LMFDB - Embedded newform 384.2.v.a.229.17

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			229.17
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.192507 - 1.40105i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.92588 - 0.539424i) q^{4} +(-1.13201 - 1.37936i) q^{5} +(-0.490674 - 1.32636i) q^{6} +(-3.27816 + 2.19039i) q^{7} +(-1.12651 + 2.59441i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.192507 - 1.40105i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.92588 - 0.539424i) q^{4} +(-1.13201 - 1.37936i) q^{5} +(-0.490674 - 1.32636i) q^{6} +(-3.27816 + 2.19039i) q^{7} +(-1.12651 + 2.59441i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-2.15047 + 1.32046i) q^{10} +(-3.58120 + 1.08634i) q^{11} +(-1.95276 + 0.432125i) q^{12} +(-5.07386 - 4.16401i) q^{13} +(2.43778 + 5.01453i) q^{14} +(-1.64857 - 0.682859i) q^{15} +(3.41804 + 2.07774i) q^{16} +(3.69412 - 1.53015i) q^{17} +(-1.05798 - 0.938446i) q^{18} +(-0.395943 - 4.02007i) q^{19} +(1.43606 + 3.26711i) q^{20} +(-1.85853 + 3.47707i) q^{21} +(0.832616 + 5.22656i) q^{22} +(4.46479 - 0.888103i) q^{23} +(0.229508 + 2.81910i) q^{24} +(0.354271 - 1.78104i) q^{25} +(-6.81074 + 6.30713i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(7.49489 - 2.45012i) q^{28} +(-0.526952 + 1.73713i) q^{29} +(-1.27408 + 2.17827i) q^{30} +(-0.107098 - 0.107098i) q^{31} +(3.56901 - 4.38887i) q^{32} +(-2.64623 + 2.64623i) q^{33} +(-1.43268 - 5.47021i) q^{34} +(6.73223 + 2.04220i) q^{35} +(-1.51848 + 1.30162i) q^{36} +(-5.97528 - 0.588514i) q^{37} +(-5.70855 - 0.219158i) q^{38} +(-6.43765 - 1.28053i) q^{39} +(4.85384 - 1.38304i) q^{40} +(-0.531807 - 2.67357i) q^{41} +(4.51376 + 3.27325i) q^{42} +(6.31201 + 3.37384i) q^{43} +(7.48296 - 0.160386i) q^{44} +(-1.77580 + 0.174901i) q^{45} +(-0.384771 - 6.42637i) q^{46} +(-2.41492 - 5.83013i) q^{47} +(3.99388 + 0.221145i) q^{48} +(3.26969 - 7.89374i) q^{49} +(-2.42713 - 0.839214i) q^{50} +(2.53661 - 3.09087i) q^{51} +(7.52549 + 10.7564i) q^{52} +(2.32073 + 7.65041i) q^{53} +(-1.37543 - 0.328907i) q^{54} +(5.55240 + 3.71000i) q^{55} +(-1.98992 - 10.9724i) q^{56} +(-2.24424 - 3.35874i) q^{57} +(2.33236 + 1.07269i) q^{58} +(-8.94984 + 7.34494i) q^{59} +(2.80659 + 2.20438i) q^{60} +(-7.19944 - 13.4692i) q^{61} +(-0.170667 + 0.129432i) q^{62} +3.94260i q^{63} +(-5.46197 - 5.84525i) q^{64} +11.7124i q^{65} +(3.19809 + 4.21693i) q^{66} +(-1.25845 - 2.35439i) q^{67} +(-7.93984 + 0.954199i) q^{68} +(3.51895 - 2.88793i) q^{69} +(4.15723 - 9.03906i) q^{70} +(5.92462 + 8.86682i) q^{71} +(1.53132 + 2.37804i) q^{72} +(3.82637 + 2.55670i) q^{73} +(-1.97482 + 8.25838i) q^{74} +(-0.527137 - 1.73774i) q^{75} +(-1.40599 + 7.95577i) q^{76} +(9.36020 - 11.4054i) q^{77} +(-3.03338 + 8.77296i) q^{78} +(-0.938124 + 2.26483i) q^{79} +(-1.00332 - 7.06671i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-3.84819 + 0.230406i) q^{82} +(-2.92711 + 0.288296i) q^{83} +(5.45492 - 5.69388i) q^{84} +(-6.29240 - 3.36336i) q^{85} +(5.94203 - 8.19396i) q^{86} +(0.354146 + 1.78041i) q^{87} +(1.21582 - 10.5149i) q^{88} +(8.98890 + 1.78800i) q^{89} +(-0.0968093 + 2.52166i) q^{90} +(25.7537 + 2.53652i) q^{91} +(-9.07773 - 0.698037i) q^{92} +(-0.144938 - 0.0439663i) q^{93} +(-8.63319 + 2.26108i) q^{94} +(-5.09690 + 5.09690i) q^{95} +(1.07869 - 5.55306i) q^{96} +(-11.0663 - 11.0663i) q^{97} +(-10.4301 - 6.10061i) q^{98} +(-1.08634 + 3.58120i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	0.192507	−	1.40105i	0.136123	−	0.990692i
$2$	0.192507	−	1.40105i	0.136123	−	0.990692i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	−1.92588	−	0.539424i	−0.962941	−	0.269712i
$5$	−1.13201	−	1.37936i	−0.506250	−	0.616867i	0.455687	−	0.890140i	$-0.349394\pi$
$5$	−1.13201	−	1.37936i	−0.506250	−	0.616867i	−0.961936	+	0.273273i	$0.911894\pi$
$6$	−0.490674	−	1.32636i	−0.200317	−	0.541485i
$7$	−3.27816	+	2.19039i	−1.23903	+	0.827891i	−0.990063	−	0.140622i	$-0.955090\pi$
$7$	−3.27816	+	2.19039i	−1.23903	+	0.827891i	−0.248963	+	0.968513i	$0.580090\pi$
$8$	−1.12651	+	2.59441i	−0.398280	+	0.917264i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−2.15047	+	1.32046i	−0.680037	+	0.417568i
$11$	−3.58120	+	1.08634i	−1.07977	+	0.327545i	−0.779560	−	0.626328i	$-0.784557\pi$
$11$	−3.58120	+	1.08634i	−1.07977	+	0.327545i	−0.300211	+	0.953873i	$0.597057\pi$
$12$	−1.95276	+	0.432125i	−0.563713	+	0.124744i
$13$	−5.07386	−	4.16401i	−1.40724	−	1.15489i	−0.966321	−	0.257340i	$-0.917154\pi$
$13$	−5.07386	−	4.16401i	−1.40724	−	1.15489i	−0.440915	−	0.897549i	$-0.645346\pi$
$14$	2.43778	+	5.01453i	0.651525	+	1.34019i
$15$	−1.64857	−	0.682859i	−0.425658	−	0.176313i
$16$	3.41804	+	2.07774i	0.854511	+	0.519434i
$17$	3.69412	−	1.53015i	0.895955	−	0.371117i	0.113292	−	0.993562i	$-0.463861\pi$
$17$	3.69412	−	1.53015i	0.895955	−	0.371117i	0.782664	+	0.622445i	$0.213861\pi$
$18$	−1.05798	−	0.938446i	−0.249368	−	0.221194i
$19$	−0.395943	−	4.02007i	−0.0908355	−	0.922268i	−0.927318	−	0.374275i	$-0.877892\pi$
$19$	−0.395943	−	4.02007i	−0.0908355	−	0.922268i	0.836482	−	0.547994i	$-0.184608\pi$
$20$	1.43606	+	3.26711i	0.321112	+	0.730548i
$21$	−1.85853	+	3.47707i	−0.405565	+	0.758758i
$22$	0.832616	+	5.22656i	0.177514	+	1.11431i
$23$	4.46479	−	0.888103i	0.930974	−	0.185182i	0.293769	−	0.955877i	$-0.405090\pi$
$23$	4.46479	−	0.888103i	0.930974	−	0.185182i	0.637205	+	0.770694i	$0.280090\pi$
$24$	0.229508	+	2.81910i	0.0468482	+	0.575446i
$25$	0.354271	−	1.78104i	0.0708542	−	0.356208i
$26$	−6.81074	+	6.30713i	−1.33570	+	1.23693i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	7.49489	−	2.45012i	1.41640	−	0.463030i
$29$	−0.526952	+	1.73713i	−0.0978525	+	0.322576i	−0.992176	−	0.124844i	$-0.960157\pi$
$29$	−0.526952	+	1.73713i	−0.0978525	+	0.322576i	0.894324	+	0.447420i	$0.147657\pi$
$30$	−1.27408	+	2.17827i	−0.232614	+	0.397696i
$31$	−0.107098	−	0.107098i	−0.0192353	−	0.0192353i	0.697424	−	0.716659i	$-0.254330\pi$
$31$	−0.107098	−	0.107098i	−0.0192353	−	0.0192353i	−0.716659	+	0.697424i	$0.754330\pi$
$32$	3.56901	−	4.38887i	0.630918	−	0.775850i
$33$	−2.64623	+	2.64623i	−0.460650	+	0.460650i
$34$	−1.43268	−	5.47021i	−0.245702	−	0.938133i
$35$	6.73223	+	2.04220i	1.13796	+	0.345195i
$36$	−1.51848	+	1.30162i	−0.253080	+	0.216937i
$37$	−5.97528	−	0.588514i	−0.982330	−	0.0967511i	−0.405918	−	0.913910i	$-0.633048\pi$
$37$	−5.97528	−	0.588514i	−0.982330	−	0.0967511i	−0.576413	+	0.817159i	$0.695548\pi$
$38$	−5.70855	−	0.219158i	−0.926048	−	0.0355520i
$39$	−6.43765	−	1.28053i	−1.03085	−	0.205049i
$40$	4.85384	−	1.38304i	0.767459	−	0.218679i
$41$	−0.531807	−	2.67357i	−0.0830543	−	0.417542i	−0.999835	−	0.0181517i	$-0.994222\pi$
$41$	−0.531807	−	2.67357i	−0.0830543	−	0.417542i	0.916781	−	0.399390i	$-0.130778\pi$
$42$	4.51376	+	3.27325i	0.696489	+	0.505074i
$43$	6.31201	+	3.37384i	0.962573	+	0.514506i	0.876300	−	0.481766i	$-0.160004\pi$
$43$	6.31201	+	3.37384i	0.962573	+	0.514506i	0.0862727	+	0.996272i	$0.472504\pi$
$44$	7.48296	−	0.160386i	1.12810	−	0.0241791i
$45$	−1.77580	+	0.174901i	−0.264721	+	0.0260728i
$46$	−0.384771	−	6.42637i	−0.0567315	−	0.947516i
$47$	−2.41492	−	5.83013i	−0.352252	−	0.850411i	−0.996341	−	0.0854612i	$-0.972764\pi$
$47$	−2.41492	−	5.83013i	−0.352252	−	0.850411i	0.644090	−	0.764950i	$-0.277236\pi$
$48$	3.99388	+	0.221145i	0.576467	+	0.0319195i
$49$	3.26969	−	7.89374i	0.467099	−	1.12768i
$50$	−2.42713	−	0.839214i	−0.343247	−	0.118683i
$51$	2.53661	−	3.09087i	0.355197	−	0.432809i
$52$	7.52549	+	10.7564i	1.04360	+	1.49164i
$53$	2.32073	+	7.65041i	0.318776	+	1.05086i	0.959173	+	0.282820i	$0.0912700\pi$
$53$	2.32073	+	7.65041i	0.318776	+	1.05086i	−0.640397	+	0.768044i	$0.721230\pi$
$54$	−1.37543	−	0.328907i	−0.187173	−	0.0447586i
$55$	5.55240	+	3.71000i	0.748686	+	0.500256i
$56$	−1.98992	−	10.9724i	−0.265915	−	1.46625i
$57$	−2.24424	−	3.35874i	−0.297257	−	0.444876i
$58$	2.33236	+	1.07269i	0.306254	+	0.140852i
$59$	−8.94984	+	7.34494i	−1.16517	+	0.956230i	−0.999551	−	0.0299597i	$-0.990462\pi$
$59$	−8.94984	+	7.34494i	−1.16517	+	0.956230i	−0.165619	+	0.986190i	$0.552962\pi$
$60$	2.80659	+	2.20438i	0.362330	+	0.284584i
$61$	−7.19944	−	13.4692i	−0.921794	−	1.72456i	−0.645998	−	0.763339i	$-0.723559\pi$
$61$	−7.19944	−	13.4692i	−0.921794	−	1.72456i	−0.275796	−	0.961216i	$-0.588941\pi$
$62$	−0.170667	+	0.129432i	−0.0216747	+	0.0164379i
$63$			3.94260i			0.496721i
$64$	−5.46197	−	5.84525i	−0.682746	−	0.730656i
$65$			11.7124i			1.45274i
$66$	3.19809	+	4.21693i	0.393657	+	0.519068i
$67$	−1.25845	−	2.35439i	−0.153744	−	0.287635i	0.793244	−	0.608904i	$-0.208391\pi$
$67$	−1.25845	−	2.35439i	−0.153744	−	0.287635i	−0.946988	+	0.321269i	$0.895891\pi$
$68$	−7.93984	+	0.954199i	−0.962847	+	0.115714i
$69$	3.51895	−	2.88793i	0.423632	−	0.347665i
$70$	4.15723	−	9.03906i	0.496884	−	1.08037i
$71$	5.92462	+	8.86682i	0.703123	+	1.05230i	0.995385	+	0.0959594i	$0.0305919\pi$
$71$	5.92462	+	8.86682i	0.703123	+	1.05230i	−0.292263	+	0.956338i	$0.594408\pi$
$72$	1.53132	+	2.37804i	0.180468	+	0.280254i
$73$	3.82637	+	2.55670i	0.447843	+	0.299239i	0.758966	−	0.651131i	$-0.225705\pi$
$73$	3.82637	+	2.55670i	0.447843	+	0.299239i	−0.311123	+	0.950370i	$0.600705\pi$
$74$	−1.97482	+	8.25838i	−0.229568	+	0.960017i
$75$	−0.527137	−	1.73774i	−0.0608686	−	0.200657i
$76$	−1.40599	+	7.95577i	−0.161278	+	0.912589i
$77$	9.36020	−	11.4054i	1.06669	−	1.29977i
$78$	−3.03338	+	8.77296i	−0.343462	+	0.993342i
$79$	−0.938124	+	2.26483i	−0.105547	+	0.254813i	−0.967826	−	0.251620i	$-0.919037\pi$
$79$	−0.938124	+	2.26483i	−0.105547	+	0.254813i	0.862279	+	0.506434i	$0.169037\pi$
$80$	−1.00332	−	7.06671i	−0.112174	−	0.790083i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−3.84819	+	0.230406i	−0.424961	+	0.0254441i
$83$	−2.92711	+	0.288296i	−0.321293	+	0.0316446i	−0.257378	−	0.966311i	$-0.582859\pi$
$83$	−2.92711	+	0.288296i	−0.321293	+	0.0316446i	−0.0639146	+	0.997955i	$0.520359\pi$
$84$	5.45492	−	5.69388i	0.595181	−	0.621253i
$85$	−6.29240	−	3.36336i	−0.682507	−	0.364808i
$86$	5.94203	−	8.19396i	0.640745	−	0.883577i
$87$	0.354146	+	1.78041i	0.0379684	+	0.190880i
$88$	1.21582	−	10.5149i	0.129606	−	1.12089i
$89$	8.98890	+	1.78800i	0.952822	+	0.189528i	0.646940	−	0.762541i	$-0.276049\pi$
$89$	8.98890	+	1.78800i	0.952822	+	0.189528i	0.305882	+	0.952069i	$0.401049\pi$
$90$	−0.0968093	+	2.52166i	−0.0102046	+	0.265806i
$91$	25.7537	+	2.53652i	2.69972	+	0.265900i
$92$	−9.07773	−	0.698037i	−0.946419	−	0.0727754i
$93$	−0.144938	−	0.0439663i	−0.0150293	−	0.00455909i
$94$	−8.63319	+	2.26108i	−0.890445	+	0.233212i
$95$	−5.09690	+	5.09690i	−0.522931	+	0.522931i
$96$	1.07869	−	5.55306i	0.110093	−	0.566756i
$97$	−11.0663	−	11.0663i	−1.12361	−	1.12361i	−0.991194	−	0.132421i	$-0.957725\pi$
$97$	−11.0663	−	11.0663i	−1.12361	−	1.12361i	−0.132421	−	0.991194i	$-0.542275\pi$
$98$	−10.4301	−	6.10061i	−1.05360	−	0.616254i
$99$	−1.08634	+	3.58120i	−0.109182	+	0.359924i
$100$	−1.64302	+	3.23897i	−0.164302	+	0.323897i
$101$	0.497143	−	5.04757i	0.0494675	−	0.502252i	−0.938245	−	0.345971i	$-0.887549\pi$
$101$	0.497143	−	5.04757i	0.0494675	−	0.502252i	0.987713	−	0.156281i	$-0.0499505\pi$
$102$	−3.84215	−	4.14894i	−0.380429	−	0.410806i
$103$	−0.529535	+	2.66215i	−0.0521766	+	0.262310i	−0.998065	−	0.0621833i	$-0.980194\pi$
$103$	−0.529535	+	2.66215i	−0.0521766	+	0.262310i	0.945888	+	0.324493i	$0.105194\pi$
$104$	16.5189	−	8.47291i	1.61981	−	0.830837i
$105$	6.89999	−	1.37249i	0.673370	−	0.133942i
$106$	11.1654	−	1.77870i	1.08448	−	0.172762i
$107$	6.29412	−	11.7755i	0.608475	−	1.13838i	−0.369416	−	0.929264i	$-0.620442\pi$
$107$	6.29412	−	11.7755i	0.608475	−	1.13838i	0.977892	−	0.209113i	$-0.0670576\pi$
$108$	−0.725596	+	1.86374i	−0.0698205	+	0.179338i
$109$	−1.51504	−	15.3824i	−0.145114	−	1.47337i	−0.741651	−	0.670786i	$-0.765957\pi$
$109$	−1.51504	−	15.3824i	−0.145114	−	1.47337i	0.596537	−	0.802586i	$-0.296543\pi$
$110$	6.26677	−	7.06499i	0.597513	−	0.673620i
$111$	−5.54715	+	2.29771i	−0.526512	+	0.218089i
$112$	−15.7559	+	0.675720i	−1.48880	+	0.0638495i
$113$	−5.02863	−	2.08293i	−0.473054	−	0.195945i	0.133403	−	0.991062i	$-0.457410\pi$
$113$	−5.02863	−	2.08293i	−0.473054	−	0.195945i	−0.606457	+	0.795117i	$0.707410\pi$
$114$	−5.13780	+	2.49771i	−0.481199	+	0.233932i
$115$	−6.27919	−	5.15320i	−0.585538	−	0.480539i
$116$	1.95189	−	3.06125i	0.181229	−	0.284230i
$117$	−6.28114	+	1.90536i	−0.580691	+	0.176151i
$118$	8.56772	+	13.9531i	0.788723	+	1.28449i
$119$	−8.75826	+	13.1077i	−0.802868	+	1.20158i
$120$	3.62874	−	3.50782i	0.331257	−	0.320219i
$121$	2.49866	−	1.66955i	0.227151	−	0.151777i
$122$	−20.2570	+	7.49386i	−1.83398	+	0.678462i
$123$	−1.72933	−	2.10719i	−0.155928	−	0.189999i
$124$	0.148487	+	0.264029i	0.0133345	+	0.0237105i
$125$	−10.7262	+	5.73328i	−0.959381	+	0.512800i
$126$	5.52378	+	0.758979i	0.492098	+	0.0676153i
$127$	11.0905			0.984122			0.492061	−	0.870561i	$-0.336244\pi$
$127$	11.0905			0.984122			0.492061	+	0.870561i	$0.336244\pi$
$128$	−9.24095	+	6.52724i	−0.816792	+	0.576932i
$129$	7.15712			0.630149
$130$	16.4096	+	2.25471i	1.43922	+	0.197751i
$131$	7.00203	−	3.74266i	0.611770	−	0.326998i	−0.136250	−	0.990675i	$-0.543505\pi$
$131$	7.00203	−	3.74266i	0.611770	−	0.326998i	0.748020	+	0.663677i	$0.231005\pi$
$132$	6.52378	−	3.66889i	0.567822	−	0.319336i
$133$	10.1035	+	12.3112i	0.876085	+	1.06751i
$134$	−3.54088	+	1.30991i	−0.305886	+	0.113159i
$135$	−1.48367	+	0.991357i	−0.127694	+	0.0853224i
$136$	−0.191596	+	11.3078i	−0.0164292	+	0.969636i
$137$	2.50473	−	3.74859i	0.213994	−	0.320264i	−0.708907	−	0.705302i	$-0.750812\pi$
$137$	2.50473	−	3.74859i	0.213994	−	0.320264i	0.922901	+	0.385038i	$0.125812\pi$
$138$	−3.36871	−	5.48617i	−0.286763	−	0.467014i
$139$	−19.7858	+	6.00195i	−1.67821	+	0.509079i	−0.978657	−	0.205503i	$-0.934117\pi$
$139$	−19.7858	+	6.00195i	−1.67821	+	0.509079i	−0.699552	+	0.714582i	$0.746617\pi$
$140$	−11.8639	−	7.56457i	−1.00268	−	0.639323i
$141$	−4.87807	−	4.00333i	−0.410808	−	0.337141i
$142$	13.5634	−	6.59376i	1.13821	−	0.553336i
$143$	22.6940	+	9.40018i	1.89777	+	0.786083i
$144$	3.62654	−	1.68767i	0.302211	−	0.140639i
$145$	2.99263	−	1.23959i	0.248524	−	0.102942i
$146$	4.31867	−	4.86876i	0.357416	−	0.402941i
$147$	−0.837470	−	8.50298i	−0.0690734	−	0.701314i
$148$	11.1902	+	4.35662i	0.919831	+	0.358112i
$149$	8.46385	−	15.8347i	0.693386	−	1.29723i	−0.250870	−	0.968021i	$-0.580717\pi$
$149$	8.46385	−	15.8347i	0.693386	−	1.29723i	0.944256	−	0.329212i	$-0.106783\pi$
$150$	−2.53614	+	0.404019i	−0.207075	+	0.0329880i
$151$	−14.6594	+	2.91593i	−1.19296	+	0.237295i	−0.751346	−	0.659909i	$-0.770595\pi$
$151$	−14.6594	+	2.91593i	−1.19296	+	0.237295i	−0.441617	+	0.897204i	$0.645595\pi$
$152$	10.8758	+	3.50140i	0.882141	+	0.284001i
$153$	0.780066	−	3.92166i	0.0630646	−	0.317047i
$154$	−14.1777	−	15.3097i	−1.14247	−	1.23369i
$155$	−0.0264904	+	0.268962i	−0.00212776	+	0.0216035i
$156$	11.7074	+	5.93877i	0.937342	+	0.475482i
$157$	−3.20835	+	10.5765i	−0.256054	+	0.844097i	0.730815	+	0.682576i	$0.239140\pi$
$157$	−3.20835	+	10.5765i	−0.256054	+	0.844097i	−0.986869	+	0.161522i	$0.948360\pi$
$158$	2.99255	+	1.75036i	0.238074	+	0.139251i
$159$	5.65308	+	5.65308i	0.448318	+	0.448318i
$160$	−10.0940	+	0.0453035i	−0.797998	+	0.00358155i
$161$	−12.6910	+	12.6910i	−1.00019	+	1.00019i
$162$	−1.36807	+	0.358305i	−0.107486	+	0.0281511i
$163$	16.7374	+	5.07723i	1.31097	+	0.397679i	0.866976	−	0.498350i	$-0.166060\pi$
$163$	16.7374	+	5.07723i	1.31097	+	0.397679i	0.443996	+	0.896029i	$0.353560\pi$
$164$	−0.417993	+	5.43586i	−0.0326398	+	0.424469i
$165$	6.64566	+	0.654540i	0.517364	+	0.0509559i
$166$	−0.159574	+	4.15653i	−0.0123853	+	0.322610i
$167$	−13.9092	−	2.76671i	−1.07632	−	0.214094i	−0.375064	−	0.926999i	$-0.622379\pi$
$167$	−13.9092	−	2.76671i	−1.07632	−	0.214094i	−0.701261	+	0.712905i	$0.747379\pi$
$168$	−6.92730	−	8.73873i	−0.534453	−	0.674208i
$169$	5.86892	+	29.5050i	0.451455	+	2.26962i
$170$	−5.92357	+	8.16850i	−0.454317	+	0.626495i
$171$	−3.56254	−	1.90422i	−0.272434	−	0.145619i
$172$	−10.3363	−	9.90247i	−0.788132	−	0.755056i
$173$	20.7586	−	2.04454i	1.57825	−	0.155444i	0.729402	−	0.684085i	$-0.239798\pi$
$173$	20.7586	−	2.04454i	1.57825	−	0.155444i	0.848846	+	0.528641i	$0.177298\pi$
$174$	2.56262	−	0.153434i	0.194272	−	0.0116318i
$175$	2.73982	+	6.61452i	0.207111	+	0.500010i
$176$	−14.4978	−	3.72761i	−1.09281	−	0.280979i
$177$	−4.43067	+	10.6966i	−0.333030	+	0.804005i
$178$	4.23551	−	12.2497i	0.317465	−	0.918154i
$179$	−3.57652	+	4.35801i	−0.267322	+	0.325733i	−0.889319	−	0.457287i	$-0.848821\pi$
$179$	−3.57652	+	4.35801i	−0.267322	+	0.325733i	0.621998	+	0.783019i	$0.286321\pi$
$180$	3.51433	+	0.621072i	0.261943	+	0.0462920i
$181$	2.50890	+	8.27073i	0.186485	+	0.614759i	0.999472	+	0.0324776i	$0.0103397\pi$
$181$	2.50890	+	8.27073i	0.186485	+	0.614759i	−0.812987	+	0.582281i	$0.802160\pi$
$182$	8.51157	−	35.5940i	0.630920	−	2.63840i
$183$	−12.6987	−	8.48499i	−0.938714	−	0.627228i
$184$	−2.72551	+	12.5840i	−0.200928	+	0.927703i
$185$	5.95230	+	8.90825i	0.437622	+	0.654947i
$186$	−0.0895005	+	0.194601i	−0.00656250	+	0.0142688i
$187$	−11.5671	+	9.49287i	−0.845870	+	0.694187i
$188$	1.50593	+	12.5308i	0.109832	+	0.913902i
$189$	1.85853	+	3.47707i	0.135188	+	0.252919i
$190$	6.15983	+	8.12221i	0.446881	+	0.589247i
$191$			10.8664i			0.786262i	0.919483	+	0.393131i	$0.128608\pi$
$191$			10.8664i			0.786262i	−0.919483	+	0.393131i	$0.871392\pi$
$192$	−7.57246	−	2.58030i	−0.546495	−	0.186217i
$193$			8.62124i			0.620571i	0.950643	+	0.310285i	$0.100425\pi$
$193$			8.62124i			0.620571i	−0.950643	+	0.310285i	$0.899575\pi$
$194$	−17.6348	+	13.3741i	−1.26611	+	0.960206i
$195$	5.52117	+	10.3294i	0.395379	+	0.739702i
$196$	−10.5551	+	13.4387i	−0.753937	+	0.959904i
$197$	−11.8346	+	9.71239i	−0.843179	+	0.691979i	−0.953328	−	0.301936i	$-0.902367\pi$
$197$	−11.8346	+	9.71239i	−0.843179	+	0.691979i	0.110149	+	0.993915i	$0.464867\pi$
$198$	4.80831	+	2.21143i	0.341711	+	0.157159i
$199$	−6.81399	−	10.1979i	−0.483031	−	0.722906i	0.507279	−	0.861782i	$-0.330651\pi$
$199$	−6.81399	−	10.1979i	−0.483031	−	0.722906i	−0.990310	+	0.138875i	$0.955651\pi$
$200$	4.22167	+	2.92548i	0.298517	+	0.206863i
$201$	−2.21971	−	1.48316i	−0.156566	−	0.104614i
$202$	−6.97620	−	1.66822i	−0.490844	−	0.117375i
$203$	−2.07756	−	6.84880i	−0.145816	−	0.480692i
$204$	−6.55251	+	4.58434i	−0.458767	+	0.320968i
$205$	−3.08580	+	3.76006i	−0.215522	+	0.262614i
$206$	3.62787	+	1.25439i	0.252766	+	0.0873974i
$207$	1.74208	−	4.20574i	0.121083	−	0.292319i
$208$	−8.69097	−	24.7749i	−0.602610	−	1.71783i
$209$	5.78513	+	13.9665i	0.400166	+	0.966086i
$210$	−0.594634	−	9.93144i	−0.0410336	−	0.685334i
$211$	1.51118	−	0.148838i	0.104034	−	0.0102464i	−0.0458663	−	0.998948i	$-0.514605\pi$
$211$	1.51118	−	0.148838i	0.104034	−	0.0102464i	0.149900	+	0.988701i	$0.452105\pi$
$212$	−0.342628	−	15.9856i	−0.0235318	−	1.09790i
$213$	9.40483	+	5.02699i	0.644409	+	0.344444i
$214$	−15.2863	−	11.0852i	−1.04495	−	0.757771i
$215$	−2.49152	−	12.5257i	−0.169920	−	0.854248i
$216$	2.47150	+	1.37538i	0.168165	+	0.0935827i
$217$	0.585670	+	0.116497i	0.0397579	+	0.00790833i
$218$	−21.8432	−	0.838586i	−1.47941	−	0.0567962i
$219$	4.57978	+	0.451069i	0.309473	+	0.0304804i
$220$	−8.69201	−	10.1401i	−0.586015	−	0.683646i
$221$	−25.1150	−	7.61856i	−1.68942	−	0.512480i
$222$	2.15133	+	8.21416i	0.144388	+	0.551299i
$223$	2.64866	−	2.64866i	0.177367	−	0.177367i	−0.612840	−	0.790207i	$-0.709973\pi$
$223$	2.64866	−	2.64866i	0.177367	−	0.177367i	0.790207	+	0.612840i	$0.209973\pi$
$224$	−2.08641	+	22.2049i	−0.139404	+	1.48363i
$225$	−1.28406	−	1.28406i	−0.0856039	−	0.0856039i
$226$	−3.88633	+	6.64439i	−0.258515	+	0.441978i
$227$	8.31547	−	27.4124i	0.551917	−	1.81943i	−0.0209530	−	0.999780i	$-0.506670\pi$
$227$	8.31547	−	27.4124i	0.551917	−	1.81943i	0.572870	−	0.819646i	$-0.305830\pi$
$228$	2.51035	+	7.67914i	0.166252	+	0.508563i
$229$	−0.275703	+	2.79926i	−0.0182190	+	0.184980i	−0.999987	−	0.00510269i	$-0.998376\pi$
$229$	−0.275703	+	2.79926i	−0.0182190	+	0.184980i	0.981768	+	0.190083i	$0.0608758\pi$
$230$	−8.42868	+	7.80544i	−0.555771	+	0.514675i
$231$	2.87847	−	14.4711i	0.189390	−	0.952126i
$232$	−3.91321	−	3.32401i	−0.256915	−	0.218232i
$233$	3.85912	−	0.767627i	0.252819	−	0.0502889i	−0.0670534	−	0.997749i	$-0.521360\pi$
$233$	3.85912	−	0.767627i	0.252819	−	0.0502889i	0.319873	+	0.947460i	$0.396360\pi$
$234$	1.46034	+	9.16698i	0.0954656	+	0.599264i
$235$	−5.30811	+	9.93078i	−0.346263	+	0.647813i
$236$	21.1984	−	9.31773i	1.37990	−	0.606533i
$237$	0.240283	+	2.43963i	0.0156080	+	0.158471i
$238$	16.6785	+	14.7941i	1.08110	+	0.958957i
$239$	11.2520	−	4.66072i	0.727830	−	0.301477i	0.0121698	−	0.999926i	$-0.496126\pi$
$239$	11.2520	−	4.66072i	0.727830	−	0.301477i	0.715660	+	0.698449i	$0.246126\pi$
$240$	−4.21607	−	5.75932i	−0.272146	−	0.371763i
$241$	−19.5697	−	8.10603i	−1.26059	−	0.522155i	−0.350502	−	0.936562i	$-0.613989\pi$
$241$	−19.5697	−	8.10603i	−1.26059	−	0.522155i	−0.910092	+	0.414407i	$0.863989\pi$
$242$	−1.85812	−	3.82215i	−0.119444	−	0.245697i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	6.59966	+	29.8237i	0.422500	+	1.90926i
$245$	−14.5896	+	4.42571i	−0.932096	+	0.282748i
$246$	−3.28519	+	2.01722i	−0.209456	+	0.128613i
$247$	−14.7307	+	22.0460i	−0.937290	+	1.40275i
$248$	0.398503	−	0.157210i	0.0253049	−	0.00998283i
$249$	−2.44558	+	1.63409i	−0.154983	+	0.103556i
$250$	5.96774	+	16.1317i	0.377433	+	1.02026i
$251$	8.29909	+	10.1125i	0.523834	+	0.638293i	0.965970	−	0.258655i	$-0.0832791\pi$
$251$	8.29909	+	10.1125i	0.523834	+	0.638293i	−0.442136	+	0.896948i	$0.645779\pi$
$252$	2.12674	−	7.59299i	0.133972	−	0.478313i
$253$	−15.0245	+	8.03077i	−0.944583	+	0.504890i
$254$	2.13500	−	15.5383i	0.133962	−	0.974962i
$255$	−7.13488			−0.446804
$256$	7.36603	+	14.2036i	0.460377	+	0.887723i
$257$	23.5319			1.46788			0.733939	−	0.679215i	$-0.237680\pi$
$257$	23.5319			1.46788			0.733939	+	0.679215i	$0.237680\pi$
$258$	1.37780	−	10.0275i	0.0857778	−	0.624283i
$259$	20.8770	−	11.1590i	1.29723	−	0.693385i
$260$	6.31793	−	22.5566i	0.391822	−	1.39890i
$261$	1.15161	+	1.40324i	0.0712828	+	0.0868584i
$262$	−3.89572	−	10.5307i	−0.240678	−	0.650588i
$263$	14.4694	−	9.66815i	0.892222	−	0.596163i	−0.0227235	−	0.999742i	$-0.507234\pi$
$263$	14.4694	−	9.66815i	0.892222	−	0.596163i	0.914945	+	0.403578i	$0.132234\pi$
$264$	−3.88443	−	9.84643i	−0.239070	−	0.606006i
$265$	7.92556	−	11.8614i	0.486863	−	0.728642i
$266$	19.1935	−	11.7855i	1.17683	−	0.722617i
$267$	8.77036	−	2.66046i	0.536738	−	0.162818i
$268$	1.15361	+	5.21312i	0.0704679	+	0.318442i
$269$	−3.03503	−	2.49079i	−0.185049	−	0.151866i	0.537308	−	0.843386i	$-0.319441\pi$
$269$	−3.03503	−	2.49079i	−0.185049	−	0.151866i	−0.722357	+	0.691520i	$0.756941\pi$
$270$	1.10332	+	2.26954i	0.0671461	+	0.138120i
$271$	−8.82116	−	3.65384i	−0.535847	−	0.221955i	0.0983148	−	0.995155i	$-0.468655\pi$
$271$	−8.82116	−	3.65384i	−0.535847	−	0.221955i	−0.634162	+	0.773200i	$0.718655\pi$
$272$	15.8059	+	2.44527i	0.958374	+	0.148266i
$273$	23.9085	−	9.90321i	1.44701	−	0.599370i
$274$	−4.76979	−	4.23088i	−0.288154	−	0.255597i
$275$	0.666109	+	6.76311i	0.0401679	+	0.407831i
$276$	−8.33490	+	3.66360i	−0.501702	+	0.220523i
$277$	12.6498	−	23.6661i	0.760051	−	1.42196i	−0.141794	−	0.989896i	$-0.545287\pi$
$277$	12.6498	−	23.6661i	0.760051	−	1.42196i	0.901845	−	0.432060i	$-0.142213\pi$
$278$	4.60013	+	28.8763i	0.275897	+	1.73189i
$279$	−0.148549	+	0.0295482i	−0.00889340	+	0.00176901i
$280$	−12.8822	+	15.1656i	−0.769860	+	0.906321i
$281$	−0.412699	+	2.07478i	−0.0246196	+	0.123771i	−0.991141	−	0.132816i	$-0.957598\pi$
$281$	−0.412699	+	2.07478i	−0.0246196	+	0.123771i	0.966521	+	0.256587i	$0.0825980\pi$
$282$	−6.54793	+	6.06375i	−0.389923	+	0.361091i
$283$	−1.35498	+	13.7574i	−0.0805453	+	0.817791i	0.867030	+	0.498257i	$0.166026\pi$
$283$	−1.35498	+	13.7574i	−0.0805453	+	0.817791i	−0.947575	+	0.319534i	$0.896474\pi$
$284$	−6.62714	−	20.2723i	−0.393248	−	1.20294i
$285$	−2.09240	+	6.89773i	−0.123943	+	0.408586i
$286$	17.5389	−	29.9859i	1.03710	−	1.77310i
$287$	7.59952	+	7.59952i	0.448586	+	0.448586i
$288$	−1.66638	−	5.40585i	−0.0981922	−	0.318543i
$289$	−0.715671	+	0.715671i	−0.0420983	+	0.0420983i
$290$	−1.16062	−	4.43145i	−0.0681541	−	0.260224i
$291$	−14.9763	−	4.54300i	−0.877923	−	0.266315i
$292$	−5.99000	−	6.98794i	−0.350538	−	0.408938i
$293$	24.5945	+	2.42235i	1.43683	+	0.141515i	0.786241	−	0.617919i	$-0.212024\pi$
$293$	24.5945	+	2.42235i	1.43683	+	0.141515i	0.650584	+	0.759434i	$0.274524\pi$
$294$	−12.0743	−	0.463547i	−0.704189	−	0.0270346i
$295$	20.2626	+	4.03048i	1.17973	+	0.234664i
$296$	8.25804	−	14.8394i	0.479989	−	0.862522i
$297$	0.730094	+	3.67043i	0.0423644	+	0.212980i
$298$	−20.5559	−	14.9066i	−1.19077	−	0.863515i
$299$	−26.3518	−	14.0853i	−1.52396	−	0.814576i
$300$	0.0778257	+	3.63103i	0.00449327	+	0.209638i
$301$	−28.0818	+	2.76582i	−1.61861	+	0.159419i
$302$	1.26333	+	21.0998i	0.0726965	+	1.21416i
$303$	−1.94097	−	4.68591i	−0.111506	−	0.269199i
$304$	6.99930	−	14.5634i	0.401437	−	0.835271i
$305$	−10.4290	+	25.1779i	−0.597163	+	1.44168i
$306$	−5.34427	−	1.84786i	−0.305511	−	0.105635i
$307$	11.0666	−	13.4846i	0.631601	−	0.769609i	−0.354625	−	0.935009i	$-0.615392\pi$
$307$	11.0666	−	13.4846i	0.631601	−	0.769609i	0.986227	+	0.165400i	$0.0528915\pi$
$308$	−24.1790	+	16.9164i	−1.37773	+	0.963901i
$309$	0.787922	+	2.59743i	0.0448233	+	0.147763i
$310$	0.371729	+	0.0888915i	0.0211128	+	0.00504870i
$311$	−21.5386	−	14.3916i	−1.22134	−	0.816074i	−0.233623	−	0.972327i	$-0.575058\pi$
$311$	−21.5386	−	14.3916i	−1.22134	−	0.816074i	−0.987717	+	0.156254i	$0.950058\pi$
$312$	10.5743	−	15.2594i	0.598650	−	0.863893i
$313$	−16.7798	−	25.1127i	−0.948448	−	1.41945i	−0.907387	−	0.420295i	$-0.861926\pi$
$313$	−16.7798	−	25.1127i	−0.948448	−	1.41945i	−0.0410602	−	0.999157i	$-0.513074\pi$
$314$	14.2006	+	6.53111i	0.801385	+	0.368572i
$315$	5.43826	−	4.46306i	0.306411	−	0.251465i
$316$	3.02842	−	3.85575i	0.170362	−	0.216903i
$317$	0.908284	+	1.69928i	0.0510143	+	0.0954411i	0.906136	−	0.422986i	$-0.139018\pi$
$317$	0.908284	+	1.69928i	0.0510143	+	0.0954411i	−0.855122	+	0.518427i	$0.826518\pi$
$318$	9.00850	−	6.83198i	0.505172	−	0.383119i
$319$		−	6.79344i		−	0.380360i
$320$	−1.87969	+	14.1509i	−0.105078	+	0.791058i
$321$		−	13.3521i		−	0.745239i
$322$	15.3376	+	20.2238i	0.854731	+	1.12703i
$323$	−7.61399	−	14.2448i	−0.423654	−	0.792601i
$324$	0.238640	+	1.98571i	0.0132578	+	0.110317i
$325$	−9.21379	+	7.56156i	−0.511089	+	0.419440i
$326$	10.3355	−	22.4725i	0.572431	−	1.24464i
$327$	−8.58738	−	12.8519i	−0.474883	−	0.710713i
$328$	7.53544	+	1.63207i	0.416075	+	0.0901160i
$329$	20.6867	+	13.8224i	1.14050	+	0.762056i
$330$	2.19638	−	9.18490i	0.120907	−	0.505612i
$331$	−3.16857	−	10.4454i	−0.174160	−	0.574130i	−0.999948	−	0.0101495i	$-0.996769\pi$
$331$	−3.16857	−	10.4454i	−0.174160	−	0.574130i	0.825788	−	0.563981i	$-0.190731\pi$
$332$	5.79279	+	1.02373i	0.317921	+	0.0561847i
$333$	−3.80902	+	4.64131i	−0.208733	+	0.254342i
$334$	−6.55391	+	18.9548i	−0.358614	+	1.03716i
$335$	−1.82297	+	4.40105i	−0.0995996	+	0.240455i
$336$	−13.5770	+	8.02323i	−0.740684	+	0.437703i
$337$	−6.10241	−	14.7325i	−0.332420	−	0.802532i	−0.998399	−	0.0565618i	$-0.981986\pi$
$337$	−6.10241	−	14.7325i	−0.332420	−	0.802532i	0.665980	−	0.745970i	$-0.268014\pi$
$338$	42.4678	−	2.54271i	2.30995	−	0.138305i
$339$	−5.41674	+	0.533503i	−0.294197	+	0.0289759i
$340$	10.3041	+	9.87171i	0.558821	+	0.535369i
$341$	0.499884	+	0.267193i	0.0270702	+	0.0144693i
$342$	−3.35372	+	4.62473i	−0.181348	+	0.250077i
$343$	1.18768	+	5.97089i	0.0641289	+	0.322398i
$344$	−15.8637	+	12.5753i	−0.855311	+	0.678016i
$345$	−7.96696	−	1.58473i	−0.428927	−	0.0853188i
$346$	1.13167	−	29.4774i	0.0608391	−	1.58472i
$347$	−9.72658	−	0.957984i	−0.522150	−	0.0514273i	−0.166491	−	0.986043i	$-0.553244\pi$
$347$	−9.72658	−	0.957984i	−0.522150	−	0.0514273i	−0.355659	+	0.934616i	$0.615744\pi$
$348$	0.278354	−	3.61990i	0.0149214	−	0.194047i
$349$	25.0573	+	7.60104i	1.34128	+	0.406874i	0.877713	−	0.479186i	$-0.159068\pi$
$349$	25.0573	+	7.60104i	1.34128	+	0.406874i	0.463571	+	0.886060i	$0.346568\pi$
$350$	9.79470	−	2.56529i	0.523549	−	0.137120i
$351$	−4.64129	+	4.64129i	−0.247734	+	0.247734i
$352$	−8.01350	+	19.5946i	−0.427121	+	1.04439i
$353$	18.5306	+	18.5306i	0.986284	+	0.986284i	0.999907	−	0.0136234i	$-0.00433658\pi$
$353$	18.5306	+	18.5306i	0.986284	+	0.986284i	−0.0136234	+	0.999907i	$0.504337\pi$
$354$	14.1335	+	8.26676i	0.751188	+	0.439373i
$355$	5.52378	−	18.2095i	0.293172	−	0.966458i
$356$	−16.3471	−	8.29232i	−0.866393	−	0.439492i
$357$	−1.54519	+	15.6885i	−0.0817799	+	0.830325i
$358$	5.41728	+	5.84983i	0.286312	+	0.309173i
$359$	−2.24449	+	11.2838i	−0.118460	+	0.595538i	0.875261	+	0.483651i	$0.160689\pi$
$359$	−2.24449	+	11.2838i	−0.118460	+	0.595538i	−0.993721	+	0.111887i	$0.964311\pi$
$360$	1.54669	−	4.80420i	0.0815176	−	0.253203i
$361$	2.63070	−	0.523278i	0.138458	−	0.0275410i
$362$	12.0707	−	1.92292i	0.634422	−	0.101066i
$363$	1.41660	−	2.65027i	0.0743523	−	0.139103i
$364$	−48.2304	−	18.7772i	−2.52796	−	0.984194i
$365$	−0.804886	−	8.17214i	−0.0421296	−	0.427749i
$366$	−14.3325	+	16.1581i	−0.749171	+	0.844596i
$367$	−15.5635	+	6.44661i	−0.812407	+	0.336510i	−0.749914	−	0.661535i	$-0.769905\pi$
$367$	−15.5635	+	6.44661i	−0.812407	+	0.336510i	−0.0624932	+	0.998045i	$0.519905\pi$
$368$	17.1061	+	6.24109i	0.891717	+	0.325339i
$369$	−2.51845	−	1.04318i	−0.131105	−	0.0543056i
$370$	13.6268	−	6.62457i	0.708422	−	0.344395i
$371$	−24.3651	−	19.9959i	−1.26497	−	1.03814i
$372$	0.255416	+	0.162857i	0.0132427	+	0.00844373i
$373$	−15.3327	+	4.65113i	−0.793898	+	0.240826i	−0.661081	−	0.750314i	$-0.729902\pi$
$373$	−15.3327	+	4.65113i	−0.793898	+	0.240826i	−0.132817	+	0.991141i	$0.542402\pi$
$374$	11.0732	+	18.0335i	0.572583	+	0.932491i
$375$	−6.75702	+	10.1126i	−0.348931	+	0.522212i
$376$	17.8462	+	0.302380i	0.920346	+	0.0155941i
$377$	9.90709	−	6.61971i	0.510241	−	0.340932i
$378$	5.22932	−	1.93453i	0.268967	−	0.0995017i
$379$	−16.0830	−	19.5972i	−0.826129	−	1.00664i	−0.999762	−	0.0218310i	$-0.993050\pi$
$379$	−16.0830	−	19.5972i	−0.826129	−	1.00664i	0.173632	−	0.984811i	$-0.444450\pi$
$380$	12.5654	−	7.06664i	0.644593	−	0.362511i
$381$	9.78094	−	5.22802i	0.501093	−	0.267840i
$382$	15.2243	+	2.09185i	0.778943	+	0.107028i
$383$	28.8724			1.47531			0.737656	−	0.675176i	$-0.235933\pi$
$383$	28.8724			1.47531			0.737656	+	0.675176i	$0.235933\pi$
$384$	−5.07287	+	10.1127i	−0.258874	+	0.516060i
$385$	−26.3280			−1.34180
$386$	12.0788	+	1.65965i	0.614794	+	0.0844740i
$387$	6.31201	−	3.37384i	0.320858	−	0.171502i
$388$	15.3430	+	27.2819i	0.778922	+	1.38503i
$389$	−12.2744	−	14.9565i	−0.622339	−	0.758323i	0.362464	−	0.931998i	$-0.381936\pi$
$389$	−12.2744	−	14.9565i	−0.622339	−	0.758323i	−0.984803	+	0.173675i	$0.944436\pi$
$390$	15.5348	−	5.74695i	0.786637	−	0.291008i
$391$	15.1345	−	10.1126i	0.765387	−	0.511415i
$392$	16.7963	+	17.3753i	0.848341	+	0.877585i
$393$	4.41096	−	6.60147i	0.222503	−	0.333000i
$394$	11.3293	+	18.4505i	0.570762	+	0.929525i
$395$	4.18597	−	1.26980i	0.210619	−	0.0638907i
$396$	4.02396	−	6.31096i	0.202211	−	0.317138i
$397$	19.1560	+	15.7209i	0.961410	+	0.789009i	0.977516	−	0.210861i	$-0.0676269\pi$
$397$	19.1560	+	15.7209i	0.961410	+	0.789009i	−0.0161059	+	0.999870i	$0.505127\pi$
$398$	−15.5994	+	7.58358i	−0.781929	+	0.380130i
$399$	14.7139	+	6.09471i	0.736618	+	0.305117i
$400$	4.91144	−	5.35159i	0.245572	−	0.267579i
$401$	−15.5917	+	6.45830i	−0.778613	+	0.322512i	−0.736356	−	0.676595i	$-0.763455\pi$
$401$	−15.5917	+	6.45830i	−0.778613	+	0.322512i	−0.0422574	+	0.999107i	$0.513455\pi$
$402$	−2.50529	+	2.82440i	−0.124953	+	0.140868i
$403$	0.0974431	+	0.989357i	0.00485399	+	0.0492834i
$404$	−3.68022	+	9.45286i	−0.183098	+	0.470297i
$405$	−0.841158	+	1.57370i	−0.0417975	+	0.0781976i
$406$	−9.99546	+	1.59232i	−0.496066	+	0.0790257i
$407$	22.0380	−	4.38363i	1.09238	−	0.217288i
$408$	5.16149	+	10.0629i	0.255532	+	0.498188i
$409$	1.88636	−	9.48335i	0.0932743	−	0.468921i	−0.905712	−	0.423895i	$-0.860663\pi$
$409$	1.88636	−	9.48335i	0.0932743	−	0.468921i	0.998986	−	0.0450268i	$-0.0143373\pi$
$410$	4.67399	+	5.04720i	0.230832	+	0.249263i
$411$	0.441900	−	4.48669i	0.0217973	−	0.221312i
$412$	2.45585	−	4.84135i	0.120991	−	0.238516i
$413$	13.2506	−	43.6815i	0.652022	−	2.14943i
$414$	−5.55709	−	3.25037i	−0.273116	−	0.159747i
$415$	3.71118	+	3.71118i	0.182175	+	0.182175i
$416$	−36.3840	+	7.40713i	−1.78387	+	0.363164i
$417$	−14.6202	+	14.6202i	−0.715955	+	0.715955i
$418$	20.6815	−	5.41660i	1.01157	−	0.264935i
$419$	−29.4538	−	8.93472i	−1.43891	−	0.436490i	−0.528056	−	0.849210i	$-0.677079\pi$
$419$	−29.4538	−	8.93472i	−1.43891	−	0.436490i	−0.910858	+	0.412720i	$0.864579\pi$
$420$	−14.0289	−	1.07876i	−0.684541	−	0.0526382i
$421$	33.5677	+	3.30613i	1.63599	+	0.161131i	0.873822	−	0.486246i	$-0.161634\pi$
$421$	33.5677	+	3.30613i	1.63599	+	0.161131i	0.762170	+	0.647377i	$0.224134\pi$
$422$	0.0823831	−	2.14589i	0.00401035	−	0.104460i
$423$	−6.18923	−	1.23111i	−0.300931	−	0.0598588i
$424$	−22.4626	−	2.59731i	−1.09088	−	0.126137i
$425$	−1.41655	−	7.12146i	−0.0687126	−	0.345442i
$426$	8.85356	−	12.2089i	0.428956	−	0.591524i
$427$	53.1037	+	28.3845i	2.56987	+	1.37362i
$428$	−18.4737	+	19.2830i	−0.892960	+	0.932077i
$429$	24.4456	−	2.40768i	1.18024	−	0.116244i
$430$	−18.0288	+	1.07945i	−0.869427	+	0.0520559i
$431$	−12.0578	−	29.1101i	−0.580803	−	1.40218i	−0.892086	−	0.451865i	$-0.850759\pi$
$431$	−12.0578	−	29.1101i	−0.580803	−	1.40218i	0.311283	−	0.950317i	$-0.399241\pi$
$432$	2.40276	−	3.19793i	0.115603	−	0.153860i
$433$	7.29294	−	17.6067i	0.350476	−	0.846125i	−0.646085	−	0.763266i	$-0.723595\pi$
$433$	7.29294	−	17.6067i	0.350476	−	0.846125i	0.996561	−	0.0828594i	$-0.0264052\pi$
$434$	0.275964	−	0.798126i	0.0132467	−	0.0383113i
$435$	2.05493	−	2.50394i	0.0985262	−	0.120055i
$436$	−5.37988	+	30.4420i	−0.257650	+	1.45791i
$437$	−5.33804	−	17.5972i	−0.255353	−	0.841786i
$438$	1.51361	−	6.32967i	0.0723231	−	0.302443i
$439$	16.1908	+	10.8184i	0.772747	+	0.516333i	0.878317	−	0.478079i	$-0.158667\pi$
$439$	16.1908	+	10.8184i	0.772747	+	0.516333i	−0.105570	+	0.994412i	$0.533667\pi$
$440$	−15.8801	+	10.2259i	−0.757053	+	0.487500i
$441$	−4.74686	−	7.10418i	−0.226041	−	0.338294i
$442$	−15.5088	+	33.7208i	−0.737679	+	1.60393i
$443$	−12.6856	+	10.4108i	−0.602712	+	0.494633i	−0.885556	−	0.464533i	$-0.846222\pi$
$443$	−12.6856	+	10.4108i	−0.602712	+	0.494633i	0.282844	+	0.959166i	$0.408722\pi$
$444$	11.9226	−	1.43284i	0.565822	−	0.0679996i
$445$	−7.70922	−	14.4229i	−0.365452	−	0.683713i
$446$	−3.20102	−	4.22079i	−0.151573	−	0.199860i
$447$		−	17.9548i		−	0.849234i
$448$	30.7086	+	7.19778i	1.45084	+	0.340063i
$449$			6.79111i			0.320492i	0.987077	+	0.160246i	$0.0512288\pi$
$449$			6.79111i			0.320492i	−0.987077	+	0.160246i	$0.948771\pi$
$450$	−2.04622	+	1.55184i	−0.0964597	+	0.0731544i
$451$	4.80893	+	8.99687i	0.226443	+	0.423646i
$452$	8.56097	+	6.72404i	0.402674	+	0.316272i
$453$	−11.5538	+	9.48200i	−0.542847	+	0.445503i
$454$	−36.8054	−	16.9275i	−1.72736	−	0.794446i
$455$	−25.6547	−	38.3949i	−1.20271	−	1.79998i
$456$	11.2421	−	2.03884i	0.526460	−	0.0954775i
$457$	8.07863	+	5.39797i	0.377902	+	0.252506i	0.729986	−	0.683462i	$-0.239527\pi$
$457$	8.07863	+	5.39797i	0.377902	+	0.252506i	−0.352083	+	0.935969i	$0.614527\pi$
$458$	3.86883	+	0.925152i	0.180779	+	0.0432295i
$459$	−1.16070	−	3.82631i	−0.0541768	−	0.178597i
$460$	9.31323	+	13.3116i	0.434231	+	0.620657i
$461$	12.6400	−	15.4018i	0.588702	−	0.717335i	−0.390414	−	0.920639i	$-0.627668\pi$
$461$	12.6400	−	15.4018i	0.588702	−	0.717335i	0.979116	+	0.203304i	$0.0651681\pi$
$462$	−19.7206	−	6.81867i	−0.917483	−	0.317233i
$463$	−6.47138	+	15.6233i	−0.300751	+	0.726076i	0.699187	+	0.714939i	$0.253545\pi$
$463$	−6.47138	+	15.6233i	−0.300751	+	0.726076i	−0.999938	+	0.0111378i	$0.996455\pi$
$464$	−5.41043	+	4.84271i	−0.251173	+	0.224817i
$465$	0.103425	+	0.249691i	0.00479623	+	0.0115791i
$466$	−0.332575	−	5.55460i	−0.0154062	−	0.257312i
$467$	−19.7365	+	1.94388i	−0.913298	+	0.0899520i	−0.543738	−	0.839255i	$-0.682991\pi$
$467$	−19.7365	+	1.94388i	−0.913298	+	0.0899520i	−0.369560	+	0.929207i	$0.620491\pi$
$468$	13.1245	−	0.281304i	0.606681	−	0.0130033i
$469$	9.28244	+	4.96157i	0.428623	+	0.229104i
$470$	12.8917	+	9.34868i	0.594649	+	0.431223i
$471$	2.15622	+	10.8401i	0.0993534	+	0.499483i
$472$	−8.97377	−	31.4937i	−0.413051	−	1.44962i
$473$	−26.2697	−	5.22537i	−1.20788	−	0.240263i
$474$	3.46430	+	0.132998i	0.159121	+	0.00610882i
$475$	−7.30018	−	0.719005i	−0.334955	−	0.0329902i
$476$	23.9380	−	20.5194i	1.09719	−	0.940504i
$477$	7.65041	+	2.32073i	0.350288	+	0.106259i
$478$	−4.36382	−	16.6618i	−0.199596	−	0.762093i
$479$	9.30545	−	9.30545i	0.425177	−	0.425177i	−0.461805	−	0.886982i	$-0.652798\pi$
$479$	9.30545	−	9.30545i	0.425177	−	0.425177i	0.886982	+	0.461805i	$0.152798\pi$
$480$	−8.88073	+	4.79822i	−0.405348	+	0.219008i
$481$	27.8672	+	27.8672i	1.27063	+	1.27063i
$482$	−15.1243	+	25.8576i	−0.688891	+	1.17778i
$483$	−5.20996	+	17.1749i	−0.237062	+	0.781487i
$484$	−5.71272	+	1.86752i	−0.259669	+	0.0848873i
$485$	−2.73723	+	27.7916i	−0.124291	+	1.26195i
$486$	−1.03763	+	0.960901i	−0.0470677	+	0.0435874i
$487$	3.74420	−	18.8233i	0.169666	−	0.852967i	−0.798372	−	0.602164i	$-0.794305\pi$
$487$	3.74420	−	18.8233i	0.169666	−	0.852967i	0.968038	−	0.250803i	$-0.0806947\pi$
$488$	43.0549	−	3.50518i	1.94900	−	0.158672i
$489$	17.1544	−	3.41223i	0.775750	−	0.154306i
$490$	3.39203	+	21.2927i	0.153237	+	0.961908i
$491$	−0.877842	+	1.64233i	−0.0396164	+	0.0741171i	−0.900951	−	0.433922i	$-0.857129\pi$
$491$	−0.877842	+	1.64233i	−0.0396164	+	0.0741171i	0.861334	+	0.508039i	$0.169629\pi$
$492$	2.19381	+	4.99104i	0.0989045	+	0.225013i
$493$	0.711450	+	7.22347i	0.0320421	+	0.325329i
$494$	28.0518	+	24.8824i	1.26211	+	1.11951i
$495$	6.16950	−	2.55549i	0.277298	−	0.114861i
$496$	−0.143544	−	0.588586i	−0.00644532	−	0.0264283i
$497$	−38.8436	−	16.0896i	−1.74237	−	0.721715i
$498$	1.81864	+	3.74096i	0.0814954	+	0.167636i
$499$	−13.3440	−	10.9511i	−0.597360	−	0.490241i	0.286445	−	0.958097i	$-0.407527\pi$
$499$	−13.3440	−	10.9511i	−0.597360	−	0.490241i	−0.883805	+	0.467856i	$0.845027\pi$
$500$	23.7501	−	5.25564i	1.06214	−	0.235039i
$501$	−13.5710	+	4.11672i	−0.606309	+	0.183922i
$502$	15.7657	−	9.68072i	0.703658	−	0.432072i
$503$	−7.39402	+	11.0659i	−0.329683	+	0.493405i	−0.958869	−	0.283850i	$-0.908388\pi$
$503$	−7.39402	+	11.0659i	−0.329683	+	0.493405i	0.629186	+	0.777255i	$0.283388\pi$
$504$	−10.2287	−	4.44137i	−0.455625	−	0.197834i
$505$	−7.52517	+	5.02816i	−0.334866	+	0.223750i
$506$	8.35919	+	22.5961i	0.371611	+	1.00452i
$507$	19.0845	+	23.2545i	0.847572	+	1.03277i
$508$	−21.3590	−	5.98248i	−0.947652	−	0.265430i
$509$	−8.76128	+	4.68300i	−0.388337	+	0.207570i	−0.653998	−	0.756496i	$-0.726910\pi$
$509$	−8.76128	+	4.68300i	−0.388337	+	0.207570i	0.265662	+	0.964066i	$0.414410\pi$
$510$	−1.37352	+	9.99632i	−0.0608203	+	0.442645i
$511$	−18.1436			−0.802627
$512$	21.3179	−	7.58589i	0.942128	−	0.335252i
$513$	−4.03953			−0.178349
$514$	4.53006	−	32.9693i	0.199812	−	1.45422i
$515$	4.27149	−	2.28316i	0.188225	−	0.100608i
$516$	−13.7838	−	3.86072i	−0.606796	−	0.169959i
$517$	14.9818	+	18.2554i	0.658900	+	0.802871i
$518$	−11.6153	−	31.3979i	−0.510348	−	1.37954i
$519$	17.3437	−	11.5887i	0.761303	−	0.508686i
$520$	−30.3867	−	13.1941i	−1.33255	−	0.578597i
$521$	−1.59889	+	2.39291i	−0.0700487	+	0.104835i	−0.864840	−	0.502047i	$-0.832580\pi$
$521$	−1.59889	+	2.39291i	−0.0700487	+	0.104835i	0.794791	+	0.606883i	$0.207580\pi$
$522$	2.18770	−	1.34333i	0.0957531	−	0.0587959i
$523$	1.10433	−	0.334994i	0.0482888	−	0.0146482i	−0.266048	−	0.963960i	$-0.585718\pi$
$523$	1.10433	−	0.334994i	0.0482888	−	0.0146482i	0.314337	+	0.949312i	$0.398218\pi$
$524$	−15.5040	+	3.43086i	−0.677294	+	0.149878i
$525$	5.53437	+	4.54194i	0.241540	+	0.198226i
$526$	−10.7601	−	22.1335i	−0.469162	−	0.965068i
$527$	−0.559509	−	0.231756i	−0.0243726	−	0.0100955i
$528$	−14.5431	+	3.54677i	−0.632908	+	0.154353i
$529$	−2.10357	+	0.871328i	−0.0914597	+	0.0378838i
$530$	−15.0927	−	13.3875i	−0.655587	−	0.581517i
$531$	1.13483	+	11.5222i	0.0492475	+	0.500019i
$532$	−12.8172	−	29.1599i	−0.555697	−	1.26424i
$533$	−8.43448	+	15.7798i	−0.365338	+	0.683499i
$534$	−2.03908	−	12.7999i	−0.0882396	−	0.553905i
$535$	−23.3676	+	4.64810i	−1.01027	+	0.200955i
$536$	7.52592	−	0.612699i	0.325070	−	0.0264646i
$537$	−1.09986	+	5.52938i	−0.0474625	+	0.238610i
$538$	−4.07398	+	3.77274i	−0.175642	+	0.162654i
$539$	−3.13410	+	31.8211i	−0.134995	+	1.37063i
$540$	3.39214	−	1.10891i	0.145974	−	0.0477198i
$541$	1.19441	−	3.93744i	0.0513517	−	0.169284i	−0.927514	−	0.373789i	$-0.878058\pi$
$541$	1.19441	−	3.93744i	0.0513517	−	0.169284i	0.978866	+	0.204505i	$0.0655585\pi$
$542$	−6.81735	+	11.6555i	−0.292830	+	0.500646i
$543$	6.11145	+	6.11145i	0.262267	+	0.262267i
$544$	6.46869	−	21.6741i	0.277343	−	0.929271i
$545$	−19.5028	+	19.5028i	−0.835410	+	0.835410i
$546$	−9.27234	−	35.4034i	−0.396820	−	1.51513i
$547$	6.26152	+	1.89941i	0.267723	+	0.0812130i	0.421292	−	0.906925i	$-0.361577\pi$
$547$	6.26152	+	1.89941i	0.267723	+	0.0812130i	−0.153569	+	0.988138i	$0.549077\pi$
$548$	−6.84590	+	5.86824i	−0.292442	+	0.250679i
$549$	−15.1990	−	1.49697i	−0.648679	−	0.0638893i
$550$	9.60369	+	0.368696i	0.409503	+	0.0157213i
$551$	7.19202	+	1.43058i	0.306390	+	0.0609448i
$552$	3.52836	+	12.3829i	0.150177	+	0.527050i
$553$	−1.88556	−	9.47933i	−0.0801820	−	0.403102i
$554$	−30.7222	−	22.2789i	−1.30526	−	0.946538i
$555$	9.44878	+	5.05048i	0.401078	+	0.214381i
$556$	41.3427	−	0.886118i	1.75332	−	0.0375798i
$557$	13.1818	−	1.29829i	0.558531	−	0.0550105i	0.185187	−	0.982703i	$-0.440711\pi$
$557$	13.1818	−	1.29829i	0.558531	−	0.0550105i	0.373344	+	0.927693i	$0.378211\pi$
$558$	0.0128018	+	0.213813i	0.000541944	+	0.00905142i
$559$	−17.9776	−	43.4017i	−0.760370	−	1.83570i
$560$	18.7679	+	20.9681i	0.793089	+	0.886065i
$561$	−5.72636	+	13.8247i	−0.241767	+	0.583677i
$562$	2.82742	+	0.977623i	0.119268	+	0.0412385i
$563$	−14.8656	+	18.1138i	−0.626509	+	0.763404i	−0.985452	−	0.169956i	$-0.945637\pi$
$563$	−14.8656	+	18.1138i	−0.626509	+	0.763404i	0.358942	+	0.933360i	$0.383137\pi$
$564$	7.23509	+	10.3413i	0.304652	+	0.435447i
$565$	2.81936	+	9.29417i	0.118611	+	0.391009i
$566$	19.0139	+	4.54679i	0.799214	+	0.191116i
$567$	3.27816	+	2.19039i	0.137670	+	0.0919879i
$568$	−29.6783	+	5.38238i	−1.24527	+	0.225840i
$569$	−5.45457	−	8.16334i	−0.228667	−	0.342225i	0.699338	−	0.714791i	$-0.253478\pi$
$569$	−5.45457	−	8.16334i	−0.228667	−	0.342225i	−0.928006	+	0.372566i	$0.878478\pi$
$570$	9.26126	+	4.25943i	0.387912	+	0.178408i
$571$	−24.4896	+	20.0981i	−1.02486	+	0.841079i	−0.987404	−	0.158220i	$-0.949425\pi$
$571$	−24.4896	+	20.0981i	−1.02486	+	0.841079i	−0.0374534	+	0.999298i	$0.511925\pi$
$572$	−38.6354	−	30.3454i	−1.61543	−	1.26880i
$573$	5.12236	+	9.58327i	0.213990	+	0.400347i
$574$	12.1103	−	9.18435i	0.505473	−	0.383347i
$575$		−	8.26660i		−	0.344741i
$576$	−7.89465	+	1.29401i	−0.328944	+	0.0539172i
$577$		−	21.3414i		−	0.888455i	−0.895914	−	0.444227i	$-0.853478\pi$
$577$		−	21.3414i		−	0.888455i	0.895914	−	0.444227i	$-0.146522\pi$
$578$	0.864920	+	1.14046i	0.0359759	+	0.0474370i
$579$	4.06403	+	7.60326i	0.168895	+	0.315981i
$580$	−6.43212	+	0.773003i	−0.267079	+	0.0320972i
$581$	8.96405	−	7.35661i	0.371892	−	0.305204i
$582$	−9.24800	+	20.1079i	−0.383342	+	0.833500i
$583$	−16.6220	−	24.8765i	−0.688411	−	1.03028i
$584$	−10.9436	+	7.04706i	−0.452848	+	0.291609i
$585$	9.73847	+	6.50704i	0.402636	+	0.269033i
$586$	8.12844	−	33.9918i	0.335783	−	1.40419i
$587$	3.99769	+	13.1786i	0.165002	+	0.543940i	0.999980	−	0.00634426i	$-0.00201945\pi$
$587$	3.99769	+	13.1786i	0.165002	+	0.543940i	−0.834978	+	0.550284i	$0.814519\pi$
$588$	−2.97385	+	16.8275i	−0.122639	+	0.693954i
$589$	−0.388137	+	0.472946i	−0.0159929	+	0.0194874i
$590$	9.54760	−	27.6130i	0.393068	−	1.13681i
$591$	−5.85878	+	14.1443i	−0.240998	+	0.581821i
$592$	−19.2010	−	14.4266i	−0.789156	−	0.592930i
$593$	−12.9909	−	31.3628i	−0.533473	−	1.28792i	−0.929210	−	0.369553i	$-0.879511\pi$
$593$	−12.9909	−	31.3628i	−0.533473	−	1.28792i	0.395737	−	0.918364i	$-0.370489\pi$
$594$	5.28301	−	0.316314i	0.216764	−	0.0129785i
$595$	27.9946	−	2.75722i	1.14766	−	0.113035i
$596$	−24.8420	+	25.9303i	−1.01757	+	1.06214i
$597$	−10.8166	−	5.78161i	−0.442695	−	0.236626i
$598$	−24.8072	+	34.2087i	−1.01444	+	1.39890i
$599$	−4.63786	−	23.3161i	−0.189498	−	0.952670i	−0.952097	−	0.305798i	$-0.901077\pi$
$599$	−4.63786	−	23.3161i	−0.189498	−	0.952670i	0.762599	−	0.646872i	$-0.223923\pi$
$600$	5.10224	+	0.589962i	0.208298	+	0.0240851i
$601$	26.1177	+	5.19512i	1.06536	+	0.211914i	0.696490	−	0.717567i	$-0.254744\pi$
$601$	26.1177	+	5.19512i	1.06536	+	0.211914i	0.368872	+	0.929480i	$0.379744\pi$
$602$	−1.53090	+	39.8764i	−0.0623949	+	1.62524i
$603$	−2.65676	−	0.261668i	−0.108192	−	0.0106560i
$604$	29.8051	+	2.29188i	1.21275	+	0.0932554i
$605$	−5.13141	−	1.55660i	−0.208622	−	0.0632847i
$606$	−6.93885	+	1.81732i	−0.281871	+	0.0738237i
$607$	−0.468586	+	0.468586i	−0.0190193	+	0.0190193i	−0.716552	−	0.697533i	$-0.754281\pi$
$607$	−0.468586	+	0.468586i	−0.0190193	+	0.0190193i	0.697533	+	0.716552i	$0.254281\pi$
$608$	−19.0567	−	12.6099i	−0.772851	−	0.511400i
$609$	−5.06075	−	5.06075i	−0.205072	−	0.205072i
$610$	33.2678	+	19.4585i	1.34697	+	0.787851i
$611$	−12.0238	+	39.6370i	−0.486429	+	1.60354i
$612$	−3.61775	+	7.13186i	−0.146239	+	0.288288i
$613$	−0.755117	+	7.66683i	−0.0304989	+	0.309660i	0.967817	+	0.251654i	$0.0809744\pi$
$613$	−0.755117	+	7.66683i	−0.0304989	+	0.309660i	−0.998316	+	0.0580066i	$0.981526\pi$
$614$	−16.7623	−	18.1007i	−0.676469	−	0.730484i
$615$	−0.948954	+	4.77071i	−0.0382655	+	0.192374i
$616$	19.0461	+	37.1325i	0.767389	+	1.49611i
$617$	−14.1892	+	2.82241i	−0.571235	+	0.113626i	−0.472252	−	0.881463i	$-0.656559\pi$
$617$	−14.1892	+	2.82241i	−0.571235	+	0.113626i	−0.0989829	+	0.995089i	$0.531559\pi$
$618$	3.79081	−	0.603894i	0.152489	−	0.0242922i
$619$	−7.11777	+	13.3164i	−0.286087	+	0.535232i	−0.983381	−	0.181554i	$-0.941887\pi$
$619$	−7.11777	+	13.3164i	−0.286087	+	0.535232i	0.697294	+	0.716785i	$0.254387\pi$
$620$	0.196102	−	0.503699i	0.00787565	−	0.0202291i
$621$	−0.446200	−	4.53034i	−0.0179054	−	0.181796i
$622$	−24.3097	+	27.4061i	−0.974730	+	1.09889i
$623$	−33.3835	+	13.8279i	−1.33748	+	0.554002i
$624$	−19.3436	−	17.7526i	−0.774362	−	0.710674i
$625$	11.6619	+	4.83051i	0.466475	+	0.193220i
$626$	−38.4143	+	18.6749i	−1.53535	+	0.746399i
$627$	11.6858	+	9.59030i	0.466687	+	0.383000i
$628$	11.8841	−	18.6384i	0.474228	−	0.743755i
$629$	−22.9739	+	6.96906i	−0.916030	+	0.277875i
$630$	−5.20607	−	8.47844i	−0.207415	−	0.337789i
$631$	9.61773	−	14.3939i	0.382876	−	0.573014i	−0.589110	−	0.808053i	$-0.700522\pi$
$631$	9.61773	−	14.3939i	0.382876	−	0.573014i	0.971986	+	0.235039i	$0.0755217\pi$
$632$	−4.81911	−	4.98523i	−0.191694	−	0.198302i
$633$	1.26258	−	0.843628i	0.0501830	−	0.0335312i
$634$	2.55563	−	0.945428i	0.101497	−	0.0375477i
$635$	−12.5545	−	15.2977i	−0.498212	−	0.607073i
$636$	−7.83775	−	13.9366i	−0.310787	−	0.552621i
$637$	−49.4596	+	26.4367i	−1.95966	+	1.04746i
$638$	−9.51795	−	1.30779i	−0.376819	−	0.0517758i
$639$	10.6640			0.421862
$640$	19.4642	+	5.35768i	0.769391	+	0.211781i
$641$	−25.1023			−0.991483			−0.495741	−	0.868470i	$-0.665104\pi$
$641$	−25.1023			−0.991483			−0.495741	+	0.868470i	$0.665104\pi$
$642$	−18.7069	−	2.57037i	−0.738302	−	0.101444i
$643$	23.4824	−	12.5516i	0.926054	−	0.494986i	0.0618263	−	0.998087i	$-0.480308\pi$
$643$	23.4824	−	12.5516i	0.926054	−	0.494986i	0.864228	+	0.503101i	$0.167808\pi$
$644$	31.2872	−	17.5955i	1.23289	−	0.693361i
$645$	−8.10192	−	9.87221i	−0.319013	−	0.388718i
$646$	−21.4234	+	7.92536i	−0.842892	+	0.311819i
$647$	−5.99339	+	4.00465i	−0.235624	+	0.157439i	−0.667777	−	0.744361i	$-0.732754\pi$
$647$	−5.99339	+	4.00465i	−0.235624	+	0.157439i	0.432153	+	0.901800i	$0.357754\pi$
$648$	2.82802	+	0.0479171i	0.111095	+	0.00188236i
$649$	24.0720	−	36.0263i	0.944909	−	1.41416i
$650$	8.82041	+	14.3646i	0.345965	+	0.563427i
$651$	0.571431	−	0.173342i	0.0223962	−	0.00679380i
$652$	−29.4954	−	18.8067i	−1.15513	−	0.736527i
$653$	25.0158	+	20.5299i	0.978942	+	0.803397i	0.980483	−	0.196602i	$-0.0629906\pi$
$653$	25.0158	+	20.5299i	0.978942	+	0.803397i	−0.00154129	+	0.999999i	$0.500491\pi$
$654$	−19.6593	+	9.55726i	−0.768740	+	0.373718i
$655$	−13.0888	−	5.42157i	−0.511423	−	0.211838i
$656$	3.73724	−	10.2433i	0.145915	−	0.399935i
$657$	4.25164	−	1.76109i	0.165872	−	0.0687065i
$658$	23.3483	−	26.3222i	0.910210	−	1.02615i
$659$	2.58284	+	26.2241i	0.100613	+	1.02154i	0.904417	+	0.426650i	$0.140306\pi$
$659$	2.58284	+	26.2241i	0.100613	+	1.02154i	−0.803804	+	0.594895i	$0.797194\pi$
$660$	−12.4457	−	4.84540i	−0.484448	−	0.188607i
$661$	12.9940	−	24.3101i	0.505408	−	0.945552i	−0.491788	−	0.870715i	$-0.663656\pi$
$661$	12.9940	−	24.3101i	0.505408	−	0.945552i	0.997196	−	0.0748366i	$-0.0238435\pi$
$662$	−15.2445	+	2.42852i	−0.592493	+	0.0943870i
$663$	−25.7408	+	5.12017i	−0.999692	+	0.198851i
$664$	2.54946	−	7.91891i	0.0989381	−	0.307313i
$665$	5.54422	−	27.8727i	0.214996	−	1.08086i
$666$	5.76944	+	6.23011i	0.223561	+	0.241412i
$667$	−0.809983	+	8.22390i	−0.0313627	+	0.318431i
$668$	25.2950	+	12.8313i	0.978694	+	0.496458i
$669$	1.08734	−	3.58448i	0.0420390	−	0.138584i
$670$	5.81515	+	3.40131i	0.224659	+	0.131404i
$671$	40.4148	+	40.4148i	1.56020	+	1.56020i
$672$	8.62728	+	20.5665i	0.332805	+	0.793371i
$673$	−17.7806	+	17.7806i	−0.685391	+	0.685391i	−0.961210	−	0.275819i	$-0.911051\pi$
$673$	−17.7806	+	17.7806i	−0.685391	+	0.685391i	0.275819	+	0.961210i	$0.411051\pi$
$674$	−21.8158	+	5.71367i	−0.840312	+	0.220082i
$675$	−1.73774	−	0.527137i	−0.0668856	−	0.0202895i
$676$	4.61289	−	59.9890i	0.177419	−	2.30727i
$677$	28.8775	+	2.84419i	1.10985	+	0.109311i	0.636291	−	0.771449i	$-0.280468\pi$
$677$	28.8775	+	2.84419i	1.10985	+	0.109311i	0.473563	+	0.880760i	$0.342968\pi$
$678$	−0.295298	+	7.69183i	−0.0113409	+	0.295403i
$679$	60.5167	+	12.0375i	2.32242	+	0.461958i
$680$	15.8144	−	12.5363i	0.606454	−	0.480743i
$681$	−5.58854	−	28.0955i	−0.214153	−	1.07662i
$682$	0.470583	−	0.648926i	0.0180195	−	0.0248486i
$683$	19.0879	+	10.2027i	0.730380	+	0.390396i	0.794273	−	0.607561i	$-0.207852\pi$
$683$	19.0879	+	10.2027i	0.730380	+	0.390396i	−0.0638935	+	0.997957i	$0.520352\pi$
$684$	5.83386	+	5.58902i	0.223063	+	0.213702i
$685$	−8.00602	+	0.788525i	−0.305894	+	0.0301280i
$686$	8.59415	−	0.514565i	0.328126	−	0.0196462i
$687$	1.07641	+	2.59869i	0.0410678	+	0.0991464i
$688$	14.5648	+	24.6466i	0.555277	+	0.939644i
$689$	20.0813	−	48.4807i	0.765038	−	1.84697i
$690$	−3.75398	+	10.8570i	−0.142911	+	0.413320i
$691$	−27.8202	+	33.8990i	−1.05833	+	1.28958i	−0.102796	+	0.994702i	$0.532779\pi$
$691$	−27.8202	+	33.8990i	−1.05833	+	1.28958i	−0.955535	+	0.294878i	$0.904721\pi$
$692$	−41.0815	−	7.26015i	−1.56168	−	0.275989i
$693$	−4.28302	−	14.1192i	−0.162699	−	0.536346i
$694$	−3.21462	+	13.4430i	−0.122025	+	0.510289i
$695$	30.6765	+	20.4974i	1.16363	+	0.777510i
$696$	−5.01807	−	1.08684i	−0.190210	−	0.0411967i
$697$	−6.05554	−	9.06275i	−0.229370	−	0.343276i
$698$	15.4731	−	33.6432i	0.585667	−	1.27341i
$699$	3.04158	−	2.49616i	0.115043	−	0.0944136i
$700$	−1.70854	−	14.2167i	−0.0645769	−	0.537341i
$701$	−8.01344	−	14.9921i	−0.302664	−	0.566244i	0.683909	−	0.729567i	$-0.260279\pi$
$701$	−8.01344	−	14.9921i	−0.302664	−	0.566244i	−0.986573	+	0.163324i	$0.947779\pi$
$702$	5.60919	+	7.39615i	0.211705	+	0.279150i
$703$			24.2541i			0.914761i
$704$	25.9103	+	14.9994i	0.976532	+	0.565311i
$705$			11.2604i			0.424091i
$706$	29.5296	−	22.3950i	1.11136	−	0.842847i
$707$	9.42646	+	17.6357i	0.354518	+	0.663257i
$708$	14.3029	−	18.2104i	0.537538	−	0.684387i
$709$	−2.04074	+	1.67479i	−0.0766416	+	0.0628981i	−0.671934	−	0.740611i	$-0.734536\pi$
$709$	−2.04074	+	1.67479i	−0.0766416	+	0.0628981i	0.595292	+	0.803509i	$0.297036\pi$
$710$	−24.4490	−	11.2445i	−0.917555	−	0.422000i
$711$	1.36195	+	2.03829i	0.0510769	+	0.0764420i
$712$	−14.7649	+	21.3067i	−0.553337	+	0.798504i
$713$	−0.573284	−	0.383056i	−0.0214697	−	0.0143456i
$714$	21.6830	+	5.18504i	0.811464	+	0.194045i
$715$	−12.7237	−	41.9443i	−0.475838	−	1.56863i
$716$	9.23877	−	6.46374i	0.345269	−	0.241561i
$717$	7.72631	−	9.41453i	0.288544	−	0.351592i
$718$	15.3771	+	5.31686i	0.573869	+	0.198424i
$719$	6.10001	−	14.7267i	0.227492	−	0.549215i	−0.768379	−	0.639995i	$-0.778936\pi$
$719$	6.10001	−	14.7267i	0.227492	−	0.549215i	0.995871	+	0.0907808i	$0.0289363\pi$
$720$	−6.43317	−	3.09183i	−0.239750	−	0.115226i
$721$	−4.09526	−	9.88684i	−0.152516	−	0.368205i
$722$	−0.226711	−	3.78647i	−0.00843730	−	0.140918i
$723$	−21.0801	+	2.07621i	−0.783977	+	0.0772150i
$724$	−0.370410	−	17.2818i	−0.0137662	−	0.642274i
$725$	2.90721	+	1.55393i	0.107971	+	0.0577117i
$726$	−3.44046	−	2.49493i	−0.127687	−	0.0925954i
$727$	−4.58626	−	23.0567i	−0.170095	−	0.855126i	−0.967731	−	0.251986i	$-0.918916\pi$
$727$	−4.58626	−	23.0567i	−0.170095	−	0.855126i	0.797636	−	0.603139i	$-0.206084\pi$
$728$	−35.5925	+	63.9584i	−1.31915	+	2.37046i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	−11.6045	−	0.445511i	−0.429503	−	0.0164891i
$731$	28.4798	+	2.80502i	1.05336	+	0.103747i
$732$	19.8792	+	23.1911i	0.734755	+	0.857166i
$733$	5.33915	+	1.61961i	0.197206	+	0.0598218i	0.387343	−	0.921936i	$-0.373393\pi$
$733$	5.33915	+	1.61961i	0.197206	+	0.0598218i	−0.190137	+	0.981758i	$0.560893\pi$
$734$	6.03593	+	23.0462i	0.222790	+	0.850652i
$735$	−10.7806	+	10.7806i	−0.397649	+	0.397649i
$736$	12.0371	−	22.7650i	0.443694	−	0.839131i
$737$	7.06444	+	7.06444i	0.260222	+	0.260222i
$738$	−1.94636	+	3.32766i	−0.0716466	+	0.122493i
$739$	−4.54020	+	14.9670i	−0.167014	+	0.550571i	−0.999996	−	0.00272825i	$-0.999132\pi$
$739$	−4.54020	+	14.9670i	−0.167014	+	0.550571i	0.832982	+	0.553300i	$0.186632\pi$
$740$	−6.65810	−	20.3671i	−0.244757	−	0.748708i
$741$	−2.59888	+	26.3868i	−0.0954721	+	0.969345i
$742$	−32.7058	+	30.2874i	−1.20067	+	1.11188i
$743$	−1.95925	+	9.84983i	−0.0718781	+	0.361355i	−0.999939	−	0.0110738i	$-0.996475\pi$
$743$	−1.95925	+	9.84983i	−0.0718781	+	0.361355i	0.928061	+	0.372429i	$0.121475\pi$
$744$	0.277340	−	0.326500i	0.0101678	−	0.0119701i
$745$	−31.4229	+	6.25041i	−1.15125	+	0.228997i
$746$	3.56481	+	22.3773i	0.130517	+	0.819291i
$747$	−1.38651	+	2.59398i	−0.0507297	+	0.0949086i
$748$	27.3975	−	12.0426i	1.00175	−	0.440320i
$749$	5.15980	+	52.3884i	0.188535	+	1.91423i
$750$	12.8675	+	11.4137i	0.469854	+	0.416768i
$751$	43.9270	−	18.1952i	1.60292	−	0.663951i	0.611094	−	0.791558i	$-0.290730\pi$
$751$	43.9270	−	18.1952i	1.60292	−	0.663951i	0.991825	+	0.127607i	$0.0407298\pi$
$752$	3.85917	−	24.9452i	0.140729	−	0.909657i
$753$	12.0861	+	5.00624i	0.440443	+	0.182437i
$754$	−7.36736	−	15.1547i	−0.268303	−	0.551901i
$755$	20.6166	+	16.9196i	0.750316	+	0.615769i
$756$	−1.70370	−	7.69896i	−0.0619628	−	0.280008i
$757$	46.3806	−	14.0694i	1.68573	−	0.511361i	0.705415	−	0.708794i	$-0.250761\pi$
$757$	46.3806	−	14.0694i	1.68573	−	0.511361i	0.980316	+	0.197433i	$0.0632606\pi$
$758$	−30.5528	+	18.7605i	−1.10973	+	0.681412i
$759$	−9.46476	+	14.1650i	−0.343549	+	0.514158i
$760$	−7.48178	−	18.9652i	−0.271393	−	0.687939i
$761$	−24.4692	+	16.3498i	−0.887007	+	0.592679i	−0.913441	−	0.406971i	$-0.866585\pi$
$761$	−24.4692	+	16.3498i	−0.887007	+	0.592679i	0.0264336	+	0.999651i	$0.491585\pi$
$762$	−5.44182	−	14.7100i	−0.197136	−	0.532888i
$763$	38.6601	+	47.1075i	1.39959	+	1.70541i
$764$	5.86157	−	20.9273i	0.212064	−	0.757123i
$765$	−6.29240	+	3.36336i	−0.227502	+	0.121603i
$766$	5.55815	−	40.4517i	0.200824	−	1.46158i
$767$	75.9947			2.74401
$768$	13.1918	+	9.05411i	0.476017	+	0.326712i
$769$	13.4439			0.484799			0.242399	−	0.970177i	$-0.422066\pi$
$769$	13.4439			0.484799			0.242399	+	0.970177i	$0.422066\pi$
$770$	−5.06833	+	36.8868i	−0.182650	+	1.32931i
$771$	20.7533	−	11.0929i	0.747411	−	0.399499i
$772$	4.65051	−	16.6035i	0.167375	−	0.597573i
$773$	−11.2434	−	13.7001i	−0.404398	−	0.492760i	0.530496	−	0.847687i	$-0.322006\pi$
$773$	−11.2434	−	13.7001i	−0.404398	−	0.492760i	−0.934894	+	0.354927i	$0.884506\pi$
$774$	−3.51181	−	9.49293i	−0.126229	−	0.341216i
$775$	−0.228687	+	0.152804i	−0.00821469	+	0.00548888i
$776$	41.1769	−	16.2443i	1.47816	−	0.583138i
$777$	13.1515	−	19.6827i	0.471809	−	0.706112i
$778$	−23.3177	+	14.3179i	−0.835979	+	0.513321i
$779$	−10.5374	+	3.19648i	−0.377541	+	0.114526i
$780$	−5.06120	−	22.8714i	−0.181220	−	0.818928i
$781$	−30.8496	−	25.3176i	−1.10389	−	0.905936i
$782$	−11.2547	−	23.1510i	−0.402468	−	0.827878i
$783$	1.67711	+	0.694682i	0.0599351	+	0.0248259i
$784$	27.5771	−	20.1876i	0.984895	−	0.720985i
$785$	18.2207	−	7.54724i	0.650323	−	0.269373i
$786$	−8.39984	−	7.45080i	−0.299612	−	0.265761i
$787$	−3.22103	−	32.7037i	−0.114817	−	1.16576i	−0.864033	−	0.503435i	$-0.832069\pi$
$787$	−3.22103	−	32.7037i	−0.114817	−	1.16576i	0.749216	−	0.662326i	$-0.230431\pi$
$788$	28.0311	−	12.3211i	0.998567	−	0.438919i
$789$	8.20334	−	15.3474i	0.292047	−	0.546381i
$790$	−0.973225	−	6.10921i	−0.0346258	−	0.217356i
$791$	21.0471	−	4.18652i	0.748348	−	0.148856i
$792$	−8.06733	−	6.85267i	−0.286660	−	0.243499i
$793$	−19.5570	+	98.3195i	−0.694488	+	3.49143i
$794$	25.7134	−	23.8121i	0.912535	−	0.845059i
$795$	1.39828	−	14.1969i	0.0495918	−	0.503514i
$796$	7.62196	+	23.3155i	0.270153	+	0.826395i
$797$	−5.83610	+	19.2390i	−0.206725	+	0.681482i	0.790858	+	0.612000i	$0.209635\pi$
$797$	−5.83610	+	19.2390i	−0.206725	+	0.681482i	−0.997583	+	0.0694820i	$0.977865\pi$
$798$	11.3715	−	19.4417i	0.402548	−	0.688228i
$799$	−17.8420	−	17.8420i	−0.631204	−	0.631204i
$800$	−6.55236	−	7.91139i	−0.231661	−	0.279710i
$801$	6.48064	−	6.48064i	0.228982	−	0.228982i
$802$	6.04688	+	23.0880i	0.213523	+	0.815267i
$803$	−16.4805	−	4.99929i	−0.581583	−	0.176421i
$804$	3.47484	+	4.05376i	0.122548	+	0.142965i
$805$	31.8717	+	3.13909i	1.12333	+	0.110638i
$806$	1.40490	+	0.0539356i	0.0494854	+	0.00189980i
$807$	−3.85081	−	0.765973i	−0.135555	−	0.0269635i
$808$	12.5355	+	6.97592i	0.440996	+	0.245412i
$809$	7.59256	+	38.1704i	0.266940	+	1.34200i	0.848802	+	0.528711i	$0.177325\pi$
$809$	7.59256	+	38.1704i	0.266940	+	1.34200i	−0.581862	+	0.813288i	$0.697675\pi$
$810$	2.04290	+	1.48145i	0.0717801	+	0.0520529i
$811$	−39.1854	−	20.9450i	−1.37599	−	0.735480i	−0.393066	−	0.919510i	$-0.628586\pi$
$811$	−39.1854	−	20.9450i	−1.37599	−	0.735480i	−0.982921	+	0.184030i	$0.941086\pi$
$812$	0.306728	+	14.3107i	0.0107640	+	0.502206i
$813$	−9.50198	+	0.935863i	−0.333249	+	0.0328221i
$814$	−1.89921	−	31.7202i	−0.0665674	−	1.11179i
$815$	−11.9435	−	28.8343i	−0.418364	−	1.01002i
$816$	15.0923	−	5.29432i	0.528335	−	0.185338i
$817$	11.0639	−	26.7106i	0.387077	−	0.934486i
$818$	−12.9235	−	4.46849i	−0.451860	−	0.156237i
$819$	16.4170	−	20.0042i	0.573658	−	0.699004i
$820$	7.97116	−	5.57687i	0.278365	−	0.194753i
$821$	−7.47795	−	24.6515i	−0.260982	−	0.860343i	−0.985294	−	0.170870i	$-0.945342\pi$
$821$	−7.47795	−	24.6515i	−0.260982	−	0.860343i	0.724311	−	0.689473i	$-0.242158\pi$
$822$	−6.20100	−	1.48284i	−0.216285	−	0.0517201i
$823$	0.918848	+	0.613954i	0.0320290	+	0.0214011i	0.571482	−	0.820615i	$-0.306369\pi$
$823$	0.918848	+	0.613954i	0.0320290	+	0.0214011i	−0.539453	+	0.842016i	$0.681369\pi$
$824$	−6.31020	−	4.37276i	−0.219826	−	0.152332i
$825$	3.77557	+	5.65053i	0.131448	+	0.196726i
$826$	−58.6492	−	26.9738i	−2.04067	−	0.938539i
$827$	−8.87782	+	7.28584i	−0.308712	+	0.253353i	−0.775973	−	0.630766i	$-0.782741\pi$
$827$	−8.87782	+	7.28584i	−0.308712	+	0.253353i	0.467261	+	0.884119i	$0.345241\pi$
$828$	−5.62371	+	7.16005i	−0.195438	+	0.248829i
$829$	17.3200	+	32.4035i	0.601550	+	1.12542i	0.979849	+	0.199737i	$0.0640089\pi$
$829$	17.3200	+	32.4035i	0.601550	+	1.12542i	−0.378300	+	0.925683i	$0.623491\pi$
$830$	5.91398	−	4.48512i	0.205277	−	0.155681i
$831$		−	26.8347i		−	0.930884i
$832$	3.37359	+	52.4017i	0.116958	+	1.81670i
$833$		−	34.1636i		−	1.18370i
$834$	17.6691	+	23.2981i	0.611832	+	0.806748i
$835$	11.9290	+	22.3177i	0.412821	+	0.772334i
$836$	−3.60759	−	30.0186i	−0.124771	−	1.03821i
$837$	−0.117080	+	0.0960848i	−0.00404686	+	0.00332118i
$838$	−18.1881	+	39.5463i	−0.628296	+	1.36610i
$839$	23.5473	+	35.2410i	0.812942	+	1.21665i	0.973287	+	0.229592i	$0.0737392\pi$
$839$	23.5473	+	35.2410i	0.812942	+	1.21665i	−0.160345	+	0.987061i	$0.551261\pi$
$840$	−4.21207	+	19.4475i	−0.145330	+	0.671004i
$841$	21.3727	+	14.2808i	0.736989	+	0.492440i
$842$	11.0941	−	46.3936i	0.382328	−	1.59883i
$843$	0.614076	+	2.02434i	0.0211499	+	0.0697219i
$844$	−2.99064	−	0.528522i	−0.102942	−	0.0181925i
$845$	34.0543	−	41.4953i	1.17150	−	1.42748i
$846$	−2.91632	+	8.43442i	−0.100265	+	0.289981i
$847$	−4.53402	+	10.9461i	−0.155791	+	0.376112i
$848$	−7.96318	+	30.9713i	−0.273457	+	1.06356i
$849$	5.29019	+	12.7716i	0.181559	+	0.438322i
$850$	−10.2502	+	0.613720i	−0.351580	+	0.0210504i
$851$	−27.2011	+	2.67907i	−0.932441	+	0.0918374i
$852$	−15.4009	−	14.7546i	−0.527627	−	0.505484i
$853$	11.6382	+	6.22073i	0.398484	+	0.212994i	0.658451	−	0.752623i	$-0.271212\pi$
$853$	11.6382	+	6.22073i	0.398484	+	0.212994i	−0.259968	+	0.965617i	$0.583712\pi$
$854$	49.9910	−	68.9368i	1.71066	−	2.35897i
$855$	1.40623	+	7.06961i	0.0480921	+	0.241776i
$856$	23.4601	+	29.5947i	0.801848	+	1.01153i
$857$	−16.0644	−	3.19540i	−0.548749	−	0.109153i	−0.0870733	−	0.996202i	$-0.527751\pi$
$857$	−16.0644	−	3.19540i	−0.548749	−	0.109153i	−0.461675	+	0.887049i	$0.652751\pi$
$858$	1.33267	−	34.7130i	0.0454966	−	1.18508i
$859$	−27.6459	−	2.72288i	−0.943265	−	0.0929035i	−0.385322	−	0.922782i	$-0.625910\pi$
$859$	−27.6459	−	2.72288i	−0.943265	−	0.0929035i	−0.557944	+	0.829879i	$0.688410\pi$
$860$	−1.95831	+	25.4671i	−0.0667776	+	0.868420i
$861$	10.2846	+	3.11979i	0.350497	+	0.106322i
$862$	−43.1059	+	11.2897i	−1.46819	+	0.384527i
$863$	−21.2405	+	21.2405i	−0.723035	+	0.723035i	−0.969222	−	0.246187i	$-0.920822\pi$
$863$	−21.2405	+	21.2405i	−0.723035	+	0.723035i	0.246187	+	0.969222i	$0.420822\pi$
$864$	−4.01791	−	3.98201i	−0.136692	−	0.135471i
$865$	−26.3191	−	26.3191i	−0.894876	−	0.894876i
$866$	−23.2640	−	13.6072i	−0.790541	−	0.462391i
$867$	−0.293801	+	0.968531i	−0.00997799	+	0.0328930i
$868$	−1.06509	−	0.540284i	−0.0361515	−	0.0183384i
$869$	0.899220	−	9.12993i	0.0305040	−	0.309712i
$870$	−3.11255	−	3.36108i	−0.105525	−	0.113951i
$871$	−3.41852	+	17.1861i	−0.115832	+	0.582328i
$872$	41.6151	+	13.3978i	1.40927	+	0.453706i
$873$	−15.3494	+	3.05319i	−0.519499	+	0.103335i
$874$	−25.6821	+	4.09128i	−0.868711	+	0.138390i
$875$	22.6040	−	42.2892i	0.764156	−	1.42964i
$876$	−8.57680	−	3.33915i	−0.289783	−	0.112819i
$877$	0.331895	+	3.36979i	0.0112073	+	0.113790i	0.999161	−	0.0409620i	$-0.0130423\pi$
$877$	0.331895	+	3.36979i	0.0112073	+	0.113790i	−0.987953	+	0.154752i	$0.950542\pi$
$878$	18.2739	−	20.6016i	0.616715	−	0.695269i
$879$	22.8323	−	9.45744i	0.770114	−	0.318992i
$880$	11.2700	+	24.2173i	0.379910	+	0.816367i
$881$	15.3685	+	6.36585i	0.517778	+	0.214471i	0.626241	−	0.779630i	$-0.284593\pi$
$881$	15.3685	+	6.36585i	0.517778	+	0.214471i	−0.108462	+	0.994101i	$0.534593\pi$
$882$	−10.8671	+	5.28298i	−0.365915	+	0.177887i
$883$	14.2112	+	11.6628i	0.478246	+	0.392486i	0.842400	−	0.538853i	$-0.181142\pi$
$883$	14.2112	+	11.6628i	0.478246	+	0.392486i	−0.364155	+	0.931339i	$0.618642\pi$
$884$	44.2589	+	28.2201i	1.48859	+	0.949145i
$885$	19.7700	−	5.99715i	0.664560	−	0.201592i
$886$	12.1440	+	19.7773i	0.407986	+	0.664433i
$887$	2.42145	−	3.62396i	0.0813044	−	0.121681i	−0.788589	−	0.614921i	$-0.789188\pi$
$887$	2.42145	−	3.62396i	0.0813044	−	0.121681i	0.869893	+	0.493241i	$0.164188\pi$
$888$	0.287704	−	16.9800i	0.00965470	−	0.569811i
$889$	−36.3564	+	24.2925i	−1.21935	+	0.814746i
$890$	−21.6913	+	8.02448i	−0.727095	+	0.268981i
$891$	2.37412	+	2.89287i	0.0795359	+	0.0969147i
$892$	−6.52976	+	3.67225i	−0.218632	+	0.122956i
$893$	−22.4814	+	12.0165i	−0.752310	+	0.402118i
$894$	−25.1556	−	3.45643i	−0.841330	−	0.115600i
$895$	10.0599			0.336265
$896$	15.9961	−	41.6386i	0.534391	−	1.39105i
$897$	−29.8800			−0.997665
$898$	9.51469	+	1.30734i	0.317509	+	0.0436264i
$899$	0.242478	−	0.129607i	0.00808709	−	0.00432264i
$900$	1.78029	+	3.16560i	0.0593431	+	0.105520i
$901$	20.2793	+	24.7105i	0.675603	+	0.823225i
$902$	13.5308	−	5.00558i	0.450527	−	0.166668i
$903$	−23.4621	+	15.6769i	−0.780771	+	0.521694i
$904$	11.0688	−	10.6999i	0.368142	−	0.355874i
$905$	8.56819	−	12.8232i	0.284816	−	0.426258i
$906$	11.0606	+	18.0129i	0.367462	+	0.598438i
$907$	−33.2565	+	10.0882i	−1.10426	+	0.334975i	−0.789225	−	0.614104i	$-0.789517\pi$
$907$	−33.2565	+	10.0882i	−1.10426	+	0.334975i	−0.315038	+	0.949079i	$0.602017\pi$
$908$	−30.8015	+	48.3075i	−1.02219	+	1.60314i
$909$	−3.92071	−	3.21764i	−0.130042	−	0.106722i
$910$	−58.7319	+	28.5522i	−1.94694	+	0.946496i
$911$	−44.4217	−	18.4001i	−1.47176	−	0.609622i	−0.504499	−	0.863412i	$-0.668323\pi$
$911$	−44.4217	−	18.4001i	−1.47176	−	0.609622i	−0.967259	+	0.253790i	$0.918323\pi$
$912$	−0.692331	−	16.1433i	−0.0229254	−	0.534557i
$913$	10.1694	−	4.21230i	0.336558	−	0.139407i
$914$	9.11801	−	10.2794i	0.301597	−	0.340013i
$915$	2.67119	+	27.1211i	0.0883069	+	0.896595i
$916$	2.04096	−	5.24233i	0.0674353	−	0.173211i
$917$	−14.7558	+	27.6062i	−0.487280	+	0.911638i
$918$	−5.58430	+	0.889605i	−0.184309	+	0.0293613i
$919$	−18.9780	+	3.77497i	−0.626028	+	0.124525i	−0.497902	−	0.867233i	$-0.665896\pi$
$919$	−18.9780	+	3.77497i	−0.626028	+	0.124525i	−0.128126	+	0.991758i	$0.540896\pi$
$920$	20.4431	−	10.4857i	0.673989	−	0.345704i
$921$	3.40322	−	17.1091i	0.112140	−	0.563765i
$922$	−19.1455	−	20.6742i	−0.630522	−	0.680868i
$923$	6.86083	−	69.6592i	0.225827	−	2.29286i
$924$	−13.3496	+	26.3168i	−0.439171	+	0.865760i
$925$	−3.16504	+	10.4337i	−0.104066	+	0.343059i
$926$	20.6432	+	12.0743i	0.678379	+	0.396787i
$927$	1.91930	+	1.91930i	0.0630382	+	0.0630382i
$928$	5.74333	+	8.51254i	0.188534	+	0.279438i
$929$	−14.9966	+	14.9966i	−0.492022	+	0.492022i	−0.908943	−	0.416921i	$-0.863109\pi$
$929$	−14.9966	+	14.9966i	−0.492022	+	0.492022i	0.416921	+	0.908943i	$0.363109\pi$
$930$	0.369739	−	0.0968367i	0.0121242	−	0.00317540i
$931$	−33.0280	−	10.0189i	−1.08245	−	0.328358i
$932$	−7.84629	−	0.603345i	−0.257014	−	0.0197632i
$933$	−25.7795	−	2.53906i	−0.843982	−	0.0831250i
$934$	−1.07595	+	28.0261i	−0.0352062	+	0.917041i
$935$	26.1881	+	5.20914i	0.856442	+	0.170357i
$936$	2.13244	−	18.4423i	0.0697011	−	0.602804i
$937$	−3.44833	−	17.3359i	−0.112652	−	0.566340i	−0.995344	−	0.0963877i	$-0.969271\pi$
$937$	−3.44833	−	17.3359i	−0.112652	−	0.566340i	0.882692	−	0.469952i	$-0.155729\pi$
$938$	8.73834	−	12.0500i	0.285317	−	0.393447i
$939$	−26.6364	−	14.2375i	−0.869248	−	0.464623i
$940$	15.5797	−	16.2622i	0.508154	−	0.530414i
$941$	24.3922	−	2.40243i	0.795165	−	0.0783169i	0.307727	−	0.951475i	$-0.400432\pi$
$941$	24.3922	−	2.40243i	0.795165	−	0.0783169i	0.487438	+	0.873158i	$0.337932\pi$
$942$	15.6025	−	0.934185i	0.508358	−	0.0304374i
$943$	−4.74882	−	11.4647i	−0.154643	−	0.373341i
$944$	−45.8518	+	6.50993i	−1.49235	+	0.211880i
$945$	2.69224	−	6.49964i	0.0875786	−	0.211433i
$946$	−12.3781	+	35.7993i	−0.402447	+	1.16393i
$947$	19.1253	−	23.3042i	0.621489	−	0.757286i	−0.363180	−	0.931719i	$-0.618309\pi$
$947$	19.1253	−	23.3042i	0.621489	−	0.757286i	0.984669	+	0.174433i	$0.0558091\pi$
$948$	0.853241	−	4.82806i	0.0277120	−	0.156808i
$949$	−8.76836	−	28.9054i	−0.284633	−	0.938309i
$950$	−2.41270	+	10.0895i	−0.0782783	+	0.327347i
$951$	1.60207	+	1.07047i	0.0519507	+	0.0347123i
$952$	−24.1405	−	37.4884i	−0.782397	−	1.21501i
$953$	−3.07186	−	4.59737i	−0.0995074	−	0.148923i	0.778375	−	0.627800i	$-0.216044\pi$
$953$	−3.07186	−	4.59737i	−0.0995074	−	0.148923i	−0.877882	+	0.478876i	$0.841044\pi$
$954$	4.72421	−	10.2719i	0.152952	−	0.332563i
$955$	14.9886	−	12.3008i	0.485019	−	0.398045i
$956$	−24.1841	+	2.90641i	−0.782169	+	0.0940000i
$957$	−3.20241	−	5.99128i	−0.103519	−	0.193671i
$958$	−11.2460	−	14.8288i	−0.363343	−	0.479096i
$959$			17.7748i			0.573979i
$960$	5.01294	+	13.3660i	0.161792	+	0.431387i
$961$		−	30.9771i		−	0.999260i
$962$	44.4079	−	33.6787i	1.43177	−	1.08584i
$963$	−6.29412	−	11.7755i	−0.202825	−	0.379459i
$964$	33.3163	+	26.1676i	1.07305	+	0.842802i
$965$	11.8918	−	9.75932i	0.382810	−	0.314164i
$966$	23.0600	+	10.6057i	0.741943	+	0.341233i
$967$	14.6294	+	21.8945i	0.470450	+	0.704078i	0.988491	−	0.151277i	$-0.0483386\pi$
$967$	14.6294	+	21.8945i	0.470450	+	0.704078i	−0.518041	+	0.855356i	$0.673339\pi$
$968$	1.51675	+	8.36332i	0.0487502	+	0.268807i
$969$	−13.4299	−	8.97356i	−0.431430	−	0.288272i
$970$	38.4104	+	9.18507i	1.23328	+	0.294915i
$971$	−13.2371	−	43.6369i	−0.424800	−	1.40038i	−0.864681	−	0.502321i	$-0.832480\pi$
$971$	−13.2371	−	43.6369i	−0.424800	−	1.40038i	0.439882	−	0.898056i	$-0.355020\pi$
$972$	1.14652	+	1.63875i	0.0367746	+	0.0525628i
$973$	51.7142	−	63.0140i	1.65788	−	2.02014i
$974$	−25.6517	−	8.86944i	−0.821932	−	0.284195i
$975$	−4.56134	+	11.0121i	−0.146080	+	0.352668i
$976$	3.37745	−	60.9969i	0.108109	−	1.95246i
$977$	13.2579	+	32.0073i	0.424156	+	1.02400i	0.981108	+	0.193459i	$0.0619707\pi$
$977$	13.2579	+	32.0073i	0.424156	+	1.02400i	−0.556952	+	0.830545i	$0.688029\pi$
$978$	−1.47835	−	24.6911i	−0.0472725	−	0.789534i
$979$	−34.1334	+	3.36185i	−1.09091	+	0.107445i
$980$	30.4852	−	0.653404i	0.973814	−	0.0208722i
$981$	−13.6317	−	7.28632i	−0.435228	−	0.232634i
$982$	2.13199	+	1.54606i	0.0680345	+	0.0493367i
$983$	−6.07524	−	30.5423i	−0.193770	−	0.974148i	−0.948177	−	0.317741i	$-0.897076\pi$
$983$	−6.07524	−	30.5423i	−0.193770	−	0.974148i	0.754407	−	0.656406i	$-0.227924\pi$
$984$	7.41502	−	2.11282i	0.236382	−	0.0673544i
$985$	26.7937	+	5.32960i	0.853718	+	0.169815i
$986$	10.2574	+	0.393793i	0.326662	+	0.0125409i
$987$	24.7599	+	2.43864i	0.788117	+	0.0776228i
$988$	40.2617	−	34.5119i	1.28090	−	1.09797i
$989$	31.1781	+	9.45779i	0.991407	+	0.300740i
$990$	−2.39270	−	9.13572i	−0.0760449	−	0.290352i
$991$	−14.9473	+	14.9473i	−0.474815	+	0.474815i	−0.903469	−	0.428654i	$-0.858988\pi$
$991$	−14.9473	+	14.9473i	−0.474815	+	0.474815i	0.428654	+	0.903469i	$0.358988\pi$
$992$	−0.852272	+	0.0878054i	−0.0270597	+	0.00278783i
$993$	−7.71835	−	7.71835i	−0.244934	−	0.244934i
$994$	−30.0200	+	51.3245i	−0.952175	+	1.62791i
$995$	−6.35298	+	20.9430i	−0.201403	+	0.663937i
$996$	5.59137	−	1.82785i	0.177169	−	0.0579177i
$997$	1.07636	−	10.9285i	0.0340886	−	0.346108i	−0.962979	−	0.269578i	$-0.913116\pi$
$997$	1.07636	−	10.9285i	0.0340886	−	0.346108i	0.997067	−	0.0765300i	$-0.0243841\pi$
$998$	−17.9119	+	16.5874i	−0.566992	+	0.525067i
$999$	−1.17136	+	5.88883i	−0.0370602	+	0.186314i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.17	yes	512
128.109	even	32	inner	384.2.v.a.109.17	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.17	✓	512	128.109	even	32	inner
384.2.v.a.229.17	yes	512	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.192507 - 1.40105i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.92588 - 0.539424i) q^{4} +(-1.13201 - 1.37936i) q^{5} +(-0.490674 - 1.32636i) q^{6} +(-3.27816 + 2.19039i) q^{7} +(-1.12651 + 2.59441i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.192507 - 1.40105i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.92588 - 0.539424i) q^{4} +(-1.13201 - 1.37936i) q^{5} +(-0.490674 - 1.32636i) q^{6} +(-3.27816 + 2.19039i) q^{7} +(-1.12651 + 2.59441i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-2.15047 + 1.32046i) q^{10} +(-3.58120 + 1.08634i) q^{11} +(-1.95276 + 0.432125i) q^{12} +(-5.07386 - 4.16401i) q^{13} +(2.43778 + 5.01453i) q^{14} +(-1.64857 - 0.682859i) q^{15} +(3.41804 + 2.07774i) q^{16} +(3.69412 - 1.53015i) q^{17} +(-1.05798 - 0.938446i) q^{18} +(-0.395943 - 4.02007i) q^{19} +(1.43606 + 3.26711i) q^{20} +(-1.85853 + 3.47707i) q^{21} +(0.832616 + 5.22656i) q^{22} +(4.46479 - 0.888103i) q^{23} +(0.229508 + 2.81910i) q^{24} +(0.354271 - 1.78104i) q^{25} +(-6.81074 + 6.30713i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(7.49489 - 2.45012i) q^{28} +(-0.526952 + 1.73713i) q^{29} +(-1.27408 + 2.17827i) q^{30} +(-0.107098 - 0.107098i) q^{31} +(3.56901 - 4.38887i) q^{32} +(-2.64623 + 2.64623i) q^{33} +(-1.43268 - 5.47021i) q^{34} +(6.73223 + 2.04220i) q^{35} +(-1.51848 + 1.30162i) q^{36} +(-5.97528 - 0.588514i) q^{37} +(-5.70855 - 0.219158i) q^{38} +(-6.43765 - 1.28053i) q^{39} +(4.85384 - 1.38304i) q^{40} +(-0.531807 - 2.67357i) q^{41} +(4.51376 + 3.27325i) q^{42} +(6.31201 + 3.37384i) q^{43} +(7.48296 - 0.160386i) q^{44} +(-1.77580 + 0.174901i) q^{45} +(-0.384771 - 6.42637i) q^{46} +(-2.41492 - 5.83013i) q^{47} +(3.99388 + 0.221145i) q^{48} +(3.26969 - 7.89374i) q^{49} +(-2.42713 - 0.839214i) q^{50} +(2.53661 - 3.09087i) q^{51} +(7.52549 + 10.7564i) q^{52} +(2.32073 + 7.65041i) q^{53} +(-1.37543 - 0.328907i) q^{54} +(5.55240 + 3.71000i) q^{55} +(-1.98992 - 10.9724i) q^{56} +(-2.24424 - 3.35874i) q^{57} +(2.33236 + 1.07269i) q^{58} +(-8.94984 + 7.34494i) q^{59} +(2.80659 + 2.20438i) q^{60} +(-7.19944 - 13.4692i) q^{61} +(-0.170667 + 0.129432i) q^{62} +3.94260i q^{63} +(-5.46197 - 5.84525i) q^{64} +11.7124i q^{65} +(3.19809 + 4.21693i) q^{66} +(-1.25845 - 2.35439i) q^{67} +(-7.93984 + 0.954199i) q^{68} +(3.51895 - 2.88793i) q^{69} +(4.15723 - 9.03906i) q^{70} +(5.92462 + 8.86682i) q^{71} +(1.53132 + 2.37804i) q^{72} +(3.82637 + 2.55670i) q^{73} +(-1.97482 + 8.25838i) q^{74} +(-0.527137 - 1.73774i) q^{75} +(-1.40599 + 7.95577i) q^{76} +(9.36020 - 11.4054i) q^{77} +(-3.03338 + 8.77296i) q^{78} +(-0.938124 + 2.26483i) q^{79} +(-1.00332 - 7.06671i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-3.84819 + 0.230406i) q^{82} +(-2.92711 + 0.288296i) q^{83} +(5.45492 - 5.69388i) q^{84} +(-6.29240 - 3.36336i) q^{85} +(5.94203 - 8.19396i) q^{86} +(0.354146 + 1.78041i) q^{87} +(1.21582 - 10.5149i) q^{88} +(8.98890 + 1.78800i) q^{89} +(-0.0968093 + 2.52166i) q^{90} +(25.7537 + 2.53652i) q^{91} +(-9.07773 - 0.698037i) q^{92} +(-0.144938 - 0.0439663i) q^{93} +(-8.63319 + 2.26108i) q^{94} +(-5.09690 + 5.09690i) q^{95} +(1.07869 - 5.55306i) q^{96} +(-11.0663 - 11.0663i) q^{97} +(-10.4301 - 6.10061i) q^{98} +(-1.08634 + 3.58120i) 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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