	0.0652529i	0.356367	+	0.934346i	$0.384015\pi$
$882$	−1.16173	+	7.29236i	−0.0391176	+	0.245547i
$883$	21.1442	+	1.03875i	0.711560	+	0.0349567i	0.401629	−	0.915802i	$-0.368444\pi$
$883$	21.1442	+	1.03875i	0.711560	+	0.0349567i	0.309931	+	0.950759i	$0.399694\pi$
$884$	−9.43865	+	0.261051i	−0.317456	+	0.00878011i
$885$	11.4487	−	2.86775i	0.384844	−	0.0963984i
$886$	2.09134	+	11.1364i	0.0702601	+	0.374135i
$887$	−22.4288	+	6.80371i	−0.753086	+	0.228446i	−0.643411	−	0.765521i	$-0.722481\pi$
$887$	−22.4288	+	6.80371i	−0.753086	+	0.228446i	−0.109675	+	0.993967i	$0.534981\pi$
$888$	−6.17260	−	28.5009i	−0.207139	−	0.956427i
$889$	6.87909	−	3.67695i	0.230717	−	0.123321i
$890$	9.10651	−	2.65618i	0.305251	−	0.0890354i
$891$	−4.04630	−	3.66735i	−0.135556	−	0.122861i
$892$	−37.4680	−	4.50310i	−1.25452	−	0.150775i
$893$	1.07389	+	0.796453i	0.0359364	+	0.0266523i
$894$	1.51198	−	1.99365i	0.0505683	−	0.0666777i
$895$		−	8.80423i		−	0.294293i
$896$	1.86786	−	14.9719i	0.0624007	−	0.500177i
$897$		−	5.47677i		−	0.182864i
$898$	−39.3351	−	29.8316i	−1.31263	−	0.995495i
$899$	−24.0355	−	17.8260i	−0.801630	−	0.594529i
$900$	−5.81912	+	4.57045i	−0.193971	+	0.152348i
$901$	19.5080	+	17.6811i	0.649907	+	0.589042i
$902$	−7.41631	−	25.4262i	−0.246936	−	0.846601i
$903$	11.8255	−	6.32087i	0.393529	−	0.210345i
$904$	−32.2659	−	46.5629i	−1.07315	−	1.54866i
$905$	9.89665	−	3.00212i	0.328976	−	0.0997937i
$906$	−9.53249	+	1.79014i	−0.316696	+	0.0594733i
$907$	−42.1817	+	10.5660i	−1.40062	+	0.350837i	−0.868440	−	0.495795i	$-0.834877\pi$
$907$	−42.1817	+	10.5660i	−1.40062	+	0.350837i	−0.532179	+	0.846632i	$0.678627\pi$
$908$	−4.84914	−	4.58813i	−0.160924	−	0.152262i
$909$	−16.0489	−	0.788430i	−0.532307	−	0.0261506i
$910$	−1.56086	−	0.248658i	−0.0517420	−	0.00824292i
$911$	43.8281	−	8.71795i	1.45209	−	0.288838i	0.594883	−	0.803812i	$-0.297198\pi$
$911$	43.8281	−	8.71795i	1.45209	−	0.288838i	0.857206	+	0.514974i	$0.172198\pi$
$912$	−1.38691	−	5.39440i	−0.0459250	−	0.178626i
$913$	−5.59509	−	1.11293i	−0.185171	−	0.0368327i
$914$	9.33932	−	25.2453i	0.308917	−	0.835040i
$915$	2.72807	+	7.62445i	0.0901873	+	0.252057i
$916$	20.2325	+	1.42925i	0.668500	+	0.0472237i
$917$	2.39010	−	16.1127i	0.0789280	−	0.532090i
$918$	−8.35557	−	3.56639i	−0.275775	−	0.117708i
$919$	−3.34444	+	2.74471i	−0.110323	+	0.0905397i	−0.687937	−	0.725770i	$-0.741484\pi$
$919$	−3.34444	+	2.74471i	−0.110323	+	0.0905397i	0.577615	+	0.816310i	$0.303984\pi$
$920$	8.47925	+	22.4899i	0.279552	+	0.741471i
$921$	31.9287	−	3.14470i	1.05209	−	0.103621i
$922$	29.3159	−	34.9509i	0.965469	−	1.15105i
$923$	0.116658	−	0.326036i	0.00383983	−	0.0107316i
$924$	−5.28424	−	13.5731i	−0.173839	−	0.446523i
$925$	−32.7177	+	19.6103i	−1.07575	+	0.644781i
$926$	23.4421	+	11.3963i	0.770356	+	0.374507i
$927$	6.33332	+	15.2900i	0.208014	+	0.502189i
$928$	−6.31479	+	17.4012i	−0.207293	+	0.571221i
$929$	2.97808	−	7.18972i	0.0977076	−	0.235887i	−0.867466	−	0.497496i	$-0.834253\pi$
$929$	2.97808	−	7.18972i	0.0977076	−	0.235887i	0.965174	+	0.261609i	$0.0842530\pi$
$930$	11.0321	−	9.78561i	0.361757	−	0.320883i
$931$	−1.76664	+	7.05283i	−0.0578993	+	0.231147i
$932$	10.5091	+	7.35257i	0.344235	+	0.240841i
$933$	12.2417	−	5.78990i	0.400776	−	0.189553i
$934$	−7.74280	+	24.5733i	−0.253352	+	0.804063i
$935$	25.3777	−	30.9228i	0.829939	−	1.01128i
$936$	1.26636	+	1.64841i	0.0413923	+	0.0538798i
$937$	−41.7462	−	4.11164i	−1.36379	−	0.134321i	−0.610502	−	0.792015i	$-0.709032\pi$
$937$	−41.7462	−	4.11164i	−1.36379	−	0.134321i	−0.753286	+	0.657693i	$0.771532\pi$
$938$	−16.1246	−	16.4740i	−0.526487	−	0.537896i
$939$	15.6473	+	21.0979i	0.510629	+	0.688504i
$940$	2.17248	−	0.274805i	0.0708585	−	0.00896315i
$941$	2.86633	−	6.06035i	0.0934397	−	0.197562i	−0.851856	−	0.523776i	$-0.824523\pi$
$941$	2.86633	−	6.06035i	0.0934397	−	0.197562i	0.945296	+	0.326214i	$0.105773\pi$
$942$	−17.9869	+	0.690477i	−0.586044	+	0.0224970i
$943$	21.2500	−	14.1988i	0.691994	−	0.462375i
$944$	−23.2145	−	34.2799i	−0.755568	−	1.11572i
$945$	−1.26443	−	0.844865i	−0.0411319	−	0.0274835i
$946$	40.6321	−	66.1718i	1.32107	−	2.15143i
$947$	−10.9414	+	9.91675i	−0.355549	+	0.322251i	−0.829718	−	0.558183i	$-0.811499\pi$
$947$	−10.9414	+	9.91675i	−0.355549	+	0.322251i	0.474169	+	0.880434i	$0.342749\pi$
$948$	27.9165	−	19.7910i	0.906685	−	0.642783i
$949$	4.30909	+	2.58277i	0.139879	+	0.0838402i
$950$	−6.10076	+	3.98248i	−0.197935	+	0.129209i
$951$	−2.64374	+	4.94609i	−0.0857292	+	0.160388i
$952$	−15.6870	−	18.4680i	−0.508420	−	0.598552i
$953$	−4.50010	−	1.36509i	−0.145772	−	0.0442196i	0.216555	−	0.976270i	$-0.430518\pi$
$953$	−4.50010	−	1.36509i	−0.145772	−	0.0442196i	−0.362328	+	0.932051i	$0.618018\pi$
$954$	0.629909	−	5.76177i	0.0203941	−	0.186544i
$955$	−23.5447	+	1.15668i	−0.761889	+	0.0374292i
$956$	−0.0643508	−	0.836930i	−0.00208125	−	0.0270683i
$957$	2.62214	+	17.6770i	0.0847617	+	0.571417i
$958$	−10.7125	+	40.9015i	−0.346104	+	1.32147i
$959$	4.26038	+	4.26038i	0.137575	+	0.137575i
$960$	−7.75230	−	4.80845i	−0.250204	−	0.155192i
$961$	37.2089	−	37.2089i	1.20029	−	1.20029i
$962$	5.41019	+	9.24977i	0.174432	+	0.298224i
$963$	12.7031	−	1.88432i	0.409351	−	0.0607215i
$964$	3.21447	+	6.33695i	0.103531	+	0.204099i
$965$	−1.47115	−	29.9459i	−0.0473579	−	0.963993i
$966$	10.9594	−	8.79930i	0.352614	−	0.283113i
$967$	10.8325	−	35.7101i	0.348351	−	1.14836i	−0.591365	−	0.806404i	$-0.701411\pi$
$967$	10.8325	−	35.7101i	0.348351	−	1.14836i	0.939716	−	0.341956i	$-0.111089\pi$
$968$	−41.7183	−	33.0713i	−1.34088	−	1.06295i
$969$	−7.88887	−	4.21669i	−0.253427	−	0.135460i
$970$	−3.59265	+	17.1014i	−0.115353	+	0.549094i
$971$	−9.32808	+	15.5630i	−0.299352	+	0.499439i	−0.970248	−	0.242112i	$-0.922160\pi$
$971$	−9.32808	+	15.5630i	−0.299352	+	0.499439i	0.670896	+	0.741552i	$0.265910\pi$
$972$	0.444263	+	1.95003i	0.0142498	+	0.0625473i
$973$	14.3135	+	15.7925i	0.458870	+	0.506285i
$974$	6.59733	−	1.57760i	0.211392	−	0.0505494i
$975$	1.51059	−	2.26076i	0.0483777	−	0.0724024i
$976$	21.8455	−	18.1565i	0.699258	−	0.581176i
$977$	−5.94248	−	8.89356i	−0.190117	−	0.284530i	0.724150	−	0.689643i	$-0.242232\pi$
$977$	−5.94248	−	8.89356i	−0.190117	−	0.284530i	−0.914267	+	0.405113i	$0.867232\pi$
$978$	9.41631	−	10.1681i	0.301100	−	0.325140i
$979$	−29.0387	−	13.7343i	−0.928079	−	0.438949i
$980$	5.90171	+	10.3429i	0.188523	+	0.330392i
$981$	6.62449	−	4.91306i	0.211504	−	0.156862i
$982$	0.296622	−	27.6731i	0.00946558	−	0.883084i
$983$	1.64756	−	16.7280i	0.0525490	−	0.533539i	−0.932489	−	0.361199i	$-0.882367\pi$
$983$	1.64756	−	16.7280i	0.0525490	−	0.533539i	0.985038	−	0.172340i	$-0.0551326\pi$
$984$	−3.11275	+	9.18705i	−0.0992307	+	0.292873i
$985$	1.99903	+	1.64056i	0.0636944	+	0.0522726i
$986$	13.7325	+	26.3677i	0.437332	+	0.839717i
$987$	−0.547482	−	1.15755i	−0.0174265	−	0.0368453i
$988$	1.10035	+	1.72575i	0.0350067	+	0.0549035i
$989$	72.6828	+	18.2061i	2.31118	+	0.578920i
$990$	−8.79079	−	0.526368i	−0.279390	−	0.0167291i
$991$	−23.7575	−	9.84068i	−0.754682	−	0.312600i	−0.0280318	−	0.999607i	$-0.508924\pi$
$991$	−23.7575	−	9.84068i	−0.754682	−	0.312600i	−0.726650	+	0.687007i	$0.758924\pi$
$992$	−45.5106	−	24.5901i	−1.44496	−	0.780737i
$993$	8.27006	−	3.42557i	0.262443	−	0.108707i
$994$	0.839851	−	0.290387i	0.0266384	−	0.00921053i
$995$	−0.320579	−	0.534854i	−0.0101630	−	0.0169560i
$996$	1.44533	+	1.50867i	0.0457971	+	0.0478039i
$997$	16.9495	+	6.06463i	0.536796	+	0.192069i	0.591310	−	0.806444i	$-0.298611\pi$
$997$	16.9495	+	6.06463i	0.536796	+	0.192069i	−0.0545140	+	0.998513i	$0.517361\pi$
$998$	38.3533	−	3.36282i	1.21405	−	0.106448i
$999$	1.01058	+	10.2606i	0.0319732	+	0.324629i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	768.2.z.a.13.30	✓	2048
256.197	even	64	inner	768.2.z.a.709.30	yes	2048

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
768.2.z.a.13.30	✓	2048	1.1	even	1	trivial
768.2.z.a.709.30	yes	2048	256.197	even	64	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 768 = 2^{8} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	768.z (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.192503 - 1.40105i) q^{2} +(-0.595699 + 0.803208i) q^{3} +(-1.92589 + 0.539412i) q^{4} +(0.765784 - 0.844912i) q^{5} +(1.24001 + 0.679985i) q^{6} +(-0.628656 - 1.17613i) q^{7} +(1.12648 + 2.59442i) q^{8} +(-0.290285 - 0.956940i) q^{9} +O(q^{10})\)	\(q+(-0.192503 - 1.40105i) q^{2} +(-0.595699 + 0.803208i) q^{3} +(-1.92589 + 0.539412i) q^{4} +(0.765784 - 0.844912i) q^{5} +(1.24001 + 0.679985i) q^{6} +(-0.628656 - 1.17613i) q^{7} +(1.12648 + 2.59442i) q^{8} +(-0.290285 - 0.956940i) q^{9} +(-1.33118 - 0.910254i) q^{10} +(1.32690 + 5.29729i) q^{11} +(0.713989 - 1.86821i) q^{12} +(-0.0360610 + 0.734039i) q^{13} +(-1.52680 + 1.10719i) q^{14} +(0.222463 + 1.11840i) q^{15} +(3.41807 - 2.07769i) q^{16} +(1.25325 - 6.30053i) q^{17} +(-1.28484 + 0.590917i) q^{18} +(-1.31106 + 0.469105i) q^{19} +(-1.01906 + 2.04028i) q^{20} +(1.31917 + 0.195680i) q^{21} +(7.16634 - 2.87880i) q^{22} +(4.72760 + 5.76060i) q^{23} +(-2.75491 - 0.640699i) q^{24} +(0.362634 + 3.68188i) q^{25} +(1.03537 - 0.0907811i) q^{26} +(0.941544 + 0.336890i) q^{27} +(1.84514 + 1.92599i) q^{28} +(-1.68235 - 2.80684i) q^{29} +(1.52411 - 0.526976i) q^{30} +(8.44839 - 3.49944i) q^{31} +(-3.56894 - 4.38893i) q^{32} +(-5.04526 - 2.08981i) q^{33} +(-9.06862 - 0.543003i) q^{34} +(-1.47514 - 0.369504i) q^{35} +(1.07524 + 1.68637i) q^{36} +(4.40818 + 9.32031i) q^{37} +(0.909622 + 1.74656i) q^{38} +(-0.568104 - 0.466231i) q^{39} +(3.05470 + 1.03499i) q^{40} +(0.336149 - 3.41297i) q^{41} +(0.0202144 - 1.88589i) q^{42} +(8.07591 - 5.98950i) q^{43} +(-5.41288 - 9.48623i) q^{44} +(-1.03083 - 0.487544i) q^{45} +(7.16082 - 7.73254i) q^{46} +(-0.533445 - 0.798357i) q^{47} +(-0.367325 + 3.98310i) q^{48} +(2.90091 - 4.34152i) q^{49} +(5.08870 - 1.21684i) q^{50} +(4.31407 + 4.75984i) q^{51} +(-0.326500 - 1.43313i) q^{52} +(-2.10703 + 3.51537i) q^{53} +(0.290750 - 1.38400i) q^{54} +(5.49187 + 2.93546i) q^{55} +(2.34322 - 2.95589i) q^{56} +(0.404209 - 1.33250i) q^{57} +(-3.60866 + 2.89739i) q^{58} +(-0.507860 - 10.3377i) q^{59} +(-1.03171 - 2.03391i) q^{60} +(7.02457 - 1.04200i) q^{61} +(-6.52923 - 11.1630i) q^{62} +(-0.943000 + 0.943000i) q^{63} +(-5.46208 + 5.84514i) q^{64} +(0.592583 + 0.592583i) q^{65} +(-1.95671 + 7.47096i) q^{66} +(1.79345 + 12.0904i) q^{67} +(0.984958 + 12.8101i) q^{68} +(-7.44319 + 0.365660i) q^{69} +(-0.233725 + 2.13788i) q^{70} +(-0.450886 - 0.136775i) q^{71} +(2.15571 - 1.83110i) q^{72} +(3.22240 - 6.02869i) q^{73} +(12.2096 - 7.97026i) q^{74} +(-3.17334 - 1.90203i) q^{75} +(2.27191 - 1.61064i) q^{76} +(5.39615 - 4.89079i) q^{77} +(-0.543852 + 0.885693i) q^{78} +(14.2265 + 9.50584i) q^{79} +(0.862036 - 4.47903i) q^{80} +(-0.831470 + 0.555570i) q^{81} +(-4.84646 + 0.186045i) q^{82} +(-0.446640 + 0.944341i) q^{83} +(-2.64612 + 0.334718i) q^{84} +(-4.36367 - 5.88373i) q^{85} +(-9.94623 - 10.1618i) q^{86} +(3.25665 + 0.320752i) q^{87} +(-12.2487 + 9.40985i) q^{88} +(-3.73167 + 4.54706i) q^{89} +(-0.484638 + 1.53809i) q^{90} +(0.885997 - 0.419046i) q^{91} +(-12.2122 - 8.54413i) q^{92} +(-2.22193 + 8.87042i) q^{93} +(-1.01585 + 0.901070i) q^{94} +(-0.607636 + 1.46696i) q^{95} +(5.65123 - 0.252116i) q^{96} +(-4.14680 - 10.0113i) q^{97} +(-6.64112 - 3.22857i) q^{98} +(4.68401 - 2.80749i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2048 q+O(q^{10}) \) 2048 * q	\( 2048 q+O(q^{100}) \) 2048 * q

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more