LMFDB - Embedded newform 384.2.v.a.109.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			109.19
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.272887 + 1.38764i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-1.85107 + 0.757334i) q^{4} +(1.21818 - 1.48436i) q^{5} +(0.413462 - 1.35242i) q^{6} +(1.92661 + 1.28732i) q^{7} +(-1.55604 - 2.36194i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(0.272887 + 1.38764i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-1.85107 + 0.757334i) q^{4} +(1.21818 - 1.48436i) q^{5} +(0.413462 - 1.35242i) q^{6} +(1.92661 + 1.28732i) q^{7} +(-1.55604 - 2.36194i) q^{8} +(0.555570 + 0.831470i) q^{9} +(2.39218 + 1.28533i) q^{10} +(0.740315 + 0.224572i) q^{11} +(1.98950 + 0.204677i) q^{12} +(1.85681 - 1.52385i) q^{13} +(-1.26058 + 3.02472i) q^{14} +(-1.77407 + 0.734842i) q^{15} +(2.85289 - 2.80375i) q^{16} +(5.13980 + 2.12898i) q^{17} +(-1.00217 + 0.997826i) q^{18} +(-0.262953 + 2.66981i) q^{19} +(-1.13078 + 3.67022i) q^{20} +(-1.09228 - 2.04351i) q^{21} +(-0.109602 + 1.08857i) q^{22} +(3.99789 + 0.795230i) q^{23} +(0.258891 + 2.81655i) q^{24} +(0.256095 + 1.28747i) q^{25} +(2.62124 + 2.16074i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(-4.54121 - 0.923824i) q^{28} +(-0.385772 - 1.27172i) q^{29} +(-1.50381 - 2.26123i) q^{30} +(-4.74198 + 4.74198i) q^{31} +(4.66910 + 3.19366i) q^{32} +(-0.547037 - 0.547037i) q^{33} +(-1.55166 + 7.71314i) q^{34} +(4.25781 - 1.29159i) q^{35} +(-1.65810 - 1.11835i) q^{36} +(-0.647732 + 0.0637961i) q^{37} +(-3.77648 + 0.363672i) q^{38} +(-2.35590 + 0.468618i) q^{39} +(-5.40151 - 0.567557i) q^{40} +(1.92727 - 9.68903i) q^{41} +(2.53758 - 2.07333i) q^{42} +(-3.77207 + 2.01621i) q^{43} +(-1.54045 + 0.144968i) q^{44} +(1.91099 + 0.188216i) q^{45} +(-0.0125186 + 5.76462i) q^{46} +(-1.55657 + 3.75789i) q^{47} +(-3.83770 + 1.12785i) q^{48} +(-0.624156 - 1.50685i) q^{49} +(-1.71666 + 0.706700i) q^{50} +(-3.52931 - 4.30048i) q^{51} +(-2.28302 + 4.22697i) q^{52} +(3.62840 - 11.9612i) q^{53} +(1.35421 - 0.407585i) q^{54} +(1.23519 - 0.825325i) q^{55} +(0.0426967 - 6.55364i) q^{56} +(1.49044 - 2.23061i) q^{57} +(1.65941 - 0.882346i) q^{58} +(-0.544937 - 0.447218i) q^{59} +(2.72739 - 2.70380i) q^{60} +(2.90426 - 5.43348i) q^{61} +(-7.87416 - 5.28611i) q^{62} +2.31711i q^{63} +(-3.15751 + 7.35052i) q^{64} -4.61251i q^{65} +(0.609809 - 0.908367i) q^{66} +(3.64798 - 6.82489i) q^{67} +(-11.1265 - 0.0483252i) q^{68} +(-3.15096 - 2.58592i) q^{69} +(2.95416 + 5.55583i) q^{70} +(2.20895 - 3.30592i) q^{71} +(1.09939 - 2.60602i) q^{72} +(-10.6853 + 7.13966i) q^{73} +(-0.265283 - 0.881407i) q^{74} +(0.381056 - 1.25617i) q^{75} +(-1.53519 - 5.14113i) q^{76} +(1.13720 + 1.38568i) q^{77} +(-1.29316 - 3.14125i) q^{78} +(2.19861 + 5.30791i) q^{79} +(-0.686437 - 7.65021i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(13.9708 + 0.0303393i) q^{82} +(-6.92680 - 0.682230i) q^{83} +(3.56950 + 2.95545i) q^{84} +(9.42140 - 5.03584i) q^{85} +(-3.82712 - 4.68406i) q^{86} +(-0.259264 + 1.30341i) q^{87} +(-0.621530 - 2.09802i) q^{88} +(4.65705 - 0.926345i) q^{89} +(0.260308 + 2.70312i) q^{90} +(5.53903 - 0.545546i) q^{91} +(-8.00261 + 1.55572i) q^{92} +(6.41740 - 1.94670i) q^{93} +(-5.63936 - 1.13447i) q^{94} +(3.64264 + 3.64264i) q^{95} +(-2.61230 - 5.01756i) q^{96} +(-12.0214 + 12.0214i) q^{97} +(1.92063 - 1.27730i) q^{98} +(0.224572 + 0.740315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	0.272887	+	1.38764i	0.192960	+	0.981207i
$2$	0.272887	+	1.38764i	0.192960	+	0.981207i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$4$	−1.85107	+	0.757334i	−0.925533	+	0.378667i
$5$	1.21818	−	1.48436i	0.544789	−	0.663827i	−0.425731	−	0.904850i	$-0.639983\pi$
$5$	1.21818	−	1.48436i	0.544789	−	0.663827i	0.970519	+	0.241023i	$0.0774830\pi$
$6$	0.413462	−	1.35242i	0.168795	−	0.552125i
$7$	1.92661	+	1.28732i	0.728189	+	0.486560i	0.863567	−	0.504234i	$-0.168225\pi$
$7$	1.92661	+	1.28732i	0.728189	+	0.486560i	−0.135378	+	0.990794i	$0.543225\pi$
$8$	−1.55604	−	2.36194i	−0.550142	−	0.835071i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	2.39218	+	1.28533i	0.756474	+	0.406458i
$11$	0.740315	+	0.224572i	0.223213	+	0.0677110i	0.399910	−	0.916554i	$-0.369041\pi$
$11$	0.740315	+	0.224572i	0.223213	+	0.0677110i	−0.176697	+	0.984265i	$0.556541\pi$
$12$	1.98950	+	0.204677i	0.574319	+	0.0590852i
$13$	1.85681	−	1.52385i	0.514987	−	0.422639i	−0.340669	−	0.940183i	$-0.610654\pi$
$13$	1.85681	−	1.52385i	0.514987	−	0.422639i	0.855657	+	0.517544i	$0.173154\pi$
$14$	−1.26058	+	3.02472i	−0.336905	+	0.808391i
$15$	−1.77407	+	0.734842i	−0.458062	+	0.189735i
$16$	2.85289	−	2.80375i	0.713222	−	0.700938i
$17$	5.13980	+	2.12898i	1.24659	+	0.516353i	0.905767	−	0.423776i	$-0.139296\pi$
$17$	5.13980	+	2.12898i	1.24659	+	0.516353i	0.340819	+	0.940129i	$0.389296\pi$
$18$	−1.00217	+	0.997826i	−0.236214	+	0.235190i
$19$	−0.262953	+	2.66981i	−0.0603256	+	0.612496i	0.916729	+	0.399509i	$0.130819\pi$
$19$	−0.262953	+	2.66981i	−0.0603256	+	0.612496i	−0.977055	+	0.212987i	$0.931681\pi$
$20$	−1.13078	+	3.67022i	−0.252850	+	0.820687i
$21$	−1.09228	−	2.04351i	−0.238355	−	0.445930i
$22$	−0.109602	+	1.08857i	−0.0233673	+	0.232084i
$23$	3.99789	+	0.795230i	0.833618	+	0.165817i	0.593406	−	0.804904i	$-0.297783\pi$
$23$	3.99789	+	0.795230i	0.833618	+	0.165817i	0.240212	+	0.970720i	$0.422783\pi$
$24$	0.258891	+	2.81655i	0.0528458	+	0.574927i
$25$	0.256095	+	1.28747i	0.0512189	+	0.257495i
$26$	2.62124	+	2.16074i	0.514068	+	0.423757i
$27$	−0.0980171	−	0.995185i	−0.0188634	−	0.191523i
$28$	−4.54121	−	0.923824i	−0.858207	−	0.174586i
$29$	−0.385772	−	1.27172i	−0.0716361	−	0.236152i	0.913810	−	0.406143i	$-0.133126\pi$
$29$	−0.385772	−	1.27172i	−0.0716361	−	0.236152i	−0.985446	+	0.169990i	$0.945626\pi$
$30$	−1.50381	−	2.26123i	−0.274557	−	0.412842i
$31$	−4.74198	+	4.74198i	−0.851684	+	0.851684i	−0.990341	−	0.138656i	$-0.955722\pi$
$31$	−4.74198	+	4.74198i	−0.851684	+	0.851684i	0.138656	+	0.990341i	$0.455722\pi$
$32$	4.66910	+	3.19366i	0.825388	+	0.564565i
$33$	−0.547037	−	0.547037i	−0.0952269	−	0.0952269i
$34$	−1.55166	+	7.71314i	−0.266107	+	1.32279i
$35$	4.25781	−	1.29159i	0.719701	−	0.218319i
$36$	−1.65810	−	1.11835i	−0.276350	−	0.186392i
$37$	−0.647732	+	0.0637961i	−0.106487	+	0.0104880i	−0.151120	−	0.988515i	$-0.548288\pi$
$37$	−0.647732	+	0.0637961i	−0.106487	+	0.0104880i	0.0446335	+	0.999003i	$0.485788\pi$
$38$	−3.77648	+	0.363672i	−0.612626	+	0.0589953i
$39$	−2.35590	+	0.468618i	−0.377246	+	0.0750389i
$40$	−5.40151	−	0.567557i	−0.854054	−	0.0897386i
$41$	1.92727	−	9.68903i	0.300989	−	1.51317i	−0.473619	−	0.880730i	$-0.657053\pi$
$41$	1.92727	−	9.68903i	0.300989	−	1.51317i	0.774608	−	0.632442i	$-0.217947\pi$
$42$	2.53758	−	2.07333i	0.391557	−	0.319922i
$43$	−3.77207	+	2.01621i	−0.575235	+	0.307470i	−0.733241	−	0.679969i	$-0.761993\pi$
$43$	−3.77207	+	2.01621i	−0.575235	+	0.307470i	0.158006	+	0.987438i	$0.449493\pi$
$44$	−1.54045	+	0.144968i	−0.232231	+	0.0218548i
$45$	1.91099	+	0.188216i	0.284873	+	0.0280576i
$46$	−0.0125186	+	5.76462i	−0.00184577	+	0.849947i
$47$	−1.55657	+	3.75789i	−0.227049	+	0.548145i	−0.995816	−	0.0913843i	$-0.970871\pi$
$47$	−1.55657	+	3.75789i	−0.227049	+	0.548145i	0.768766	+	0.639530i	$0.220871\pi$
$48$	−3.83770	+	1.12785i	−0.553925	+	0.162790i
$49$	−0.624156	−	1.50685i	−0.0891652	−	0.215264i
$50$	−1.71666	+	0.706700i	−0.242772	+	0.0999425i
$51$	−3.52931	−	4.30048i	−0.494202	−	0.602187i
$52$	−2.28302	+	4.22697i	−0.316598	+	0.586175i
$53$	3.62840	−	11.9612i	0.498400	−	1.64300i	−0.241585	−	0.970380i	$-0.577667\pi$
$53$	3.62840	−	11.9612i	0.498400	−	1.64300i	0.739985	−	0.672624i	$-0.234833\pi$
$54$	1.35421	−	0.407585i	0.184284	−	0.0554652i
$55$	1.23519	−	0.825325i	0.166552	−	0.111287i
$56$	0.0426967	−	6.55364i	0.00570558	−	0.875767i
$57$	1.49044	−	2.23061i	0.197414	−	0.295451i
$58$	1.65941	−	0.882346i	0.217891	−	0.115858i
$59$	−0.544937	−	0.447218i	−0.0709447	−	0.0582228i	0.598253	−	0.801308i	$-0.295862\pi$
$59$	−0.544937	−	0.447218i	−0.0709447	−	0.0582228i	−0.669197	+	0.743085i	$0.733362\pi$
$60$	2.72739	−	2.70380i	0.352105	−	0.349059i
$61$	2.90426	−	5.43348i	0.371852	−	0.695686i	−0.624500	−	0.781025i	$-0.714697\pi$
$61$	2.90426	−	5.43348i	0.371852	−	0.695686i	0.996352	+	0.0853385i	$0.0271972\pi$
$62$	−7.87416	−	5.28611i	−1.00002	−	0.671337i
$63$			2.31711i			0.291928i
$64$	−3.15751	+	7.35052i	−0.394689	+	0.918815i
$65$		−	4.61251i		−	0.572111i
$66$	0.609809	−	0.908367i	0.0750623	−	0.111812i
$67$	3.64798	−	6.82489i	0.445671	−	0.833793i	−0.554327	−	0.832299i	$-0.687024\pi$
$67$	3.64798	−	6.82489i	0.445671	−	0.833793i	0.999999	−	0.00149398i	$-0.000475548\pi$
$68$	−11.1265	−	0.0483252i	−1.34928	−	0.00586029i
$69$	−3.15096	−	2.58592i	−0.379331	−	0.311309i
$70$	2.95416	+	5.55583i	0.353089	+	0.664048i
$71$	2.20895	−	3.30592i	0.262154	−	0.392341i	−0.676920	−	0.736057i	$-0.736686\pi$
$71$	2.20895	−	3.30592i	0.262154	−	0.392341i	0.939074	+	0.343716i	$0.111686\pi$
$72$	1.09939	−	2.60602i	0.129565	−	0.307122i
$73$	−10.6853	+	7.13966i	−1.25061	+	0.835634i	−0.991487	−	0.130209i	$-0.958435\pi$
$73$	−10.6853	+	7.13966i	−1.25061	+	0.835634i	−0.259128	+	0.965843i	$0.583435\pi$
$74$	−0.265283	−	0.881407i	−0.0308385	−	0.102462i
$75$	0.381056	−	1.25617i	0.0440005	−	0.145050i
$76$	−1.53519	−	5.14113i	−0.176099	−	0.589729i
$77$	1.13720	+	1.38568i	0.129596	+	0.157913i
$78$	−1.29316	−	3.14125i	−0.146422	−	0.355677i
$79$	2.19861	+	5.30791i	0.247363	+	0.597187i	0.997979	−	0.0635523i	$-0.0202430\pi$
$79$	2.19861	+	5.30791i	0.247363	+	0.597187i	−0.750616	+	0.660739i	$0.770243\pi$
$80$	−0.686437	−	7.65021i	−0.0767460	−	0.855319i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	13.9708	+	0.0303393i	1.54281	+	0.00335041i
$83$	−6.92680	−	0.682230i	−0.760315	−	0.0748845i	−0.289573	−	0.957156i	$-0.593513\pi$
$83$	−6.92680	−	0.682230i	−0.760315	−	0.0748845i	−0.470741	+	0.882271i	$0.656013\pi$
$84$	3.56950	+	2.95545i	0.389464	+	0.322466i
$85$	9.42140	−	5.03584i	1.02189	−	0.546214i
$86$	−3.82712	−	4.68406i	−0.412689	−	0.505095i
$87$	−0.259264	+	1.30341i	−0.0277960	+	0.139740i
$88$	−0.621530	−	2.09802i	−0.0662554	−	0.223650i
$89$	4.65705	−	0.926345i	0.493646	−	0.0981923i	0.0580116	−	0.998316i	$-0.481524\pi$
$89$	4.65705	−	0.926345i	0.493646	−	0.0981923i	0.435635	+	0.900124i	$0.356524\pi$
$90$	0.260308	+	2.70312i	0.0274389	+	0.284934i
$91$	5.53903	−	0.545546i	0.580648	−	0.0571888i
$92$	−8.00261	+	1.55572i	−0.834330	+	0.162195i
$93$	6.41740	−	1.94670i	0.665454	−	0.201863i
$94$	−5.63936	−	1.13447i	−0.581655	−	0.117012i
$95$	3.64264	+	3.64264i	0.373727	+	0.373727i
$96$	−2.61230	−	5.01756i	−0.266616	−	0.512103i
$97$	−12.0214	+	12.0214i	−1.22059	+	1.22059i	−0.253162	+	0.967424i	$0.581471\pi$
$97$	−12.0214	+	12.0214i	−1.22059	+	1.22059i	−0.967424	+	0.253162i	$0.918529\pi$
$98$	1.92063	−	1.27730i	0.194013	−	0.129027i
$99$	0.224572	+	0.740315i	0.0225703	+	0.0744044i
$100$	−1.44910	−	2.18925i	−0.144910	−	0.218925i
$101$	1.29132	+	13.1110i	0.128491	+	1.30459i	0.815847	+	0.578268i	$0.196271\pi$
$101$	1.29132	+	13.1110i	0.128491	+	1.30459i	−0.687356	+	0.726321i	$0.741229\pi$
$102$	5.00439	−	6.07094i	0.495509	−	0.601112i
$103$	−0.663447	−	3.33538i	−0.0653714	−	0.328644i	0.934236	−	0.356655i	$-0.116083\pi$
$103$	−0.663447	−	3.33538i	−0.0653714	−	0.328644i	−0.999608	+	0.0280106i	$0.991083\pi$
$104$	−6.48850	−	2.01452i	−0.636250	−	0.197540i
$105$	−4.36390	−	0.868034i	−0.425873	−	0.0847115i
$106$	17.5880	+	1.77084i	1.70830	+	0.171999i
$107$	−1.10196	−	2.06162i	−0.106531	−	0.199305i	0.823008	−	0.568030i	$-0.192294\pi$
$107$	−1.10196	−	2.06162i	−0.106531	−	0.199305i	−0.929538	+	0.368725i	$0.879794\pi$
$108$	0.935124	+	1.76792i	0.0899823	+	0.170118i
$109$	−0.490109	+	4.97616i	−0.0469439	+	0.476629i	0.942757	+	0.333480i	$0.108223\pi$
$109$	−0.490109	+	4.97616i	−0.0469439	+	0.476629i	−0.989701	+	0.143149i	$0.954277\pi$
$110$	1.48232	+	1.48877i	0.141333	+	0.141948i
$111$	0.601322	+	0.249076i	0.0570750	+	0.0236412i
$112$	9.10572	−	1.72915i	0.860409	−	0.163390i
$113$	0.215074	−	0.0890866i	0.0202325	−	0.00838056i	−0.372544	−	0.928014i	$-0.621515\pi$
$113$	0.215074	−	0.0890866i	0.0202325	−	0.00838056i	0.392777	+	0.919634i	$0.371515\pi$
$114$	3.50199	+	1.45949i	0.327991	+	0.136694i
$115$	6.05058	−	4.96558i	0.564219	−	0.463043i
$116$	1.67721	+	2.06188i	0.155725	+	0.191441i
$117$	2.29862	+	0.697280i	0.212508	+	0.0644635i
$118$	0.471870	−	0.878213i	0.0434391	−	0.0808461i
$119$	7.16171	+	10.7183i	0.656513	+	0.982541i
$120$	4.49616	+	3.04679i	0.410441	+	0.278133i
$121$	−8.64853	−	5.77876i	−0.786230	−	0.525342i
$122$	8.33223	+	2.54733i	0.754365	+	0.230624i
$123$	−6.26707	+	7.63645i	−0.565083	+	0.688556i
$124$	5.18645	−	12.3690i	0.465757	−	1.11077i
$125$	10.6905	+	5.71421i	0.956190	+	0.511094i
$126$	−3.21531	+	0.632308i	−0.286442	+	0.0563305i
$127$	−19.9405			−1.76943			−0.884715	−	0.466132i	$-0.845647\pi$
$127$	−19.9405			−1.76943			−0.884715	+	0.466132i	$0.845647\pi$
$128$	−11.0615	−	2.37561i	−0.977706	−	0.209976i
$129$	4.27710			0.376578
$130$	6.40048	−	1.25869i	0.561360	−	0.110395i
$131$	−19.2343	−	10.2810i	−1.68051	−	0.898253i	−0.983436	−	0.181256i	$-0.941984\pi$
$131$	−19.2343	−	10.2810i	−1.68051	−	0.898253i	−0.697077	−	0.716996i	$-0.745516\pi$
$132$	1.42689	+	0.598311i	0.124195	+	0.0520763i
$133$	−3.94350	+	4.80517i	−0.341945	+	0.416661i
$134$	10.4659	+	3.19964i	0.904120	+	0.276407i
$135$	−1.59662	−	1.06683i	−0.137415	−	0.0918177i
$136$	−2.96920	−	15.4527i	−0.254607	−	1.32505i
$137$	−10.5674	−	15.8152i	−0.902830	−	1.35118i	−0.936100	−	0.351734i	$-0.885592\pi$
$137$	−10.5674	−	15.8152i	−0.902830	−	1.35118i	0.0332700	−	0.999446i	$-0.489408\pi$
$138$	2.72847	−	5.07804i	0.232262	−	0.432272i
$139$	−12.1237	−	3.67767i	−1.02832	−	0.311936i	−0.269333	−	0.963047i	$-0.586803\pi$
$139$	−12.1237	−	3.67767i	−1.02832	−	0.311936i	−0.758983	+	0.651111i	$0.774303\pi$
$140$	−6.90331	+	5.61541i	−0.583437	+	0.474588i
$141$	3.14423	−	2.58040i	0.264792	−	0.217309i
$142$	5.19021	+	2.16307i	0.435553	+	0.181521i
$143$	1.71684	−	0.711138i	0.143569	−	0.0594684i
$144$	3.91621	+	0.814410i	0.326351	+	0.0678675i
$145$	−2.35763	−	0.976564i	−0.195791	−	0.0810992i
$146$	−12.8231	−	12.8789i	−1.06125	−	1.06587i
$147$	−0.159866	+	1.62314i	−0.0131855	+	0.133875i
$148$	1.15068	−	0.608641i	0.0945853	−	0.0500299i
$149$	3.41818	+	6.39497i	0.280029	+	0.523897i	0.982136	−	0.188175i	$-0.0602572\pi$
$149$	3.41818	+	6.39497i	0.280029	+	0.523897i	−0.702107	+	0.712072i	$0.747757\pi$
$150$	1.84710	+	0.185974i	0.150815	+	0.0151847i
$151$	18.7526	+	3.73013i	1.52607	+	0.303553i	0.885606	−	0.464438i	$-0.153744\pi$
$151$	18.7526	+	3.73013i	1.52607	+	0.303553i	0.640460	+	0.767991i	$0.278744\pi$
$152$	6.71509	−	3.53324i	0.544666	−	0.286583i
$153$	1.08534	+	5.45639i	0.0877448	+	0.441123i
$154$	−1.61250	+	1.95615i	−0.129939	+	0.157631i
$155$	1.26221	+	12.8154i	0.101383	+	1.02936i
$156$	4.00603	−	2.65165i	0.320739	−	0.212302i
$157$	−3.42685	−	11.2968i	−0.273492	−	0.901584i	−0.980856	−	0.194734i	$-0.937616\pi$
$157$	−3.42685	−	11.2968i	−0.273492	−	0.901584i	0.707364	−	0.706850i	$-0.249884\pi$
$158$	−6.76548	+	4.49933i	−0.538232	+	0.357947i
$159$	−8.83846	+	8.83846i	−0.700935	+	0.700935i
$160$	10.4284	−	3.04016i	0.824436	−	0.240346i
$161$	6.67865	+	6.67865i	0.526351	+	0.526351i
$162$	−1.38644	−	0.278911i	−0.108929	−	0.0219133i
$163$	4.73071	−	1.43505i	0.370538	−	0.112401i	−0.0995234	−	0.995035i	$-0.531732\pi$
$163$	4.73071	−	1.43505i	0.370538	−	0.112401i	0.470061	+	0.882634i	$0.344232\pi$
$164$	3.77034	+	19.3946i	0.294414	+	1.51446i
$165$	−1.47839	+	0.145609i	−0.115093	+	0.0113356i
$166$	−0.943543	−	9.79804i	−0.0732332	−	0.760475i
$167$	−10.6703	+	2.12245i	−0.825690	+	0.164240i	−0.589810	−	0.807542i	$-0.700797\pi$
$167$	−10.6703	+	2.12245i	−0.825690	+	0.164240i	−0.235880	+	0.971782i	$0.575797\pi$
$168$	−3.12702	+	5.75967i	−0.241255	+	0.444368i
$169$	−1.41053	+	7.09121i	−0.108502	+	0.545478i
$170$	9.55889	+	11.6993i	0.733133	+	0.897292i
$171$	−2.36595	+	1.26463i	−0.180929	+	0.0967086i
$172$	5.45540	−	6.58886i	0.415970	−	0.502396i
$173$	−2.23709	−	0.220334i	−0.170083	−	0.0167517i	0.0126171	−	0.999920i	$-0.495984\pi$
$173$	−2.23709	−	0.220334i	−0.170083	−	0.0167517i	−0.182700	+	0.983169i	$0.558484\pi$
$174$	−1.87941	−	0.00408136i	−0.142477	−	0.000309407i
$175$	−1.16399	+	2.81013i	−0.0879897	+	0.212426i
$176$	2.74168	−	1.43498i	0.206662	−	0.108166i
$177$	0.269774	+	0.651292i	0.0202775	+	0.0489541i
$178$	2.55628	+	6.20950i	0.191601	+	0.465422i
$179$	−8.53103	−	10.3951i	−0.637639	−	0.776965i	0.349482	−	0.936943i	$-0.386358\pi$
$179$	−8.53103	−	10.3951i	−0.637639	−	0.776965i	−0.987121	+	0.159978i	$0.948858\pi$
$180$	−3.67991	+	1.09886i	−0.274284	+	0.0819040i
$181$	−2.29785	+	7.57500i	−0.170798	+	0.563046i	0.829194	+	0.558961i	$0.188800\pi$
$181$	−2.29785	+	7.57500i	−0.170798	+	0.563046i	−0.999992	+	0.00408417i	$0.998700\pi$
$182$	2.26855	+	7.53728i	0.168156	+	0.558700i
$183$	−5.12265	+	3.42285i	−0.378677	+	0.253024i
$184$	−4.34257	−	10.6802i	−0.320139	−	0.787353i
$185$	−0.694361	+	1.03918i	−0.0510504	+	0.0764023i
$186$	4.45253	+	8.37379i	0.326475	+	0.613996i
$187$	3.32696	+	2.73037i	0.243292	+	0.199664i
$188$	0.0353323	−	8.13496i	0.00257687	−	0.593303i
$189$	1.09228	−	2.04351i	0.0794516	−	0.148643i
$190$	−4.06063	+	6.04868i	−0.294589	+	0.438817i
$191$			11.4815i			0.830774i	0.909645	+	0.415387i	$0.136354\pi$
$191$			11.4815i			0.830774i	−0.909645	+	0.415387i	$0.863646\pi$
$192$	6.24968	−	4.99414i	0.451032	−	0.360421i
$193$			16.9313i			1.21874i	0.792886	+	0.609370i	$0.208577\pi$
$193$			16.9313i			1.21874i	−0.792886	+	0.609370i	$0.791423\pi$
$194$	−19.9618	−	13.4008i	−1.43317	−	0.962123i
$195$	−2.17432	+	4.06787i	−0.155706	+	0.291306i
$196$	2.29654	+	2.31658i	0.164039	+	0.165470i
$197$	12.4011	+	10.1773i	0.883540	+	0.725103i	0.962358	−	0.271787i	$-0.0876145\pi$
$197$	12.4011	+	10.1773i	0.883540	+	0.725103i	−0.0788176	+	0.996889i	$0.525114\pi$
$198$	−0.966004	+	0.513646i	−0.0686509	+	0.0365032i
$199$	5.41231	−	8.10009i	0.383668	−	0.574200i	−0.588496	−	0.808500i	$-0.700280\pi$
$199$	5.41231	−	8.10009i	0.383668	−	0.574200i	0.972164	+	0.234300i	$0.0752797\pi$
$200$	2.64244	−	2.60823i	0.186849	−	0.184430i
$201$	−6.43446	+	4.29937i	−0.453852	+	0.303254i
$202$	−17.8409	+	5.36968i	−1.25528	+	0.377810i
$203$	0.893876	−	2.94672i	0.0627378	−	0.206819i
$204$	9.78988	+	5.28760i	0.685429	+	0.370206i
$205$	−12.0343	−	14.6638i	−0.840509	−	1.02416i
$206$	4.44724	−	1.83080i	0.309854	−	0.127558i
$207$	1.55990	+	3.76593i	0.108421	+	0.261750i
$208$	1.02479	−	9.55341i	0.0710566	−	0.662410i
$209$	−0.794232	+	1.91745i	−0.0549382	+	0.132633i
$210$	0.0136647	−	6.29238i	0.000942953	−	0.434216i
$211$	20.2342	+	1.99289i	1.39298	+	0.137196i	0.766500	−	0.642244i	$-0.221996\pi$
$211$	20.2342	+	1.99289i	1.39298	+	0.137196i	0.626477	+	0.779440i	$0.284496\pi$
$212$	2.34225	+	24.8890i	0.160866	+	1.70938i
$213$	−3.50652	+	1.87427i	−0.240263	+	0.128423i
$214$	2.56007	−	2.09171i	0.175003	−	0.142986i
$215$	−1.60229	+	8.05523i	−0.109275	+	0.549362i
$216$	−2.19805	+	1.78005i	−0.149558	+	0.121117i
$217$	−15.2404	+	3.03149i	−1.03458	+	0.205791i
$218$	−7.03884	+	0.677834i	−0.476730	+	0.0459087i
$219$	12.7892	−	1.25962i	0.864212	−	0.0851174i
$220$	−1.66136	+	2.46318i	−0.112009	+	0.166067i
$221$	12.7879	−	3.87916i	0.860207	−	0.260941i
$222$	−0.181534	+	0.902385i	−0.0121837	+	0.0605641i
$223$	−5.62093	−	5.62093i	−0.376405	−	0.376405i	0.493398	−	0.869804i	$-0.335755\pi$
$223$	−5.62093	−	5.62093i	−0.376405	−	0.376405i	−0.869804	+	0.493398i	$0.835755\pi$
$224$	4.88426	+	12.1636i	0.326343	+	0.812712i
$225$	−0.928217	+	0.928217i	−0.0618811	+	0.0618811i
$226$	0.182311	+	0.274134i	0.0121271	+	0.0182351i
$227$	−5.93458	−	19.5637i	−0.393892	−	1.29849i	−0.899952	−	0.435989i	$-0.856399\pi$
$227$	−5.93458	−	19.5637i	−0.393892	−	1.29849i	0.506061	−	0.862498i	$-0.331101\pi$
$228$	−1.06959	+	5.25776i	−0.0708356	+	0.348204i
$229$	1.93195	+	19.6154i	0.127667	+	1.29622i	0.819045	+	0.573729i	$0.194504\pi$
$229$	1.93195	+	19.6154i	0.127667	+	1.29622i	−0.691378	+	0.722493i	$0.742996\pi$
$230$	8.54154	+	7.04096i	0.563212	+	0.464267i
$231$	−0.349715	−	1.75813i	−0.0230095	−	0.115677i
$232$	−2.40345	+	2.89001i	−0.157794	+	0.189739i
$233$	−15.5797	−	3.09900i	−1.02066	−	0.203023i	−0.343731	−	0.939068i	$-0.611691\pi$
$233$	−15.5797	−	3.09900i	−1.02066	−	0.203023i	−0.676932	+	0.736046i	$0.736691\pi$
$234$	−0.340307	+	3.37993i	−0.0222465	+	0.220953i
$235$	3.68189	+	6.88832i	0.240180	+	0.449345i
$236$	1.34741	+	0.415131i	0.0877087	+	0.0270227i
$237$	0.563132	−	5.71758i	0.0365794	−	0.371397i
$238$	−12.9187	+	12.8627i	−0.837395	+	0.833766i
$239$	11.1856	+	4.63323i	0.723536	+	0.299698i	0.713893	−	0.700255i	$-0.246930\pi$
$239$	11.1856	+	4.63323i	0.723536	+	0.299698i	0.00964327	+	0.999954i	$0.496930\pi$
$240$	−3.00090	+	7.07046i	−0.193707	+	0.456396i
$241$	−1.25428	+	0.519540i	−0.0807953	+	0.0334665i	−0.422715	−	0.906263i	$-0.638923\pi$
$241$	−1.25428	+	0.519540i	−0.0807953	+	0.0334665i	0.341920	+	0.939729i	$0.388923\pi$
$242$	5.65875	−	13.5780i	0.363758	−	0.872824i
$243$	0.773010	−	0.634393i	0.0495886	−	0.0406963i
$244$	−1.26101	+	12.2572i	−0.0807278	+	0.784689i
$245$	−2.99704	−	0.909143i	−0.191474	−	0.0580830i
$246$	−12.3068	−	6.61253i	−0.784654	−	0.421600i
$247$	3.58013	+	5.35804i	0.227798	+	0.340924i
$248$	18.5789	+	3.82157i	1.17976	+	0.242670i
$249$	5.78729	+	3.86694i	0.366754	+	0.245057i
$250$	−5.01194	+	16.3939i	−0.316983	+	1.03684i
$251$	−13.5766	+	16.5432i	−0.856950	+	1.04420i	0.141576	+	0.989927i	$0.454783\pi$
$251$	−13.5766	+	16.5432i	−0.856950	+	1.04420i	−0.998526	+	0.0542692i	$0.982717\pi$
$252$	−1.75483	−	4.28912i	−0.110544	−	0.270189i
$253$	2.78111	+	1.48653i	0.174847	+	0.0934576i
$254$	−5.44148	−	27.6701i	−0.341429	−	1.73618i
$255$	−10.6828			−0.668984
$256$	0.277953	−	15.9976i	0.0173721	−	0.999849i
$257$	21.2385			1.32482			0.662409	−	0.749142i	$-0.269534\pi$
$257$	21.2385			1.32482			0.662409	+	0.749142i	$0.269534\pi$
$258$	1.16716	+	5.93506i	0.0726645	+	0.369501i
$259$	−1.33005	−	0.710927i	−0.0826454	−	0.0441749i
$260$	3.49321	+	8.53806i	0.216640	+	0.529508i
$261$	0.843073	−	1.02729i	0.0521849	−	0.0635875i
$262$	9.01745	−	29.4958i	0.557100	−	1.82226i
$263$	17.4224	+	11.6413i	1.07431	+	0.717834i	0.961229	−	0.275752i	$-0.0889267\pi$
$263$	17.4224	+	11.6413i	1.07431	+	0.717834i	0.113085	+	0.993585i	$0.463927\pi$
$264$	−0.440859	+	2.14328i	−0.0271330	+	0.131909i
$265$	−13.3347	−	19.9569i	−0.819147	−	1.22594i
$266$	−7.74395	−	4.16087i	−0.474812	−	0.255120i
$267$	−4.54383	−	1.37835i	−0.278078	−	0.0843539i
$268$	−1.58393	+	15.3961i	−0.0967537	+	0.940464i
$269$	19.0108	−	15.6018i	1.15911	−	0.951256i	0.159753	−	0.987157i	$-0.448930\pi$
$269$	19.0108	−	15.6018i	1.15911	−	0.951256i	0.999355	+	0.0359009i	$0.0114301\pi$
$270$	1.04467	−	2.50665i	0.0635766	−	0.152550i
$271$	27.8566	−	11.5386i	1.69217	−	0.700919i	0.692380	−	0.721533i	$-0.256562\pi$
$271$	27.8566	−	11.5386i	1.69217	−	0.700919i	0.999787	+	0.0206145i	$0.00656225\pi$
$272$	20.6324	−	8.33700i	1.25102	−	0.505505i
$273$	−5.14215	−	2.12995i	−0.311217	−	0.128910i
$274$	19.0620	−	18.9794i	1.15158	−	1.14659i
$275$	−0.0995401	+	1.01065i	−0.00600249	+	0.0609443i
$276$	7.79104	+	2.40039i	0.468965	+	0.144486i
$277$	−2.15973	−	4.04057i	−0.129766	−	0.242774i	0.808645	−	0.588297i	$-0.200202\pi$
$277$	−2.15973	−	4.04057i	−0.129766	−	0.242774i	−0.938410	+	0.345523i	$0.887702\pi$
$278$	1.79488	−	17.8268i	0.107650	−	1.06918i
$279$	−6.57731	−	1.30831i	−0.393773	−	0.0783264i
$280$	−9.67596	−	8.04692i	−0.578249	−	0.480895i
$281$	2.22275	+	11.1745i	0.132598	+	0.666615i	0.988712	+	0.149828i	$0.0478720\pi$
$281$	2.22275	+	11.1745i	0.132598	+	0.666615i	−0.856114	+	0.516787i	$0.827128\pi$
$282$	4.43868	+	3.65889i	0.264320	+	0.217884i
$283$	−1.17357	−	11.9154i	−0.0697614	−	0.708300i	−0.964919	−	0.262549i	$-0.915437\pi$
$283$	−1.17357	−	11.9154i	−0.0697614	−	0.708300i	0.895157	−	0.445751i	$-0.147063\pi$
$284$	−1.58522	+	7.79240i	−0.0940654	+	0.462394i
$285$	−1.49539	−	4.92965i	−0.0885793	−	0.292007i
$286$	1.45530	+	2.18829i	0.0860539	+	0.129396i
$287$	16.1859	−	16.1859i	0.955426	−	0.955426i
$288$	−0.0614215	+	5.65652i	−0.00361930	+	0.333314i
$289$	9.86422	+	9.86422i	0.580248	+	0.580248i
$290$	0.711748	−	3.53803i	0.0417953	−	0.207760i
$291$	16.2687	−	4.93507i	0.953691	−	0.289299i
$292$	14.3720	−	21.3083i	0.841058	−	1.24697i
$293$	−25.4279	+	2.50443i	−1.48552	+	0.146311i	−0.807993	−	0.589191i	$-0.799446\pi$
$293$	−25.4279	+	2.50443i	−1.48552	+	0.146311i	−0.677523	+	0.735502i	$0.736946\pi$
$294$	−2.29596	+	0.221099i	−0.133903	+	0.0128948i
$295$	−1.32767	+	0.264089i	−0.0772997	+	0.0153759i
$296$	1.15858	+	1.43063i	0.0673409	+	0.0831540i
$297$	0.150927	−	0.758762i	0.00875768	−	0.0440278i
$298$	−7.94112	+	6.48830i	−0.460017	+	0.375857i
$299$	8.63515	−	4.61558i	0.499383	−	0.266926i
$300$	0.245983	+	2.61385i	0.0142019	+	0.150910i
$301$	−9.86280	−	0.971401i	−0.568482	−	0.0559906i
$302$	−0.0587201	+	27.0397i	−0.00337896	+	1.55596i
$303$	5.04162	−	12.1716i	0.289634	−	0.699238i
$304$	6.73530	+	8.35392i	0.386296	+	0.479130i
$305$	−4.52734	−	10.9300i	−0.259234	−	0.625847i
$306$	−7.27530	+	2.99504i	−0.415901	+	0.171215i
$307$	−1.61460	−	1.96740i	−0.0921501	−	0.112285i	0.724894	−	0.688861i	$-0.241889\pi$
$307$	−1.61460	−	1.96740i	−0.0921501	−	0.112285i	−0.817044	+	0.576575i	$0.804389\pi$
$308$	−3.15446	−	1.70375i	−0.179742	−	0.0970801i
$309$	−0.987177	+	3.25429i	−0.0561585	+	0.185130i
$310$	−17.4387	+	5.24864i	−0.990450	+	0.298103i
$311$	10.6194	−	7.09564i	0.602170	−	0.402357i	−0.216782	−	0.976220i	$-0.569556\pi$
$311$	10.6194	−	7.09564i	0.602170	−	0.402357i	0.818951	+	0.573863i	$0.194556\pi$
$312$	4.77271	+	4.83531i	0.270201	+	0.273745i
$313$	13.0718	−	19.5633i	0.738862	−	1.10579i	−0.251577	−	0.967837i	$-0.580949\pi$
$313$	13.0718	−	19.5633i	0.738862	−	1.10579i	0.990439	−	0.137948i	$-0.0440508\pi$
$314$	14.7407	−	7.83797i	0.831867	−	0.442322i
$315$	3.43943	+	2.82267i	0.193790	+	0.159039i
$316$	−8.08963	−	8.16021i	−0.455078	−	0.459048i
$317$	−4.46881	+	8.36056i	−0.250993	+	0.469576i	−0.975591	−	0.219597i	$-0.929526\pi$
$317$	−4.46881	+	8.36056i	−0.250993	+	0.469576i	0.724597	+	0.689173i	$0.242026\pi$
$318$	−14.6765	−	9.85266i	−0.823015	−	0.552510i
$319$		−	1.02811i		−	0.0575629i
$320$	7.06440	+	13.6412i	0.394912	+	0.762565i
$321$			2.33765i			0.130475i
$322$	−7.44502	+	11.0900i	−0.414895	+	0.618024i
$323$	−7.03549	+	13.1625i	−0.391465	+	0.732379i
$324$	0.00868646	−	1.99998i	0.000482581	−	0.111110i
$325$	2.43743	+	2.00035i	0.135205	+	0.110959i
$326$	3.28227	+	6.17290i	0.181788	+	0.341885i
$327$	2.77798	−	4.15754i	0.153623	−	0.229913i
$328$	−25.8838	+	10.5244i	−1.42919	+	0.581112i
$329$	−7.83651	+	5.23619i	−0.432041	+	0.288680i
$330$	−0.605485	−	2.01173i	−0.0333309	−	0.110742i
$331$	8.70674	−	28.7023i	0.478566	−	1.57762i	−0.302486	−	0.953154i	$-0.597817\pi$
$331$	8.70674	−	28.7023i	0.478566	−	1.57762i	0.781052	−	0.624466i	$-0.214683\pi$
$332$	13.3386	−	3.98305i	0.732053	−	0.218598i
$333$	−0.412905	−	0.503126i	−0.0226271	−	0.0275712i
$334$	−5.85696	−	14.2273i	−0.320479	−	0.778481i
$335$	−5.68669	−	13.7289i	−0.310697	−	0.750089i
$336$	−8.84564	−	2.76743i	−0.482569	−	0.150976i
$337$	−0.764852	+	1.84652i	−0.0416642	+	0.100586i	−0.943342	−	0.331823i	$-0.892336\pi$
$337$	−0.764852	+	1.84652i	−0.0416642	+	0.100586i	0.901678	+	0.432409i	$0.142336\pi$
$338$	−10.2249	−	0.0222047i	−0.556163	−	0.00120778i
$339$	−0.231673	−	0.0228178i	−0.0125828	−	0.00123930i
$340$	−13.6258	+	16.4568i	−0.738963	+	0.892497i
$341$	−4.57547	+	2.44564i	−0.247776	+	0.132439i
$342$	−2.40048	−	2.93798i	−0.129803	−	0.158868i
$343$	3.90161	−	19.6147i	0.210667	−	1.05909i
$344$	10.6316	+	5.77210i	0.573220	+	0.311211i
$345$	−7.67689	+	1.52703i	−0.413310	+	0.0822124i
$346$	−0.304729	−	3.16440i	−0.0163823	−	0.170119i
$347$	−24.2003	+	2.38352i	−1.29914	+	0.127954i	−0.723828	−	0.689980i	$-0.757619\pi$
$347$	−24.2003	+	2.38352i	−1.29914	+	0.127954i	−0.575312	+	0.817934i	$0.695119\pi$
$348$	−0.507201	−	2.60904i	−0.0271888	−	0.139859i
$349$	−21.7908	+	6.61015i	−1.16643	+	0.353833i	−0.813359	−	0.581762i	$-0.802363\pi$
$349$	−21.7908	+	6.61015i	−1.16643	+	0.353833i	−0.353074	+	0.935596i	$0.614863\pi$
$350$	−4.21708	−	0.848353i	−0.225412	−	0.0453464i
$351$	−1.69851	−	1.69851i	−0.0906597	−	0.0906597i
$352$	2.73940	+	3.41287i	0.146010	+	0.181906i
$353$	−8.43155	+	8.43155i	−0.448766	+	0.448766i	−0.894944	−	0.446178i	$-0.852785\pi$
$353$	−8.43155	+	8.43155i	−0.448766	+	0.448766i	0.446178	+	0.894944i	$0.352785\pi$
$354$	−0.830139	+	0.552077i	−0.0441214	+	0.0293426i
$355$	−2.21628	−	7.30610i	−0.117628	−	0.387768i
$356$	−7.91895	+	5.24167i	−0.419704	+	0.277808i
$357$	−1.26351	−	12.8287i	−0.0668722	−	0.678965i
$358$	12.0966	−	14.6746i	0.639325	−	0.775579i
$359$	−1.86064	−	9.35406i	−0.0982007	−	0.493688i	−0.998315	−	0.0580337i	$-0.981517\pi$
$359$	−1.86064	−	9.35406i	−0.0982007	−	0.493688i	0.900114	−	0.435655i	$-0.143483\pi$
$360$	−2.52901	−	4.80651i	−0.133291	−	0.253325i
$361$	11.5762	+	2.30265i	0.609273	+	0.121192i
$362$	−11.1384	−	1.12146i	−0.585421	−	0.0589429i
$363$	4.90323	+	9.17331i	0.257353	+	0.481474i
$364$	−9.83994	+	5.20474i	−0.515753	+	0.272802i
$365$	−2.41877	+	24.5582i	−0.126604	+	1.28544i
$366$	−6.14757	−	6.17433i	−0.321339	−	0.322737i
$367$	−27.9860	−	11.5922i	−1.46086	−	0.605107i	−0.496104	−	0.868263i	$-0.665237\pi$
$367$	−27.9860	−	11.5922i	−1.46086	−	0.605107i	−0.964753	+	0.263156i	$0.915237\pi$
$368$	13.6352	−	8.94039i	0.710782	−	0.466050i
$369$	9.12686	−	3.78047i	0.475126	−	0.196803i
$370$	−1.63149	−	0.679940i	−0.0848172	−	0.0353484i
$371$	22.3884	−	18.3737i	1.16235	−	0.953915i
$372$	−10.4047	+	8.46358i	−0.539460	+	0.438816i
$373$	−7.43321	−	2.25484i	−0.384877	−	0.116751i	0.0919160	−	0.995767i	$-0.470701\pi$
$373$	−7.43321	−	2.25484i	−0.384877	−	0.116751i	−0.476793	+	0.879016i	$0.658201\pi$
$374$	−2.88087	+	5.36169i	−0.148966	+	0.277247i
$375$	−6.73455	−	10.0790i	−0.347770	−	0.520475i
$376$	11.2980	−	2.17089i	0.582650	−	0.111955i
$377$	−2.65421	−	1.77349i	−0.136699	−	0.0913393i
$378$	3.13371	+	0.958038i	0.161181	+	0.0492762i
$379$	−3.17311	+	3.86645i	−0.162992	+	0.198606i	−0.848101	−	0.529834i	$-0.822254\pi$
$379$	−3.17311	+	3.86645i	−0.162992	+	0.198606i	0.685110	+	0.728440i	$0.259754\pi$
$380$	−9.50145	−	3.98407i	−0.487414	−	0.204378i
$381$	17.5859	+	9.39987i	0.900954	+	0.481570i
$382$	−15.9322	+	3.13315i	−0.815161	+	0.160306i
$383$	−22.2956			−1.13925			−0.569627	−	0.821904i	$-0.692912\pi$
$383$	−22.2956			−1.13925			−0.569627	+	0.821904i	$0.692912\pi$
$384$	8.63550	+	7.30945i	0.440679	+	0.373009i
$385$	3.44217			0.175429
$386$	−23.4944	+	4.62032i	−1.19584	+	0.235168i
$387$	−3.77207	−	2.01621i	−0.191745	−	0.102490i
$388$	13.1482	−	31.3566i	0.667497	−	1.59189i
$389$	−10.5969	+	12.9123i	−0.537282	+	0.654680i	−0.968922	−	0.247366i	$-0.920435\pi$
$389$	−10.5969	+	12.9123i	−0.537282	+	0.654680i	0.431640	+	0.902046i	$0.357935\pi$
$390$	−6.23807	−	1.90710i	−0.315877	−	0.0965697i
$391$	18.8553	+	12.5987i	0.953556	+	0.637146i
$392$	−2.58787	+	3.81892i	−0.130707	+	0.192885i
$393$	12.1168	+	18.1340i	0.611210	+	0.914740i
$394$	−10.7383	+	19.9854i	−0.540988	+	1.00685i
$395$	10.5572	+	3.20248i	0.531189	+	0.161134i
$396$	−0.976363	−	1.20029i	−0.0490641	−	0.0603171i
$397$	20.4940	−	16.8190i	1.02856	−	0.844119i	0.0406560	−	0.999173i	$-0.487055\pi$
$397$	20.4940	−	16.8190i	1.02856	−	0.844119i	0.987906	+	0.155054i	$0.0495552\pi$
$398$	12.7169	+	5.29991i	0.637442	+	0.265660i
$399$	5.74300	−	2.37883i	0.287509	−	0.119090i
$400$	4.34037	+	2.95500i	0.217018	+	0.147750i
$401$	−9.78326	−	4.05236i	−0.488553	−	0.202365i	0.124788	−	0.992183i	$-0.460175\pi$
$401$	−9.78326	−	4.05236i	−0.488553	−	0.202365i	−0.613341	+	0.789818i	$0.710175\pi$
$402$	−7.72183	−	7.75545i	−0.385130	−	0.386806i
$403$	−1.57892	+	16.0310i	−0.0786515	+	0.798562i
$404$	−12.3197	−	23.2913i	−0.612928	−	1.15878i
$405$	0.905193	+	1.69350i	0.0449794	+	0.0841505i
$406$	4.33289	+	0.436256i	0.215038	+	0.0216510i
$407$	−0.493852	−	0.0982333i	−0.0244794	−	0.00486925i
$408$	−4.66573	+	15.0277i	−0.230988	+	0.743982i
$409$	−0.635243	−	3.19358i	−0.0314108	−	0.157913i	0.961897	−	0.273413i	$-0.0881527\pi$
$409$	−0.635243	−	3.19358i	−0.0314108	−	0.157913i	−0.993307	+	0.115501i	$0.963153\pi$
$410$	17.0640	−	20.7007i	0.842731	−	1.02234i
$411$	1.86436	+	18.9291i	0.0919620	+	0.933706i
$412$	3.75408	+	5.67155i	0.184950	+	0.279417i
$413$	−0.474167	−	1.56312i	−0.0233322	−	0.0769161i
$414$	−4.80006	+	3.19224i	−0.235910	+	0.156890i
$415$	−9.45079	+	9.45079i	−0.463921	+	0.463921i
$416$	13.5363	−	1.18496i	0.663672	−	0.0580974i
$417$	8.95847	+	8.95847i	0.438698	+	0.438698i
$418$	−2.87745	−	0.578860i	−0.140741	−	0.0283129i
$419$	−20.2317	+	6.13722i	−0.988384	+	0.299823i	−0.742771	−	0.669545i	$-0.766489\pi$
$419$	−20.2317	+	6.13722i	−0.988384	+	0.299823i	−0.245612	+	0.969368i	$0.578989\pi$
$420$	8.73526	−	1.69815i	0.426237	−	0.0828610i
$421$	−16.1029	+	1.58600i	−0.784809	+	0.0772969i	−0.482480	−	0.875907i	$-0.660264\pi$
$421$	−16.1029	+	1.58600i	−0.784809	+	0.0772969i	−0.302329	+	0.953204i	$0.597764\pi$
$422$	2.75622	+	28.6215i	0.134171	+	1.39327i
$423$	−3.98936	+	0.793533i	−0.193969	+	0.0385829i
$424$	−33.8976	+	10.0421i	−1.64622	+	0.487685i
$425$	−1.42473	+	7.16258i	−0.0691094	+	0.347436i
$426$	−3.55769	−	4.35431i	−0.172371	−	0.210967i
$427$	12.5900	−	6.72949i	0.609272	−	0.325663i
$428$	3.60114	+	2.98165i	0.174068	+	0.144123i
$429$	−1.84935	−	0.182145i	−0.0892872	−	0.00879403i
$430$	−11.6150	−	0.0252234i	−0.560124	−	0.00121638i
$431$	13.4653	−	32.5081i	0.648601	−	1.56586i	−0.166183	−	0.986095i	$-0.553144\pi$
$431$	13.4653	−	32.5081i	0.648601	−	1.56586i	0.814783	−	0.579766i	$-0.196856\pi$
$432$	−3.06988	−	2.56434i	−0.147700	−	0.123377i
$433$	5.41086	+	13.0630i	0.260029	+	0.627767i	0.998940	−	0.0460371i	$-0.0146593\pi$
$433$	5.41086	+	13.0630i	0.260029	+	0.627767i	−0.738910	+	0.673804i	$0.764659\pi$
$434$	−8.36550	−	20.3208i	−0.401557	−	0.975430i
$435$	1.61890	+	1.97263i	0.0776202	+	0.0945805i
$436$	−2.86139	−	9.58237i	−0.137036	−	0.458912i
$437$	−3.17437	+	10.4645i	−0.151851	+	0.500585i
$438$	5.23789	+	17.4030i	0.250276	+	0.831546i
$439$	15.6696	−	10.4701i	0.747869	−	0.499710i	−0.122282	−	0.992495i	$-0.539021\pi$
$439$	15.6696	−	10.4701i	0.747869	−	0.499710i	0.870151	+	0.492785i	$0.164021\pi$
$440$	−3.87136	−	1.63320i	−0.184560	−	0.0778597i
$441$	0.906134	−	1.35613i	0.0431492	−	0.0645774i
$442$	8.87251	+	16.6864i	0.422022	+	0.793689i
$443$	10.7563	+	8.82751i	0.511049	+	0.419407i	0.854256	−	0.519853i	$-0.174013\pi$
$443$	10.7563	+	8.82751i	0.511049	+	0.419407i	−0.343207	+	0.939260i	$0.611513\pi$
$444$	−1.30172	−	0.00565372i	−0.0617769	−	0.000268314i
$445$	4.29811	−	8.04120i	0.203750	−	0.381190i
$446$	6.26593	−	9.33368i	0.296700	−	0.441963i
$447$		−	7.25119i		−	0.342969i
$448$	−15.5457	+	10.0968i	−0.734467	+	0.477031i
$449$		−	39.2811i		−	1.85379i	−0.375321	−	0.926895i	$-0.622468\pi$
$449$		−	39.2811i		−	1.85379i	0.375321	−	0.926895i	$-0.377532\pi$
$450$	−1.54133	−	1.03473i	−0.0726588	−	0.0487776i
$451$	3.60267	−	6.74012i	0.169643	−	0.317380i
$452$	−0.330648	+	0.327788i	−0.0155524	+	0.0154179i
$453$	−14.7800	−	12.1296i	−0.694423	−	0.569898i
$454$	25.5278	−	13.5737i	1.19808	−	0.637045i
$455$	5.93777	−	8.88649i	0.278367	−	0.416605i
$456$	−7.58774	−	0.0494338i	−0.355328	−	0.00231495i
$457$	2.92068	−	1.95154i	0.136624	−	0.0912891i	−0.485380	−	0.874303i	$-0.661319\pi$
$457$	2.92068	−	1.95154i	0.136624	−	0.0912891i	0.622004	+	0.783014i	$0.286319\pi$
$458$	−26.6918	+	8.03362i	−1.24723	+	0.375386i
$459$	1.61494	−	5.32373i	0.0753787	−	0.248490i
$460$	−7.43941	+	13.7739i	−0.346864	+	0.642213i
$461$	−17.9361	−	21.8552i	−0.835366	−	1.01790i	−0.999505	−	0.0314590i	$-0.989985\pi$
$461$	−17.9361	−	21.8552i	−0.835366	−	1.01790i	0.164139	−	0.986437i	$-0.447515\pi$
$462$	2.34422	−	0.965048i	0.109063	−	0.0448981i
$463$	7.15218	+	17.2669i	0.332390	+	0.802461i	0.998402	+	0.0565192i	$0.0180002\pi$
$463$	7.15218	+	17.2669i	0.332390	+	0.802461i	−0.666011	+	0.745942i	$0.732000\pi$
$464$	−4.66615	−	2.54647i	−0.216621	−	0.118217i
$465$	4.92797	−	11.8972i	0.228529	−	0.551719i
$466$	0.0487849	−	22.4647i	0.00225992	−	1.04066i
$467$	1.56739	+	0.154375i	0.0725302	+	0.00714360i	0.134217	−	0.990952i	$-0.457148\pi$
$467$	1.56739	+	0.154375i	0.0725302	+	0.00714360i	−0.0616869	+	0.998096i	$0.519648\pi$
$468$	−4.78298	+	0.450116i	−0.221093	+	0.0208066i
$469$	15.8140	−	8.45277i	0.730224	−	0.390313i
$470$	−8.55375	+	6.98885i	−0.394555	+	0.322371i
$471$	−2.30307	+	11.5783i	−0.106120	+	0.533500i
$472$	−0.208361	+	1.98299i	−0.00959058	+	0.0912747i
$473$	−3.24530	+	0.645531i	−0.149219	+	0.0296815i
$474$	8.08759	−	0.778828i	0.371475	−	0.0357728i
$475$	−3.50465	+	0.345178i	−0.160804	+	0.0158378i
$476$	−21.3741	−	14.4164i	−0.979681	−	0.660774i
$477$	11.9612	−	3.62840i	0.547668	−	0.166133i
$478$	−3.37683	+	16.7859i	−0.154453	+	0.767768i
$479$	10.8102	+	10.8102i	0.493931	+	0.493931i	0.909542	−	0.415611i	$-0.136432\pi$
$479$	10.8102	+	10.8102i	0.493931	+	0.493931i	−0.415611	+	0.909542i	$0.636432\pi$
$480$	−10.6301	−	2.23472i	−0.485197	−	0.102001i
$481$	−1.10550	+	1.10550i	−0.0504066	+	0.0504066i
$482$	−1.06321	−	1.59871i	−0.0484278	−	0.0728191i
$483$	−2.74175	−	9.03834i	−0.124754	−	0.411259i
$484$	20.3855	+	4.14704i	0.926612	+	0.188502i
$485$	3.19982	+	32.4883i	0.145296	+	1.47522i
$486$	1.09125	+	0.899539i	0.0495001	+	0.0408039i
$487$	−4.87785	−	24.5226i	−0.221037	−	1.11123i	−0.918747	−	0.394846i	$-0.870798\pi$
$487$	−4.87785	−	24.5226i	−0.221037	−	1.11123i	0.697711	−	0.716380i	$-0.254202\pi$
$488$	−17.3527	+	1.59501i	−0.785519	+	0.0722029i
$489$	−4.84859	−	0.964444i	−0.219261	−	0.0436137i
$490$	0.443706	−	4.40690i	0.0200446	−	0.199083i
$491$	−2.52545	−	4.72479i	−0.113972	−	0.213227i	0.818467	−	0.574553i	$-0.194824\pi$
$491$	−2.52545	−	4.72479i	−0.113972	−	0.213227i	−0.932439	+	0.361326i	$0.882324\pi$
$492$	5.81742	−	18.8818i	0.262269	−	0.851259i
$493$	0.724669	−	7.35769i	0.0326375	−	0.331374i
$494$	−6.45803	+	6.43005i	−0.290561	+	0.289301i
$495$	1.37246	+	0.568493i	0.0616877	+	0.0255519i
$496$	−0.233009	+	26.8237i	−0.0104624	+	1.20442i
$497$	8.51155	−	3.52560i	0.381795	−	0.158145i
$498$	−3.78663	+	9.08588i	−0.169683	+	0.407148i
$499$	5.63323	−	4.62307i	0.252178	−	0.206957i	−0.499808	−	0.866136i	$-0.666596\pi$
$499$	5.63323	−	4.62307i	0.252178	−	0.206957i	0.751986	+	0.659179i	$0.229096\pi$
$500$	−24.1164	−	2.48107i	−1.07852	−	0.110957i
$501$	10.4109	+	3.15810i	0.465123	+	0.141093i
$502$	−26.6608	−	14.3250i	−1.18993	−	0.639357i
$503$	14.4869	+	21.6812i	0.645938	+	0.966715i	0.999510	+	0.0313075i	$0.00996710\pi$
$503$	14.4869	+	21.6812i	0.645938	+	0.966715i	−0.353572	+	0.935407i	$0.615033\pi$
$504$	5.47287	−	3.60551i	0.243781	−	0.160602i
$505$	21.0345	+	14.0548i	0.936022	+	0.625430i
$506$	−1.30384	+	4.26482i	−0.0579628	+	0.189595i
$507$	4.58675	−	5.58897i	0.203705	−	0.248215i
$508$	36.9111	−	15.1016i	1.63767	−	0.670025i
$509$	19.6423	+	10.4990i	0.870630	+	0.465362i	0.845284	−	0.534317i	$-0.179431\pi$
$509$	19.6423	+	10.4990i	0.870630	+	0.465362i	0.0253463	+	0.999679i	$0.491931\pi$
$510$	−2.91520	−	14.8239i	−0.129087	−	0.656411i
$511$	−29.7773			−1.31727
$512$	22.2747	−	3.97983i	0.984411	−	0.175885i
$513$	2.68273			0.118445
$514$	5.79569	+	29.4712i	0.255637	+	1.29992i
$515$	−5.75910	−	3.07831i	−0.253776	−	0.135646i
$516$	−7.91720	+	3.23920i	−0.348535	+	0.142598i
$517$	−1.99627	+	2.43246i	−0.0877959	+	0.106980i
$518$	0.623555	−	2.03963i	0.0273974	−	0.0896162i
$519$	1.86908	+	1.24888i	0.0820433	+	0.0548196i
$520$	−10.8945	+	7.17723i	−0.477754	+	0.314742i
$521$	−9.88611	−	14.7956i	−0.433118	−	0.648207i	0.549142	−	0.835729i	$-0.314955\pi$
$521$	−9.88611	−	14.7956i	−0.433118	−	0.648207i	−0.982260	+	0.187522i	$0.939955\pi$
$522$	1.65556	+	0.889545i	0.0724621	+	0.0389343i
$523$	27.6851	+	8.39818i	1.21058	+	0.367227i	0.830128	−	0.557573i	$-0.188267\pi$
$523$	27.6851	+	8.39818i	1.21058	+	0.367227i	0.380456	+	0.924799i	$0.375767\pi$
$524$	43.3902	+	4.46392i	1.89551	+	0.195007i
$525$	2.35124	−	1.92961i	0.102616	−	0.0842152i
$526$	−11.3995	+	27.3528i	−0.497044	+	1.19264i
$527$	−34.4684	+	14.2773i	−1.50147	+	0.621928i
$528$	−3.09439	−	0.0268800i	−0.134666	−	0.00116980i
$529$	−5.89849	−	2.44323i	−0.256456	−	0.106228i
$530$	24.0540	−	23.9497i	1.04484	−	1.04031i
$531$	0.0690976	−	0.701559i	0.00299858	−	0.0304451i
$532$	3.66056	−	11.8812i	0.158705	−	0.515117i
$533$	−11.1860	−	20.9276i	−0.484520	−	0.906474i
$534$	0.672705	−	6.68131i	0.0291108	−	0.289129i
$535$	−4.40259	−	0.875729i	−0.190341	−	0.0378611i
$536$	−21.7963	+	2.00347i	−0.941459	+	0.0865365i
$537$	2.62348	+	13.1891i	0.113212	+	0.569154i
$538$	26.8373	+	22.1226i	1.15704	+	0.953771i
$539$	−0.123676	−	1.25571i	−0.00532712	−	0.0540872i
$540$	3.76339	+	0.765591i	0.161950	+	0.0329458i
$541$	12.6736	+	41.7793i	0.544881	+	1.79623i	0.602779	+	0.797908i	$0.294060\pi$
$541$	12.6736	+	41.7793i	0.544881	+	1.79623i	−0.0578985	+	0.998322i	$0.518440\pi$
$542$	23.6130	+	35.5061i	1.01427	+	1.52512i
$543$	5.59736	−	5.59736i	0.240206	−	0.240206i
$544$	17.1990	+	26.3552i	0.737402	+	1.12997i
$545$	6.78937	+	6.78937i	0.290825	+	0.290825i
$546$	1.55237	−	7.71667i	0.0664353	−	0.330243i
$547$	−24.7935	+	7.52102i	−1.06009	+	0.321576i	−0.771733	−	0.635946i	$-0.780610\pi$
$547$	−24.7935	+	7.52102i	−1.06009	+	0.321576i	−0.288360	+	0.957522i	$0.593110\pi$
$548$	31.5382	+	21.2719i	1.34725	+	0.908690i
$549$	6.13130	−	0.603880i	0.261677	−	0.0257730i
$550$	−1.42957	+	0.137667i	−0.0609572	+	0.00587013i
$551$	3.49669	−	0.695535i	0.148964	−	0.0296308i
$552$	−1.20479	+	11.4662i	−0.0512793	+	0.488032i
$553$	−2.59711	+	13.0566i	−0.110440	+	0.555222i
$554$	5.01748	−	4.09954i	0.213172	−	0.174173i
$555$	1.10224	−	0.589159i	0.0467875	−	0.0250084i
$556$	25.2269	−	2.37405i	1.06986	−	0.100682i
$557$	−3.08537	−	0.303882i	−0.130731	−	0.0128759i	0.0324399	−	0.999474i	$-0.489672\pi$
$557$	−3.08537	−	0.303882i	−0.130731	−	0.0128759i	−0.163171	+	0.986598i	$0.552172\pi$
$558$	0.0205955	−	9.48393i	0.000871878	−	0.401487i
$559$	−3.93163	+	9.49179i	−0.166290	+	0.401460i
$560$	8.52575	−	15.6226i	0.360279	−	0.660175i
$561$	−1.64703	−	3.97629i	−0.0695378	−	0.167879i
$562$	−14.8996	+	6.13373i	−0.628501	+	0.258736i
$563$	−9.84542	−	11.9967i	−0.414935	−	0.505600i	0.523037	−	0.852310i	$-0.324799\pi$
$563$	−9.84542	−	11.9967i	−0.414935	−	0.505600i	−0.937972	+	0.346710i	$0.887299\pi$
$564$	−3.86595	+	7.15773i	−0.162786	+	0.301395i
$565$	0.129763	−	0.427771i	0.00545917	−	0.0179965i
$566$	16.2140	−	4.88005i	0.681527	−	0.205124i
$567$	−1.92661	+	1.28732i	−0.0809099	+	0.0540623i
$568$	−11.2456	−	0.0732645i	−0.471855	−	0.00307411i
$569$	19.5447	−	29.2507i	0.819357	−	1.22626i	−0.151941	−	0.988390i	$-0.548552\pi$
$569$	19.5447	−	29.2507i	0.819357	−	1.22626i	0.971298	−	0.237865i	$-0.0764477\pi$
$570$	6.43248	−	3.42029i	0.269427	−	0.143260i
$571$	34.5546	+	28.3582i	1.44607	+	1.18676i	0.947438	+	0.319938i	$0.103662\pi$
$571$	34.5546	+	28.3582i	1.44607	+	1.18676i	0.498627	+	0.866817i	$0.333838\pi$
$572$	−2.63941	+	2.61659i	−0.110359	+	0.109405i
$573$	5.41235	−	10.1258i	0.226104	−	0.423011i
$574$	26.8771	+	18.0433i	1.12183	+	0.753111i
$575$			5.35083i			0.223145i
$576$	−7.86595	+	1.45836i	−0.327748	+	0.0607649i
$577$			39.2847i			1.63544i	0.575615	+	0.817721i	$0.304763\pi$
$577$			39.2847i			1.63544i	−0.575615	+	0.817721i	$0.695237\pi$
$578$	−10.9961	+	16.3798i	−0.457379	+	0.681308i
$579$	7.98134	−	14.9320i	0.331693	−	0.620555i
$580$	5.10372	+	0.0221668i	0.211920	+	0.000920428i
$581$	−12.4670	−	10.2314i	−0.517217	−	0.424469i
$582$	11.2876	+	21.2284i	0.467886	+	0.879945i
$583$	5.37232	−	8.04024i	0.222499	−	0.332993i
$584$	33.4901	+	14.1284i	1.38583	+	0.584636i
$585$	3.83516	−	2.56257i	0.158564	−	0.105949i
$586$	−10.4142	−	34.6013i	−0.430206	−	1.42937i
$587$	0.701223	−	2.31162i	0.0289426	−	0.0954109i	−0.941279	−	0.337629i	$-0.890375\pi$
$587$	0.701223	−	2.31162i	0.0289426	−	0.0954109i	0.970222	+	0.242218i	$0.0778750\pi$
$588$	−0.933341	−	3.12562i	−0.0384903	−	0.128898i
$589$	−11.4132	−	13.9071i	−0.470275	−	0.573031i
$590$	−0.728762	−	1.77025i	−0.0300027	−	0.0728801i
$591$	−6.13923	−	14.8214i	−0.252534	−	0.609671i
$592$	−1.66904	+	1.99808i	−0.0685971	+	0.0821207i
$593$	0.490048	−	1.18308i	0.0201239	−	0.0485833i	−0.913498	−	0.406843i	$-0.866630\pi$
$593$	0.490048	−	1.18308i	0.0201239	−	0.0485833i	0.933622	+	0.358259i	$0.116630\pi$
$594$	1.09407	+	0.00237591i	0.0448903	+	9.74848e-5i
$595$	24.6341	+	2.42624i	1.00990	+	0.0994663i
$596$	−11.1704	−	9.24881i	−0.457558	−	0.378846i
$597$	−8.59159	+	4.59230i	−0.351630	+	0.187950i
$598$	8.76116	+	10.7229i	0.358271	+	0.438492i
$599$	1.37958	−	6.93559i	0.0563679	−	0.283381i	−0.942313	−	0.334734i	$-0.891354\pi$
$599$	1.37958	−	6.93559i	0.0563679	−	0.283381i	0.998681	+	0.0513535i	$0.0163535\pi$
$600$	−3.55994	+	1.05462i	−0.145334	+	0.0430546i
$601$	14.2062	−	2.82579i	0.579482	−	0.115266i	0.103358	−	0.994644i	$-0.467041\pi$
$601$	14.2062	−	2.82579i	0.579482	−	0.115266i	0.476124	+	0.879378i	$0.342041\pi$
$602$	−1.34348	−	13.9511i	−0.0547560	−	0.568603i
$603$	7.70139	−	0.758521i	0.313625	−	0.0308894i
$604$	−37.5373	+	7.29729i	−1.52737	+	0.296922i
$605$	−19.1133	+	5.79795i	−0.777065	+	0.235720i
$606$	18.2655	+	3.67448i	0.741984	+	0.149266i
$607$	1.46066	+	1.46066i	0.0592862	+	0.0592862i	0.736128	−	0.676842i	$-0.236652\pi$
$607$	1.46066	+	1.46066i	0.0592862	+	0.0592862i	−0.676842	+	0.736128i	$0.736652\pi$
$608$	−9.75423	+	11.6258i	−0.395586	+	0.471489i
$609$	−2.17740	+	2.17740i	−0.0882327	+	0.0882327i
$610$	13.9313	−	9.26493i	0.564064	−	0.375126i
$611$	2.83620	+	9.34969i	0.114740	+	0.378248i
$612$	−6.14135	−	9.27816i	−0.248249	−	0.375047i
$613$	1.65639	+	16.8177i	0.0669012	+	0.679259i	0.968889	+	0.247497i	$0.0796080\pi$
$613$	1.65639	+	16.8177i	0.0669012	+	0.679259i	−0.901988	+	0.431762i	$0.857892\pi$
$614$	2.28943	−	2.77735i	0.0923937	−	0.112085i
$615$	3.70081	+	18.6052i	0.149231	+	0.750234i
$616$	1.50337	−	4.84217i	0.0605726	−	0.195096i
$617$	1.60305	+	0.318866i	0.0645364	+	0.0128371i	0.227253	−	0.973836i	$-0.427026\pi$
$617$	1.60305	+	0.318866i	0.0645364	+	0.0128371i	−0.162717	+	0.986673i	$0.552026\pi$
$618$	−4.78515	−	0.481791i	−0.192487	−	0.0193805i
$619$	−7.37466	−	13.7970i	−0.296413	−	0.554549i	0.688994	−	0.724767i	$-0.258053\pi$
$619$	−7.37466	−	13.7970i	−0.296413	−	0.554549i	−0.985406	+	0.170218i	$0.945553\pi$
$620$	−12.0420	−	22.7663i	−0.483618	−	0.914315i
$621$	0.399539	−	4.05659i	0.0160329	−	0.162785i
$622$	12.7441	+	12.7995i	0.510990	+	0.513214i
$623$	10.1648	+	4.21040i	0.407244	+	0.168686i
$624$	−5.40723	+	7.94227i	−0.216463	+	0.317945i
$625$	15.4411	−	6.39592i	0.617644	−	0.255837i
$626$	30.7139	+	12.8003i	1.22758	+	0.511604i
$627$	1.60433	−	1.31664i	0.0640707	−	0.0525815i
$628$	14.8988	+	18.3159i	0.594527	+	0.730883i
$629$	−3.46504	−	1.05111i	−0.138160	−	0.0419104i
$630$	−2.97826	+	5.54294i	−0.118657	+	0.220836i
$631$	24.3305	+	36.4132i	0.968583	+	1.44959i	0.891742	+	0.452544i	$0.149483\pi$
$631$	24.3305	+	36.4132i	0.968583	+	1.44959i	0.0768411	+	0.997043i	$0.475517\pi$
$632$	9.11585	−	13.4523i	0.362609	−	0.535103i
$633$	−16.9055	−	11.2959i	−0.671933	−	0.448971i
$634$	−12.8209	−	3.91960i	−0.509183	−	0.155667i
$635$	−24.2912	+	29.5989i	−0.963965	+	1.17459i
$636$	9.66690	−	23.0542i	0.383317	−	0.914160i
$637$	−3.45514	−	1.84681i	−0.136898	−	0.0731734i
$638$	1.42664	−	0.280556i	0.0564811	−	0.0111073i
$639$	3.97600			0.157288
$640$	−17.0012	+	13.5253i	−0.672031	+	0.534635i
$641$	23.5722			0.931048			0.465524	−	0.885035i	$-0.345866\pi$
$641$	23.5722			0.931048			0.465524	+	0.885035i	$0.345866\pi$
$642$	−3.24381	+	0.637914i	−0.128023	+	0.0251764i
$643$	−26.7661	−	14.3068i	−1.05555	−	0.564204i	−0.150108	−	0.988670i	$-0.547962\pi$
$643$	−26.7661	−	14.3068i	−1.05555	−	0.564204i	−0.905444	+	0.424465i	$0.860462\pi$
$644$	−17.4206	−	7.30465i	−0.686468	−	0.287844i
$645$	5.21030	−	6.34877i	0.205155	−	0.249983i
$646$	−20.1846	−	6.17083i	−0.794153	−	0.242788i
$647$	−35.8888	−	23.9801i	−1.41093	−	0.942755i	−0.999510	−	0.0313112i	$-0.990032\pi$
$647$	−35.8888	−	23.9801i	−1.41093	−	0.942755i	−0.411424	−	0.911444i	$-0.634968\pi$
$648$	2.77762	−	0.533714i	0.109115	−	0.0209663i
$649$	−0.302992	−	0.453460i	−0.0118935	−	0.0177998i
$650$	−2.11061	+	3.92814i	−0.0827851	+	0.154074i
$651$	14.8698	+	4.51071i	0.582795	+	0.176789i
$652$	−7.67005	+	6.23909i	−0.300382	+	0.244342i
$653$	−20.4056	+	16.7465i	−0.798534	+	0.655340i	−0.942486	−	0.334245i	$-0.891519\pi$
$653$	−20.4056	+	16.7465i	−0.798534	+	0.655340i	0.143952	+	0.989585i	$0.454019\pi$
$654$	6.52723	+	2.72029i	0.255235	+	0.106372i
$655$	−38.6917	+	16.0266i	−1.51181	+	0.626212i
$656$	−21.6673	−	33.0453i	−0.845968	−	1.29020i
$657$	−11.8728	−	4.91788i	−0.463203	−	0.191865i
$658$	−9.40440	−	9.44533i	−0.366621	−	0.368217i
$659$	−1.61618	+	16.4093i	−0.0629574	+	0.639217i	0.910988	+	0.412433i	$0.135321\pi$
$659$	−1.61618	+	16.4093i	−0.0629574	+	0.639217i	−0.973945	+	0.226784i	$0.927179\pi$
$660$	2.62633	−	1.38917i	0.102230	−	0.0540733i
$661$	−1.23372	−	2.30813i	−0.0479862	−	0.0897759i	0.856785	−	0.515674i	$-0.172458\pi$
$661$	−1.23372	−	2.30813i	−0.0479862	−	0.0897759i	−0.904771	+	0.425898i	$0.859958\pi$
$662$	42.2043	+	4.24932i	1.64032	+	0.165154i
$663$	−13.1065	−	2.60705i	−0.509016	−	0.101250i
$664$	9.16695	+	17.4222i	0.355747	+	0.676114i
$665$	2.32870	+	11.7072i	0.0903031	+	0.453984i
$666$	0.585480	−	0.710258i	0.0226869	−	0.0275220i
$667$	−0.530965	−	5.39097i	−0.0205590	−	0.208739i
$668$	18.1440	−	12.0098i	0.702011	−	0.464671i
$669$	2.30753	+	7.60691i	0.0892143	+	0.294100i
$670$	17.4989	−	11.6375i	0.676041	−	0.449595i
$671$	3.37027	−	3.37027i	0.130108	−	0.130108i
$672$	1.42632	−	13.0297i	0.0550217	−	0.502632i
$673$	21.9818	+	21.9818i	0.847337	+	0.847337i	0.989800	−	0.142463i	$-0.0455023\pi$
$673$	21.9818	+	21.9818i	0.847337	+	0.847337i	−0.142463	+	0.989800i	$0.545502\pi$
$674$	−2.77101	−	0.557447i	−0.106735	−	0.0214720i
$675$	1.25617	−	0.381056i	0.0483501	−	0.0146668i
$676$	−2.75943	−	14.1945i	−0.106132	−	0.545944i
$677$	−40.7515	+	4.01368i	−1.56621	+	0.154258i	−0.843590	−	0.536988i	$-0.819562\pi$
$677$	−40.7515	+	4.01368i	−1.56621	+	0.154258i	−0.722619	+	0.691246i	$0.757062\pi$
$678$	−0.0315577	−	0.327705i	−0.00121197	−	0.0125854i
$679$	−38.6358	+	7.68514i	−1.48271	+	0.294929i
$680$	−26.5544	−	14.4168i	−1.01831	−	0.552860i
$681$	−3.98842	+	20.0512i	−0.152837	+	0.768362i
$682$	−4.64224	−	5.68170i	−0.177761	−	0.217564i
$683$	−12.1659	+	6.50280i	−0.465515	+	0.248823i	−0.687440	−	0.726241i	$-0.741266\pi$
$683$	−12.1659	+	6.50280i	−0.465515	+	0.248823i	0.221926	+	0.975064i	$0.428766\pi$
$684$	3.42179	−	4.13273i	0.130835	−	0.158019i
$685$	−36.3484	−	3.58001i	−1.38880	−	0.136785i
$686$	28.2828	+	0.0614195i	1.07984	+	0.00234501i
$687$	7.54281	−	18.2100i	0.287776	−	0.694753i
$688$	−5.10834	+	16.3280i	−0.194753	+	0.622498i
$689$	−11.4898	−	27.7389i	−0.437728	−	1.05677i
$690$	−4.21388	−	10.2360i	−0.160420	−	0.389679i
$691$	18.7989	+	22.9065i	0.715145	+	0.871406i	0.996092	−	0.0883169i	$-0.0281488\pi$
$691$	18.7989	+	22.9065i	0.715145	+	0.871406i	−0.280948	+	0.959723i	$0.590649\pi$
$692$	4.30787	−	1.28637i	0.163761	−	0.0489006i
$693$	−0.520358	+	1.71539i	−0.0197668	+	0.0651623i
$694$	−9.91140	−	32.9308i	−0.376231	−	1.25003i
$695$	−20.2279	+	13.5158i	−0.767286	+	0.512684i
$696$	3.48199	−	1.41578i	0.131985	−	0.0536651i
$697$	30.5335	−	45.6966i	1.15654	−	1.73088i
$698$	−15.1189	−	28.4338i	−0.572259	−	1.07624i
$699$	12.2792	+	10.0773i	0.464444	+	0.381159i
$700$	0.0264213	−	6.08327i	0.000998631	−	0.229926i
$701$	−8.50790	+	15.9172i	−0.321339	+	0.601183i	−0.989783	−	0.142579i	$-0.954460\pi$
$701$	−8.50790	+	15.9172i	−0.321339	+	0.601183i	0.668445	+	0.743762i	$0.266960\pi$
$702$	1.89341	−	2.82041i	0.0714622	−	0.106450i
$703$		−	1.74610i		−	0.0658553i
$704$	−3.98827	+	4.73261i	−0.150314	+	0.178367i
$705$		−	7.81059i		−	0.294164i
$706$	−14.0008	−	9.39907i	−0.526926	−	0.353739i
$707$	−14.3901	+	26.9220i	−0.541196	+	1.01251i
$708$	−0.992616	−	1.00128i	−0.0373048	−	0.0376303i
$709$	−11.8669	−	9.73892i	−0.445671	−	0.365753i	0.384627	−	0.923072i	$-0.374330\pi$
$709$	−11.8669	−	9.73892i	−0.445671	−	0.365753i	−0.830298	+	0.557319i	$0.811830\pi$
$710$	9.53342	−	5.06913i	0.357783	−	0.190241i
$711$	−3.19189	+	4.77699i	−0.119705	+	0.179151i
$712$	−9.43450	−	9.55824i	−0.353573	−	0.358210i
$713$	−22.7289	+	15.1869i	−0.851203	+	0.568755i
$714$	17.4567	−	5.25407i	0.653301	−	0.196629i
$715$	1.03584	−	3.41471i	0.0387382	−	0.127703i
$716$	23.6640	+	12.7811i	0.884367	+	0.477654i
$717$	−7.68073	−	9.35899i	−0.286842	−	0.349518i
$718$	12.4723	−	5.13448i	0.465461	−	0.191617i
$719$	5.20479	+	12.5655i	0.194106	+	0.468613i	0.990727	−	0.135866i	$-0.0433815\pi$
$719$	5.20479	+	12.5655i	0.194106	+	0.468613i	−0.796621	+	0.604479i	$0.793382\pi$
$720$	5.97955	−	4.82098i	0.222845	−	0.179667i
$721$	3.01548	−	7.28002i	0.112303	−	0.271122i
$722$	−0.0362485	+	16.6919i	−0.00134903	+	0.621208i
$723$	1.35109	+	0.133070i	0.0502474	+	0.00494894i
$724$	−1.48334	−	15.7621i	−0.0551277	−	0.585793i
$725$	1.53851	−	0.822352i	0.0571389	−	0.0305414i
$726$	−11.3912	+	9.30717i	−0.422766	+	0.345422i
$727$	5.49311	−	27.6157i	0.203728	−	1.02421i	−0.734609	−	0.678491i	$-0.762634\pi$
$727$	5.49311	−	27.6157i	0.203728	−	1.02421i	0.938337	−	0.345721i	$-0.112366\pi$
$728$	−9.90747	−	12.2339i	−0.367195	−	0.453420i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−34.7379	+	3.34523i	−1.28571	+	0.123813i
$731$	−23.6802	+	2.33229i	−0.875843	+	0.0862630i
$732$	6.89013	−	10.2155i	0.254666	−	0.377575i
$733$	−2.02255	+	0.613535i	−0.0747047	+	0.0226614i	−0.327416	−	0.944880i	$-0.606178\pi$
$733$	−2.02255	+	0.613535i	−0.0747047	+	0.0226614i	0.252711	+	0.967542i	$0.418678\pi$
$734$	8.44872	−	41.9977i	0.311848	−	1.55016i
$735$	2.21459	+	2.21459i	0.0816863	+	0.0816863i
$736$	16.1269	+	16.4809i	0.594444	+	0.607495i
$737$	4.23333	−	4.23333i	0.155937	−	0.155937i
$738$	7.73652	+	11.6331i	0.284785	+	0.428221i
$739$	13.9553	+	46.0044i	0.513353	+	1.69230i	0.703628	+	0.710568i	$0.251562\pi$
$739$	13.9553	+	46.0044i	0.513353	+	1.69230i	−0.190275	+	0.981731i	$0.560938\pi$
$740$	0.498297	−	2.44946i	0.0183178	−	0.0900440i
$741$	−0.631628	−	6.41303i	−0.0232034	−	0.235588i
$742$	31.6055	+	26.0530i	1.16027	+	0.956437i
$743$	−3.56605	−	17.9277i	−0.130826	−	0.657705i	−0.989424	−	0.145055i	$-0.953664\pi$
$743$	−3.56605	−	17.9277i	−0.130826	−	0.657705i	0.858598	−	0.512650i	$-0.171336\pi$
$744$	−14.5837	−	12.1284i	−0.534664	−	0.444648i
$745$	13.6564	+	2.71643i	0.500333	+	0.0995224i
$746$	1.10047	−	10.9299i	0.0402912	−	0.400172i
$747$	−3.28107	−	6.13845i	−0.120048	−	0.224594i
$748$	−8.22623	−	2.53447i	−0.300781	−	0.0926693i
$749$	0.530919	−	5.39051i	0.0193994	−	0.196965i
$750$	12.1482	−	12.0955i	0.443588	−	0.441666i
$751$	22.8622	+	9.46982i	0.834252	+	0.345559i	0.758585	−	0.651575i	$-0.225891\pi$
$751$	22.8622	+	9.46982i	0.834252	+	0.345559i	0.0756676	+	0.997133i	$0.475891\pi$
$752$	6.09548	+	15.0851i	0.222279	+	0.550097i
$753$	19.7719	−	8.18980i	0.720529	−	0.298453i
$754$	1.73666	−	4.16704i	0.0632453	−	0.151755i
$755$	28.3810	−	23.2917i	1.03289	−	0.847671i
$756$	−0.474259	+	4.60989i	−0.0172486	+	0.167660i
$757$	32.8521	+	9.96557i	1.19403	+	0.362205i	0.823878	−	0.566767i	$-0.191806\pi$
$757$	32.8521	+	9.96557i	1.19403	+	0.362205i	0.370151	+	0.928972i	$0.379306\pi$
$758$	−6.23112	−	3.34802i	−0.226325	−	0.121606i
$759$	−1.75197	−	2.62201i	−0.0635926	−	0.0951730i
$760$	2.93561	−	14.2718i	0.106486	−	0.517691i
$761$	38.7401	+	25.8853i	1.40433	+	0.938342i	0.999715	+	0.0238530i	$0.00759338\pi$
$761$	38.7401	+	25.8853i	1.40433	+	0.938342i	0.404612	+	0.914489i	$0.367407\pi$
$762$	−8.24463	+	26.9679i	−0.298672	+	0.976946i
$763$	−7.35014	+	8.95617i	−0.266093	+	0.324235i
$764$	−8.69535	−	21.2531i	−0.314587	−	0.768908i
$765$	9.42140	+	5.03584i	0.340631	+	0.182071i
$766$	−6.08418	−	30.9382i	−0.219830	−	1.11784i
$767$	−1.69334			−0.0611429
$768$	−7.78634	+	13.9776i	−0.280965	+	0.504373i
$769$	−50.9128			−1.83596			−0.917982	−	0.396623i	$-0.870182\pi$
$769$	−50.9128			−1.83596			−0.917982	+	0.396623i	$0.870182\pi$
$770$	0.939323	+	4.77648i	0.0338508	+	0.172132i
$771$	−18.7306	−	10.0117i	−0.674568	−	0.360564i
$772$	−12.8226	−	31.3409i	−0.461497	−	1.12798i
$773$	−5.93005	+	7.22579i	−0.213289	+	0.259894i	−0.868654	−	0.495418i	$-0.835015\pi$
$773$	−5.93005	+	7.22579i	−0.213289	+	0.259894i	0.655365	+	0.755312i	$0.272515\pi$
$774$	1.76842	−	5.78446i	0.0635646	−	0.207918i
$775$	−7.31957	−	4.89078i	−0.262927	−	0.175682i
$776$	47.0995	+	9.68807i	1.69077	+	0.347781i
$777$	0.837872	+	1.25396i	0.0300585	+	0.0449857i
$778$	−20.8093	−	11.1810i	−0.746051	−	0.400858i
$779$	25.3611	+	7.69320i	0.908654	+	0.275637i
$780$	0.944075	−	9.17658i	0.0338033	−	0.328574i
$781$	2.37773	−	1.95136i	0.0850820	−	0.0698250i
$782$	−12.3371	+	29.6024i	−0.441173	+	1.05858i
$783$	−1.22778	+	0.508565i	−0.0438774	+	0.0181746i
$784$	−6.00547	−	2.54889i	−0.214481	−	0.0910317i
$785$	−20.9431	−	8.67491i	−0.747491	−	0.309621i
$786$	−21.8569	+	21.7622i	−0.779610	+	0.776231i
$787$	−3.53873	+	35.9293i	−0.126142	+	1.28074i	0.698715	+	0.715400i	$0.253756\pi$
$787$	−3.53873	+	35.9293i	−0.126142	+	1.28074i	−0.824857	+	0.565341i	$0.808744\pi$
$788$	−30.6628	−	9.44709i	−1.09232	−	0.336539i
$789$	−9.87755	−	18.4796i	−0.351650	−	0.657891i
$790$	−1.56297	+	15.5234i	−0.0556080	+	0.552299i
$791$	0.529046	+	0.105234i	0.0188107	+	0.00374168i
$792$	1.39914	−	1.68238i	0.0497161	−	0.0597808i
$793$	−2.88714	−	14.5146i	−0.102525	−	0.515429i
$794$	28.9311	+	23.8485i	1.02673	+	0.846351i
$795$	2.35260	+	23.8863i	0.0834381	+	0.847161i
$796$	−3.88406	+	19.0927i	−0.137667	+	0.676724i
$797$	1.56653	+	5.16415i	0.0554893	+	0.182924i	0.980304	−	0.197494i	$-0.0632803\pi$
$797$	1.56653	+	5.16415i	0.0554893	+	0.182924i	−0.924815	+	0.380418i	$0.875780\pi$
$798$	4.86813	+	7.32004i	0.172330	+	0.259126i
$799$	−16.0009	+	16.0009i	−0.566072	+	0.566072i
$800$	−2.91603	+	6.82923i	−0.103097	+	0.241450i
$801$	3.35755	+	3.35755i	0.118633	+	0.118633i
$802$	2.95348	−	14.6814i	0.104291	−	0.518419i
$803$	−9.51382	+	2.88599i	−0.335735	+	0.101844i
$804$	8.65455	−	12.8315i	0.305222	−	0.452530i
$805$	18.0494	−	1.77771i	0.636156	−	0.0626559i
$806$	−22.6761	+	2.18369i	−0.798731	+	0.0769171i
$807$	−24.1206	+	4.79789i	−0.849087	+	0.168894i
$808$	28.9579	−	23.4511i	1.01874	−	0.825008i
$809$	2.66522	−	13.3990i	0.0937041	−	0.471082i	−0.905230	−	0.424922i	$-0.860302\pi$
$809$	2.66522	−	13.3990i	0.0937041	−	0.471082i	0.998934	−	0.0461603i	$-0.0146985\pi$
$810$	−2.10294	+	1.71821i	−0.0738898	+	0.0603717i
$811$	−42.1506	+	22.5300i	−1.48011	+	0.791134i	−0.996455	−	0.0841264i	$-0.973190\pi$
$811$	−42.1506	+	22.5300i	−1.48011	+	0.791134i	−0.483652	+	0.875260i	$0.660690\pi$
$812$	0.577025	+	6.13153i	0.0202496	+	0.215174i
$813$	−30.0066	−	2.95539i	−1.05238	−	0.103650i
$814$	0.00154640	−	0.712094i	5.42013e−5	−	0.0249589i
$815$	3.63275	−	8.77023i	0.127250	−	0.307208i
$816$	−22.1262	−	2.37347i	−0.774572	−	0.0830882i
$817$	−4.39103	−	10.6009i	−0.153623	−	0.370878i
$818$	4.25818	−	1.75297i	0.148884	−	0.0612913i
$819$	3.53092	+	4.30244i	0.123380	+	0.150339i
$820$	33.3816	+	18.0297i	1.16574	+	0.629623i
$821$	2.36970	−	7.81186i	0.0827031	−	0.272636i	−0.905830	−	0.423642i	$-0.860751\pi$
$821$	2.36970	−	7.81186i	0.0827031	−	0.272636i	0.988533	+	0.151006i	$0.0482514\pi$
$822$	−25.7580	+	7.75256i	−0.898413	+	0.270402i
$823$	−16.2051	+	10.8279i	−0.564874	+	0.377437i	−0.804973	−	0.593312i	$-0.797820\pi$
$823$	−16.2051	+	10.8279i	−0.564874	+	0.377437i	0.240099	+	0.970748i	$0.422820\pi$
$824$	−6.84560	+	6.75698i	−0.238478	+	0.235391i
$825$	0.564202	−	0.844389i	0.0196430	−	0.0293978i
$826$	2.03965	−	1.08453i	0.0709684	−	0.0377355i
$827$	−5.77689	−	4.74097i	−0.200882	−	0.164860i	0.528574	−	0.848887i	$-0.322727\pi$
$827$	−5.77689	−	4.74097i	−0.200882	−	0.164860i	−0.729456	+	0.684027i	$0.760227\pi$
$828$	−5.73955	−	5.78962i	−0.199463	−	0.201203i
$829$	17.6403	−	33.0027i	0.612673	−	1.14623i	−0.363980	−	0.931407i	$-0.618582\pi$
$829$	17.6403	−	33.0027i	0.612673	−	1.14623i	0.976653	−	0.214824i	$-0.0689178\pi$
$830$	−15.6932	−	10.5353i	−0.544721	−	0.365684i
$831$			4.58155i			0.158932i
$832$	5.33817	+	18.4601i	0.185068	+	0.639989i
$833$		−	9.07371i		−	0.314385i
$834$	−9.98645	+	14.8757i	−0.345802	+	0.515105i
$835$	−9.84787	+	18.4241i	−0.340800	+	0.637591i
$836$	0.0180281	−	4.15082i	0.000623516	−	0.143559i
$837$	5.18394	+	4.25435i	0.179183	+	0.147052i
$838$	−14.0372	−	26.3995i	−0.484907	−	0.911955i
$839$	10.4109	−	15.5810i	0.359424	−	0.537916i	−0.607055	−	0.794659i	$-0.707649\pi$
$839$	10.4109	−	15.5810i	0.359424	−	0.537916i	0.966480	+	0.256743i	$0.0826494\pi$
$840$	4.74014	+	11.6580i	0.163550	+	0.402238i
$841$	22.6442	−	15.1303i	0.780833	−	0.521736i
$842$	−6.59507	−	21.9122i	−0.227281	−	0.755145i
$843$	3.30734	−	10.9028i	0.113911	−	0.375513i
$844$	−38.9640	+	11.6351i	−1.34120	+	0.400495i
$845$	8.80763	+	10.7321i	0.302992	+	0.369197i
$846$	−2.18978	−	5.31923i	−0.0752861	−	0.182879i
$847$	−9.22322	−	22.2668i	−0.316914	−	0.765097i
$848$	−23.1849	−	44.2972i	−0.796173	−	1.52117i
$849$	−4.58191	+	11.0617i	−0.157251	+	0.379637i
$850$	−10.3278	−	0.0224282i	−0.354242	−	0.000769281i
$851$	−2.64029	−	0.260046i	−0.0905081	−	0.00891427i
$852$	5.07135	−	6.12501i	0.173742	−	0.209840i
$853$	26.8976	−	14.3770i	0.920955	−	0.492261i	0.0584390	−	0.998291i	$-0.481388\pi$
$853$	26.8976	−	14.3770i	0.920955	−	0.492261i	0.862516	+	0.506030i	$0.168888\pi$
$854$	12.7737	+	15.6339i	0.437108	+	0.534982i
$855$	−1.00500	+	5.05248i	−0.0343703	+	0.172791i
$856$	−3.15474	+	5.81073i	−0.107827	+	0.198607i
$857$	37.0168	−	7.36310i	1.26447	−	0.251519i	0.483088	−	0.875572i	$-0.339515\pi$
$857$	37.0168	−	7.36310i	1.26447	−	0.251519i	0.781382	+	0.624053i	$0.214515\pi$
$858$	−0.251911	−	2.61592i	−0.00860011	−	0.0893061i
$859$	−38.0370	+	3.74632i	−1.29781	+	0.127823i	−0.723218	−	0.690620i	$-0.757338\pi$
$859$	−38.0370	+	3.74632i	−1.29781	+	0.127823i	−0.574588	+	0.818443i	$0.694838\pi$
$860$	−3.13457	−	16.1242i	−0.106888	−	0.549832i
$861$	−21.9047	+	6.64473i	−0.746511	+	0.226452i
$862$	48.7839	+	9.81390i	1.66159	+	0.334263i
$863$	12.5928	+	12.5928i	0.428663	+	0.428663i	0.888173	−	0.459510i	$-0.151975\pi$
$863$	12.5928	+	12.5928i	0.428663	+	0.428663i	−0.459510	+	0.888173i	$0.651975\pi$
$864$	2.72063	−	4.95965i	0.0925579	−	0.168731i
$865$	−3.05225	+	3.05225i	−0.103780	+	0.103780i
$866$	−16.6501	+	11.0730i	−0.565794	+	0.376277i
$867$	−4.04951	−	13.3494i	−0.137528	−	0.453370i
$868$	25.9150	−	17.1535i	0.879614	−	0.582229i
$869$	0.435654	+	4.42327i	0.0147786	+	0.150049i
$870$	−2.29552	+	2.78475i	−0.0778254	+	0.0944117i
$871$	−3.62647	−	18.2315i	−0.122878	−	0.617751i
$872$	12.5160	−	6.58547i	0.423845	−	0.223012i
$873$	−16.6741	−	3.31669i	−0.564334	−	0.112253i
$874$	−15.3871	−	1.54925i	−0.520478	−	0.0524041i
$875$	13.2404	+	24.7711i	0.447609	+	0.837417i
$876$	−22.7196	+	12.0173i	−0.767625	+	0.406028i
$877$	−2.22192	+	22.5595i	−0.0750288	+	0.761781i	0.881896	+	0.471444i	$0.156267\pi$
$877$	−2.22192	+	22.5595i	−0.0750288	+	0.761781i	−0.956925	+	0.290336i	$0.906233\pi$
$878$	18.8047	+	18.8866i	0.634628	+	0.637390i
$879$	23.6060	+	9.77793i	0.796211	+	0.329802i
$880$	1.20984	−	5.81771i	0.0407838	−	0.196115i
$881$	37.5686	−	15.5614i	1.26572	−	0.524278i	0.354059	−	0.935223i	$-0.384801\pi$
$881$	37.5686	−	15.5614i	1.26572	−	0.524278i	0.911660	+	0.410945i	$0.134801\pi$
$882$	2.12908	+	0.887316i	0.0716899	+	0.0298775i
$883$	−15.3710	+	12.6146i	−0.517274	+	0.424516i	−0.856468	−	0.516201i	$-0.827346\pi$
$883$	−15.3710	+	12.6146i	−0.517274	+	0.424516i	0.339194	+	0.940717i	$0.389846\pi$
$884$	−20.7334	+	16.8653i	−0.697340	+	0.567241i
$885$	1.29539	+	0.392952i	0.0435440	+	0.0132089i
$886$	−9.31410	+	17.3348i	−0.312913	+	0.582374i
$887$	18.0026	+	26.9428i	0.604469	+	0.904652i	0.999904	−	0.0138417i	$-0.00440608\pi$
$887$	18.0026	+	26.9428i	0.604469	+	0.904652i	−0.395435	+	0.918494i	$0.629406\pi$
$888$	−0.347377	−	1.80786i	−0.0116572	−	0.0606677i
$889$	−38.4174	−	25.6697i	−1.28848	−	0.860934i
$890$	12.3312	+	3.76988i	0.413341	+	0.126367i
$891$	−0.490784	+	0.598022i	−0.0164419	+	0.0200345i
$892$	14.6616	+	6.14779i	0.490908	+	0.205843i
$893$	−9.62355	−	5.14390i	−0.322040	−	0.172134i
$894$	10.0620	−	1.97875i	0.336524	−	0.0661793i
$895$	−25.8224			−0.863149
$896$	−18.2530	−	18.8165i	−0.609789	−	0.628616i
$897$	−9.79129			−0.326922
$898$	54.5079	−	10.7193i	1.81895	−	0.357707i
$899$	7.85979	+	4.20114i	0.262139	+	0.140116i
$900$	1.01522	−	2.42116i	0.0338407	−	0.0807054i
$901$	44.1145	−	53.7537i	1.46967	−	1.79079i
$902$	10.3359	+	3.15990i	0.344149	+	0.105213i
$903$	8.24030	+	5.50599i	0.274220	+	0.183228i
$904$	−0.545080	−	0.369370i	−0.0181291	−	0.0122851i
$905$	8.44484	+	12.6386i	0.280716	+	0.420121i
$906$	12.7982	−	23.8192i	0.425192	−	0.791340i
$907$	−55.4620	−	16.8242i	−1.84159	−	0.558639i	−0.999823	−	0.0187906i	$-0.994018\pi$
$907$	−55.4620	−	16.8242i	−1.84159	−	0.558639i	−0.841762	−	0.539848i	$-0.818482\pi$
$908$	25.8015	+	31.7192i	0.856254	+	1.05264i
$909$	−10.1839	+	8.35775i	−0.337780	+	0.277209i
$910$	13.9516	+	5.81445i	0.462489	+	0.192747i
$911$	−1.80894	+	0.749287i	−0.0599328	+	0.0248250i	−0.412448	−	0.910981i	$-0.635326\pi$
$911$	−1.80894	+	0.749287i	−0.0599328	+	0.0248250i	0.352516	+	0.935806i	$0.385326\pi$
$912$	−2.00200	−	10.5425i	−0.0662927	−	0.349097i
$913$	−4.97480	−	2.06063i	−0.164642	−	0.0681969i
$914$	3.50504	+	3.52030i	0.115936	+	0.116441i
$915$	−1.15959	+	11.7735i	−0.0383349	+	0.389221i
$916$	−18.4316	−	34.8463i	−0.608997	−	1.15135i
$917$	−23.8222	−	44.5681i	−0.786677	−	1.47177i
$918$	7.82809	+	0.788168i	0.258366	+	0.0260134i
$919$	−39.5365	−	7.86430i	−1.30419	−	0.259419i	−0.506370	−	0.862316i	$-0.669013\pi$
$919$	−39.5365	−	7.86430i	−1.30419	−	0.259419i	−0.797819	+	0.602897i	$0.794013\pi$
$920$	−21.1433	−	6.56447i	−0.697074	−	0.216424i
$921$	0.496526	+	2.49621i	0.0163611	+	0.0822528i
$922$	25.4325	−	30.8527i	0.837574	−	1.01608i
$923$	−0.936120	−	9.50459i	−0.0308128	−	0.312847i
$924$	1.97884	+	2.98957i	0.0650991	+	0.0983497i
$925$	−0.248016	−	0.817601i	−0.00815473	−	0.0268825i
$926$	−22.0084	+	14.6365i	−0.723242	+	0.480986i
$927$	2.40467	−	2.40467i	0.0789798	−	0.0789798i
$928$	2.26024	−	7.16982i	0.0741960	−	0.235361i
$929$	−25.1159	−	25.1159i	−0.824025	−	0.824025i	0.162657	−	0.986683i	$-0.447993\pi$
$929$	−25.1159	−	25.1159i	−0.824025	−	0.824025i	−0.986683	+	0.162657i	$0.947993\pi$
$930$	17.8537	+	3.59165i	0.585447	+	0.117775i
$931$	4.18711	−	1.27015i	0.137227	−	0.0416274i
$932$	31.1861	−	6.06262i	1.02154	−	0.198588i
$933$	−12.7103	+	1.25186i	−0.416117	+	0.0409840i
$934$	0.213504	+	2.21709i	0.00698608	+	0.0725455i
$935$	8.10571	−	1.61233i	0.265085	−	0.0527287i
$936$	−1.92981	−	6.51420i	−0.0630777	−	0.212923i
$937$	0.485245	−	2.43949i	0.0158523	−	0.0796948i	−0.972049	−	0.234777i	$-0.924564\pi$
$937$	0.485245	−	2.43949i	0.0158523	−	0.0796948i	0.987902	+	0.155082i	$0.0495641\pi$
$938$	16.0448	+	19.6374i	0.523881	+	0.641185i
$939$	−20.7504	+	11.0913i	−0.677164	+	0.361952i
$940$	−12.0322	−	9.96232i	−0.392446	−	0.324935i
$941$	58.9728	+	5.80831i	1.92246	+	0.189346i	0.986615	−	0.163070i	$-0.0521395\pi$
$941$	58.9728	+	5.80831i	1.92246	+	0.189346i	0.935844	+	0.352415i	$0.114639\pi$
$942$	−16.6949	−	0.0362552i	−0.543951	−	0.00118126i
$943$	15.4100	−	37.2030i	0.501819	−	1.21150i
$944$	−2.80853	+	0.252004i	−0.0914099	+	0.00820202i
$945$	−1.70271	−	4.11071i	−0.0553892	−	0.133721i
$946$	−1.78136	−	4.32714i	−0.0579171	−	0.140688i
$947$	3.10136	+	3.77902i	0.100781	+	0.122802i	0.820958	−	0.570988i	$-0.193440\pi$
$947$	3.10136	+	3.77902i	0.100781	+	0.122802i	−0.720178	+	0.693790i	$0.755940\pi$
$948$	3.28772	+	11.0101i	0.106780	+	0.357591i
$949$	−8.96078	+	29.5397i	−0.290879	+	0.958900i
$950$	−1.43535	−	4.76898i	−0.0465690	−	0.154726i
$951$	7.88228	−	5.26677i	0.255600	−	0.170787i
$952$	14.1720	−	33.5935i	0.459317	−	1.08877i
$953$	6.34935	−	9.50247i	0.205676	−	0.307815i	−0.714263	−	0.699877i	$-0.753238\pi$
$953$	6.34935	−	9.50247i	0.205676	−	0.307815i	0.919939	+	0.392062i	$0.128238\pi$
$954$	8.29897	+	15.6077i	0.268689	+	0.505318i
$955$	17.0427	+	13.9866i	0.551490	+	0.452596i
$956$	−24.2142	−	0.105169i	−0.783142	−	0.00340140i
$957$	−0.484646	+	0.906709i	−0.0156664	+	0.0293097i
$958$	−12.0507	+	17.9506i	−0.389339	+	0.579957i
$959$		−	44.0731i		−	1.42320i
$960$	0.200155	−	15.3606i	0.00645999	−	0.495760i
$961$		−	13.9727i		−	0.450731i
$962$	−1.83571	−	1.23236i	−0.0591857	−	0.0397328i
$963$	1.10196	−	2.06162i	0.0355102	−	0.0664349i
$964$	1.92829	−	1.91161i	0.0621060	−	0.0615689i
$965$	25.1321	+	20.6254i	0.809032	+	0.663955i
$966$	11.7937	−	6.27099i	0.379457	−	0.201766i
$967$	9.23122	−	13.8155i	0.296856	−	0.444276i	−0.652819	−	0.757514i	$-0.726414\pi$
$967$	9.23122	−	13.8155i	0.296856	−	0.444276i	0.949675	+	0.313238i	$0.101414\pi$
$968$	−0.191665	+	29.4193i	−0.00616035	+	0.945571i
$969$	12.4095	−	8.29176i	0.398650	−	0.266370i
$970$	−44.2088	+	13.3058i	−1.41946	+	0.427224i
$971$	0.630069	−	2.07706i	0.0202199	−	0.0666560i	−0.946250	−	0.323437i	$-0.895162\pi$
$971$	0.630069	−	2.07706i	0.0202199	−	0.0666560i	0.966470	+	0.256781i	$0.0826618\pi$
$972$	−0.950445	+	1.75973i	−0.0304855	+	0.0564434i
$973$	−18.6232	−	22.6924i	−0.597032	−	0.727486i
$974$	32.6974	−	13.4606i	1.04769	−	0.431305i
$975$	−1.20667	−	2.91315i	−0.0386442	−	0.0932955i
$976$	−6.94862	−	23.6439i	−0.222420	−	0.756824i
$977$	−11.7796	+	28.4384i	−0.376861	+	0.909824i	0.615689	+	0.787989i	$0.288878\pi$
$977$	−11.7796	+	28.4384i	−0.376861	+	0.909824i	−0.992550	+	0.121835i	$0.961122\pi$
$978$	0.0151824	−	6.99126i	0.000485479	−	0.223556i
$979$	3.65571	+	0.360056i	0.116837	+	0.0115074i
$980$	6.23625	−	0.586880i	0.199210	−	0.0187472i
$981$	−4.40981	+	2.35709i	−0.140794	+	0.0752562i
$982$	5.86712	−	4.79374i	0.187227	−	0.152974i
$983$	−0.447080	+	2.24762i	−0.0142596	+	0.0716881i	−0.987260	−	0.159116i	$-0.949136\pi$
$983$	−0.447080	+	2.24762i	−0.0142596	+	0.0716881i	0.973000	+	0.230804i	$0.0741356\pi$
$984$	27.7886	+	2.91986i	0.885869	+	0.0930816i
$985$	30.2136	−	6.00986i	0.962685	−	0.191490i
$986$	10.4075	−	1.00224i	0.331444	−	0.0319178i
$987$	9.37950	−	0.923800i	0.298553	−	0.0294049i
$988$	−10.6849	−	7.20673i	−0.339931	−	0.229277i
$989$	−16.6837	+	5.06094i	−0.530510	+	0.160928i
$990$	−0.414335	+	2.05962i	−0.0131684	+	0.0654589i
$991$	32.1317	+	32.1317i	1.02070	+	1.02070i	0.999781	+	0.0209154i	$0.00665808\pi$
$991$	32.1317	+	32.1317i	1.02070	+	1.02070i	0.0209154	+	0.999781i	$0.493342\pi$
$992$	−37.2850	+	6.99648i	−1.18380	+	0.222139i
$993$	−21.2088	+	21.2088i	−0.673042	+	0.673042i
$994$	7.21494	+	10.8488i	0.228844	+	0.344104i
$995$	−5.43028	−	17.9012i	−0.172151	−	0.567507i
$996$	−13.6412	−	2.77505i	−0.432239	−	0.0879309i
$997$	−2.75907	−	28.0133i	−0.0873806	−	0.887191i	−0.934542	−	0.355854i	$-0.884190\pi$
$997$	−2.75907	−	28.0133i	−0.0873806	−	0.887191i	0.847161	−	0.531336i	$-0.178310\pi$
$998$	7.95238	+	6.55530i	0.251728	+	0.207504i
$999$	0.126978	+	0.638360i	0.00401740	+	0.0201968i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.109.19	✓	512
128.101	even	32	inner	384.2.v.a.229.19	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.19	✓	512	1.1	even	1	trivial
384.2.v.a.229.19	yes	512	128.101	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.272887 + 1.38764i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-1.85107 + 0.757334i) q^{4} +(1.21818 - 1.48436i) q^{5} +(0.413462 - 1.35242i) q^{6} +(1.92661 + 1.28732i) q^{7} +(-1.55604 - 2.36194i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.272887 + 1.38764i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-1.85107 + 0.757334i) q^{4} +(1.21818 - 1.48436i) q^{5} +(0.413462 - 1.35242i) q^{6} +(1.92661 + 1.28732i) q^{7} +(-1.55604 - 2.36194i) q^{8} +(0.555570 + 0.831470i) q^{9} +(2.39218 + 1.28533i) q^{10} +(0.740315 + 0.224572i) q^{11} +(1.98950 + 0.204677i) q^{12} +(1.85681 - 1.52385i) q^{13} +(-1.26058 + 3.02472i) q^{14} +(-1.77407 + 0.734842i) q^{15} +(2.85289 - 2.80375i) q^{16} +(5.13980 + 2.12898i) q^{17} +(-1.00217 + 0.997826i) q^{18} +(-0.262953 + 2.66981i) q^{19} +(-1.13078 + 3.67022i) q^{20} +(-1.09228 - 2.04351i) q^{21} +(-0.109602 + 1.08857i) q^{22} +(3.99789 + 0.795230i) q^{23} +(0.258891 + 2.81655i) q^{24} +(0.256095 + 1.28747i) q^{25} +(2.62124 + 2.16074i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(-4.54121 - 0.923824i) q^{28} +(-0.385772 - 1.27172i) q^{29} +(-1.50381 - 2.26123i) q^{30} +(-4.74198 + 4.74198i) q^{31} +(4.66910 + 3.19366i) q^{32} +(-0.547037 - 0.547037i) q^{33} +(-1.55166 + 7.71314i) q^{34} +(4.25781 - 1.29159i) q^{35} +(-1.65810 - 1.11835i) q^{36} +(-0.647732 + 0.0637961i) q^{37} +(-3.77648 + 0.363672i) q^{38} +(-2.35590 + 0.468618i) q^{39} +(-5.40151 - 0.567557i) q^{40} +(1.92727 - 9.68903i) q^{41} +(2.53758 - 2.07333i) q^{42} +(-3.77207 + 2.01621i) q^{43} +(-1.54045 + 0.144968i) q^{44} +(1.91099 + 0.188216i) q^{45} +(-0.0125186 + 5.76462i) q^{46} +(-1.55657 + 3.75789i) q^{47} +(-3.83770 + 1.12785i) q^{48} +(-0.624156 - 1.50685i) q^{49} +(-1.71666 + 0.706700i) q^{50} +(-3.52931 - 4.30048i) q^{51} +(-2.28302 + 4.22697i) q^{52} +(3.62840 - 11.9612i) q^{53} +(1.35421 - 0.407585i) q^{54} +(1.23519 - 0.825325i) q^{55} +(0.0426967 - 6.55364i) q^{56} +(1.49044 - 2.23061i) q^{57} +(1.65941 - 0.882346i) q^{58} +(-0.544937 - 0.447218i) q^{59} +(2.72739 - 2.70380i) q^{60} +(2.90426 - 5.43348i) q^{61} +(-7.87416 - 5.28611i) q^{62} +2.31711i q^{63} +(-3.15751 + 7.35052i) q^{64} -4.61251i q^{65} +(0.609809 - 0.908367i) q^{66} +(3.64798 - 6.82489i) q^{67} +(-11.1265 - 0.0483252i) q^{68} +(-3.15096 - 2.58592i) q^{69} +(2.95416 + 5.55583i) q^{70} +(2.20895 - 3.30592i) q^{71} +(1.09939 - 2.60602i) q^{72} +(-10.6853 + 7.13966i) q^{73} +(-0.265283 - 0.881407i) q^{74} +(0.381056 - 1.25617i) q^{75} +(-1.53519 - 5.14113i) q^{76} +(1.13720 + 1.38568i) q^{77} +(-1.29316 - 3.14125i) q^{78} +(2.19861 + 5.30791i) q^{79} +(-0.686437 - 7.65021i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(13.9708 + 0.0303393i) q^{82} +(-6.92680 - 0.682230i) q^{83} +(3.56950 + 2.95545i) q^{84} +(9.42140 - 5.03584i) q^{85} +(-3.82712 - 4.68406i) q^{86} +(-0.259264 + 1.30341i) q^{87} +(-0.621530 - 2.09802i) q^{88} +(4.65705 - 0.926345i) q^{89} +(0.260308 + 2.70312i) q^{90} +(5.53903 - 0.545546i) q^{91} +(-8.00261 + 1.55572i) q^{92} +(6.41740 - 1.94670i) q^{93} +(-5.63936 - 1.13447i) q^{94} +(3.64264 + 3.64264i) q^{95} +(-2.61230 - 5.01756i) q^{96} +(-12.0214 + 12.0214i) q^{97} +(1.92063 - 1.27730i) q^{98} +(0.224572 + 0.740315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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