LMFDB - Embedded newform 384.2.v.a.229.18

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			229.18
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.208677 + 1.39873i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.91291 + 0.583766i) q^{4} +(1.48823 + 1.81341i) q^{5} +(0.843395 + 1.13520i) q^{6} +(2.68193 - 1.79201i) q^{7} +(-1.21571 - 2.55383i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})$	\(q+(0.208677 + 1.39873i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.91291 + 0.583766i) q^{4} +(1.48823 + 1.81341i) q^{5} +(0.843395 + 1.13520i) q^{6} +(2.68193 - 1.79201i) q^{7} +(-1.21571 - 2.55383i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-2.22592 + 2.46005i) q^{10} +(-0.671156 + 0.203593i) q^{11} +(-1.41185 + 1.41657i) q^{12} +(4.24699 + 3.48542i) q^{13} +(3.06620 + 3.37735i) q^{14} +(2.16734 + 0.897740i) q^{15} +(3.31843 - 2.23338i) q^{16} +(-4.31273 + 1.78639i) q^{17} +(1.27894 + 0.603586i) q^{18} +(-0.0391274 - 0.397267i) q^{19} +(-3.90545 - 2.60011i) q^{20} +(1.52050 - 2.84466i) q^{21} +(-0.424827 - 0.896283i) q^{22} +(-2.48258 + 0.493815i) q^{23} +(-2.27603 - 1.67919i) q^{24} +(-0.0981862 + 0.493616i) q^{25} +(-3.98892 + 6.66774i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-4.08417 + 4.99357i) q^{28} +(-0.449375 + 1.48139i) q^{29} +(-0.803426 + 3.21886i) q^{30} +(-3.23930 - 3.23930i) q^{31} +(3.81638 + 4.17555i) q^{32} +(-0.495934 + 0.495934i) q^{33} +(-3.39865 - 5.65958i) q^{34} +(7.24097 + 2.19653i) q^{35} +(-0.577371 + 1.91485i) q^{36} +(-6.20193 - 0.610836i) q^{37} +(0.547505 - 0.137629i) q^{38} +(5.38853 + 1.07184i) q^{39} +(2.82189 - 6.00527i) q^{40} +(1.22543 + 6.16066i) q^{41} +(4.29622 + 1.53316i) q^{42} +(10.2279 + 5.46694i) q^{43} +(1.16501 - 0.781253i) q^{44} +(2.33461 - 0.229939i) q^{45} +(-1.20877 - 3.36941i) q^{46} +(-3.46695 - 8.36996i) q^{47} +(1.87379 - 3.53397i) q^{48} +(1.30267 - 3.14492i) q^{49} +(-0.710925 - 0.0343303i) q^{50} +(-2.96139 + 3.60846i) q^{51} +(-10.1588 - 4.18803i) q^{52} +(-2.45565 - 8.09520i) q^{53} +(1.41245 - 0.0705720i) q^{54} +(-1.36803 - 0.914089i) q^{55} +(-7.83694 - 4.67063i) q^{56} +(-0.221777 - 0.331913i) q^{57} +(-2.16585 - 0.319424i) q^{58} +(2.49418 - 2.04692i) q^{59} +(-4.66999 - 0.452077i) q^{60} +(-5.58448 - 10.4478i) q^{61} +(3.85495 - 5.20688i) q^{62} -3.22553i q^{63} +(-5.04409 + 6.20944i) q^{64} +12.8886i q^{65} +(-0.797169 - 0.590189i) q^{66} +(-6.84973 - 12.8149i) q^{67} +(7.20702 - 5.93483i) q^{68} +(-1.95665 + 1.60578i) q^{69} +(-1.56133 + 10.5866i) q^{70} +(7.22361 + 10.8109i) q^{71} +(-2.79884 - 0.408004i) q^{72} +(-4.10328 - 2.74172i) q^{73} +(-0.439800 - 8.80231i) q^{74} +(0.146096 + 0.481615i) q^{75} +(0.306758 + 0.737094i) q^{76} +(-1.43515 + 1.74874i) q^{77} +(-0.374765 + 7.76078i) q^{78} +(3.49016 - 8.42599i) q^{79} +(8.98863 + 2.69391i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-8.36141 + 2.99964i) q^{82} +(2.18497 - 0.215201i) q^{83} +(-1.24797 + 6.32920i) q^{84} +(-9.65779 - 5.16220i) q^{85} +(-5.51246 + 15.4470i) q^{86} +(0.302010 + 1.51831i) q^{87} +(1.33587 + 1.46651i) q^{88} +(-0.00810227 - 0.00161164i) q^{89} +(0.808803 + 3.21752i) q^{90} +(17.6360 + 1.73700i) q^{91} +(4.46067 - 2.39387i) q^{92} +(-4.38380 - 1.32981i) q^{93} +(10.9839 - 6.59595i) q^{94} +(0.662178 - 0.662178i) q^{95} +(5.33409 + 1.88348i) q^{96} +(2.67206 + 2.67206i) q^{97} +(4.67075 + 1.16582i) q^{98} +(-0.203593 + 0.671156i) 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 $

$2$	0.208677	+	1.39873i	0.147557	+	0.989054i
$2$	0.208677	+	1.39873i	0.147557	+	0.989054i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	−1.91291	+	0.583766i	−0.956454	+	0.291883i
$5$	1.48823	+	1.81341i	0.665556	+	0.810982i	0.990898	−	0.134614i	$-0.0429795\pi$
$5$	1.48823	+	1.81341i	0.665556	+	0.810982i	−0.325342	+	0.945596i	$0.605479\pi$
$6$	0.843395	+	1.13520i	0.344314	+	0.463445i
$7$	2.68193	−	1.79201i	1.01367	−	0.677315i	0.0664177	−	0.997792i	$-0.478843\pi$
$7$	2.68193	−	1.79201i	1.01367	−	0.677315i	0.947256	+	0.320476i	$0.103843\pi$
$8$	−1.21571	−	2.55383i	−0.429819	−	0.902915i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	−2.22592	+	2.46005i	−0.703898	+	0.777936i
$11$	−0.671156	+	0.203593i	−0.202361	+	0.0613856i	−0.389838	−	0.920883i	$-0.627469\pi$
$11$	−0.671156	+	0.203593i	−0.202361	+	0.0613856i	0.187477	+	0.982269i	$0.439969\pi$
$12$	−1.41185	+	1.41657i	−0.407566	+	0.408930i
$13$	4.24699	+	3.48542i	1.17790	+	0.966681i	0.999850	−	0.0173397i	$-0.00551967\pi$
$13$	4.24699	+	3.48542i	1.17790	+	0.966681i	0.178054	+	0.984021i	$0.443020\pi$
$14$	3.06620	+	3.37735i	0.819476	+	0.902636i
$15$	2.16734	+	0.897740i	0.559604	+	0.231796i
$16$	3.31843	−	2.23338i	0.829609	−	0.558345i
$17$	−4.31273	+	1.78639i	−1.04599	+	0.433264i	−0.838459	−	0.544965i	$-0.816543\pi$
$17$	−4.31273	+	1.78639i	−1.04599	+	0.433264i	−0.207532	+	0.978228i	$0.566543\pi$
$18$	1.27894	+	0.603586i	0.301449	+	0.142267i
$19$	−0.0391274	−	0.397267i	−0.00897643	−	0.0911392i	0.989653	−	0.143484i	$-0.0458305\pi$
$19$	−0.0391274	−	0.397267i	−0.00897643	−	0.0911392i	−0.998629	+	0.0523447i	$0.983331\pi$
$20$	−3.90545	−	2.60011i	−0.873286	−	0.581403i
$21$	1.52050	−	2.84466i	0.331801	−	0.620756i
$22$	−0.424827	−	0.896283i	−0.0905734	−	0.191088i
$23$	−2.48258	+	0.493815i	−0.517653	+	0.102968i	−0.447001	−	0.894533i	$-0.647508\pi$
$23$	−2.48258	+	0.493815i	−0.517653	+	0.102968i	−0.0706520	+	0.997501i	$0.522508\pi$
$24$	−2.27603	−	1.67919i	−0.464592	−	0.342764i
$25$	−0.0981862	+	0.493616i	−0.0196372	+	0.0987231i
$26$	−3.98892	+	6.66774i	−0.782292	+	1.30765i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−4.08417	+	4.99357i	−0.771836	+	0.943695i
$29$	−0.449375	+	1.48139i	−0.0834469	+	0.275088i	−0.988727	−	0.149727i	$-0.952161\pi$
$29$	−0.449375	+	1.48139i	−0.0834469	+	0.275088i	0.905280	+	0.424814i	$0.139661\pi$
$30$	−0.803426	+	3.21886i	−0.146685	+	0.587681i
$31$	−3.23930	−	3.23930i	−0.581795	−	0.581795i	0.353601	−	0.935396i	$-0.384957\pi$
$31$	−3.23930	−	3.23930i	−0.581795	−	0.581795i	−0.935396	+	0.353601i	$0.884957\pi$
$32$	3.81638	+	4.17555i	0.674648	+	0.738140i
$33$	−0.495934	+	0.495934i	−0.0863310	+	0.0863310i
$34$	−3.39865	−	5.65958i	−0.582864	−	0.970610i
$35$	7.24097	+	2.19653i	1.22395	+	0.371281i
$36$	−0.577371	+	1.91485i	−0.0962285	+	0.319141i
$37$	−6.20193	−	0.610836i	−1.01959	−	0.100421i	−0.425615	−	0.904904i	$-0.639942\pi$
$37$	−6.20193	−	0.610836i	−1.01959	−	0.100421i	−0.593975	+	0.804483i	$0.702442\pi$
$38$	0.547505	−	0.137629i	0.0888171	−	0.0223264i
$39$	5.38853	+	1.07184i	0.862855	+	0.171633i
$40$	2.82189	−	6.00527i	0.446179	−	0.949516i
$41$	1.22543	+	6.16066i	0.191380	+	0.962134i	0.950391	+	0.311056i	$0.100683\pi$
$41$	1.22543	+	6.16066i	0.191380	+	0.962134i	−0.759011	+	0.651078i	$0.774317\pi$
$42$	4.29622	+	1.53316i	0.662921	+	0.236572i
$43$	10.2279	+	5.46694i	1.55974	+	0.833701i	0.999987	+	0.00504352i	$0.00160541\pi$
$43$	10.2279	+	5.46694i	1.55974	+	0.833701i	0.559757	+	0.828657i	$0.310895\pi$
$44$	1.16501	−	0.781253i	0.175632	−	0.117778i
$45$	2.33461	−	0.229939i	0.348023	−	0.0342773i
$46$	−1.20877	−	3.36941i	−0.178224	−	0.496793i
$47$	−3.46695	−	8.36996i	−0.505707	−	1.22088i	−0.946333	−	0.323193i	$-0.895244\pi$
$47$	−3.46695	−	8.36996i	−0.505707	−	1.22088i	0.440626	−	0.897691i	$-0.354756\pi$
$48$	1.87379	−	3.53397i	0.270458	−	0.510084i
$49$	1.30267	−	3.14492i	0.186096	−	0.449275i
$50$	−0.710925	−	0.0343303i	−0.100540	−	0.00485503i
$51$	−2.96139	+	3.60846i	−0.414678	+	0.505286i
$52$	−10.1588	−	4.18803i	−1.40877	−	0.580776i
$53$	−2.45565	−	8.09520i	−0.337310	−	1.11196i	−0.947513	−	0.319716i	$-0.896412\pi$
$53$	−2.45565	−	8.09520i	−0.337310	−	1.11196i	0.610204	−	0.792245i	$-0.291088\pi$
$54$	1.41245	−	0.0705720i	0.192210	−	0.00960364i
$55$	−1.36803	−	0.914089i	−0.184465	−	0.123256i
$56$	−7.83694	−	4.67063i	−1.04725	−	0.624139i
$57$	−0.221777	−	0.331913i	−0.0293751	−	0.0439630i
$58$	−2.16585	−	0.319424i	−0.284390	−	0.0419425i
$59$	2.49418	−	2.04692i	0.324715	−	0.266486i	−0.457885	−	0.889011i	$-0.651393\pi$
$59$	2.49418	−	2.04692i	0.324715	−	0.266486i	0.782600	+	0.622525i	$0.213893\pi$
$60$	−4.66999	−	0.452077i	−0.602893	−	0.0583629i
$61$	−5.58448	−	10.4478i	−0.715019	−	1.33771i	−0.932332	−	0.361605i	$-0.882229\pi$
$61$	−5.58448	−	10.4478i	−0.715019	−	1.33771i	0.217312	−	0.976102i	$-0.430271\pi$
$62$	3.85495	−	5.20688i	0.489579	−	0.661275i
$63$		−	3.22553i		−	0.406379i
$64$	−5.04409	+	6.20944i	−0.630511	+	0.776180i
$65$			12.8886i			1.59864i
$66$	−0.797169	−	0.590189i	−0.0981247	−	0.0726472i
$67$	−6.84973	−	12.8149i	−0.836827	−	1.56559i	−0.824633	−	0.565668i	$-0.808618\pi$
$67$	−6.84973	−	12.8149i	−0.836827	−	1.56559i	−0.0121942	−	0.999926i	$-0.503882\pi$
$68$	7.20702	−	5.93483i	0.873980	−	0.719704i
$69$	−1.95665	+	1.60578i	−0.235553	+	0.193314i
$70$	−1.56133	+	10.5866i	−0.186615	+	1.26533i
$71$	7.22361	+	10.8109i	0.857285	+	1.28302i	0.957611	+	0.288063i	$0.0930113\pi$
$71$	7.22361	+	10.8109i	0.857285	+	1.28302i	−0.100326	+	0.994955i	$0.531989\pi$
$72$	−2.79884	−	0.408004i	−0.329847	−	0.0480837i
$73$	−4.10328	−	2.74172i	−0.480252	−	0.320894i	0.291771	−	0.956488i	$-0.405755\pi$
$73$	−4.10328	−	2.74172i	−0.480252	−	0.320894i	−0.772024	+	0.635594i	$0.780755\pi$
$74$	−0.439800	−	8.80231i	−0.0511257	−	1.02325i
$75$	0.146096	+	0.481615i	0.0168697	+	0.0556121i
$76$	0.306758	+	0.737094i	0.0351875	+	0.0845504i
$77$	−1.43515	+	1.74874i	−0.163551	+	0.199287i
$78$	−0.374765	+	7.76078i	−0.0424337	+	0.878736i
$79$	3.49016	−	8.42599i	0.392674	−	0.947998i	−0.596682	−	0.802478i	$-0.703514\pi$
$79$	3.49016	−	8.42599i	0.392674	−	0.947998i	0.989355	−	0.145520i	$-0.0464856\pi$
$80$	8.98863	+	2.69391i	1.00496	+	0.301188i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−8.36141	+	2.99964i	−0.923363	+	0.331255i
$83$	2.18497	−	0.215201i	0.239832	−	0.0236214i	0.0226128	−	0.999744i	$-0.492801\pi$
$83$	2.18497	−	0.215201i	0.239832	−	0.0236214i	0.217219	+	0.976123i	$0.430301\pi$
$84$	−1.24797	+	6.32920i	−0.136164	+	0.690572i
$85$	−9.65779	−	5.16220i	−1.04753	−	0.559919i
$86$	−5.51246	+	15.4470i	−0.594424	+	1.66569i
$87$	0.302010	+	1.51831i	0.0323788	+	0.162779i
$88$	1.33587	+	1.46651i	0.142405	+	0.156330i
$89$	−0.00810227	−	0.00161164i	−0.000858839	−	0.000170834i	0.194661	−	0.980871i	$-0.437639\pi$
$89$	−0.00810227	−	0.00161164i	−0.000858839	−	0.000170834i	−0.195520	+	0.980700i	$0.562639\pi$
$90$	0.808803	+	3.21752i	0.0852553	+	0.339156i
$91$	17.6360	+	1.73700i	1.84876	+	0.182087i
$92$	4.46067	−	2.39387i	0.465057	−	0.249578i
$93$	−4.38380	−	1.32981i	−0.454579	−	0.137895i
$94$	10.9839	−	6.59595i	1.13290	−	0.680321i
$95$	0.662178	−	0.662178i	0.0679380	−	0.0679380i
$96$	5.33409	+	1.88348i	0.544408	+	0.192231i
$97$	2.67206	+	2.67206i	0.271306	+	0.271306i	0.829626	−	0.558320i	$-0.188554\pi$
$97$	2.67206	+	2.67206i	0.271306	+	0.271306i	−0.558320	+	0.829626i	$0.688554\pi$
$98$	4.67075	+	1.16582i	0.471817	+	0.117765i
$99$	−0.203593	+	0.671156i	−0.0204619	+	0.0674537i
$100$	−0.100335	−	1.00156i	−0.0100335	−	0.100156i
$101$	0.803229	−	8.15532i	0.0799243	−	0.811485i	−0.868754	−	0.495243i	$-0.835079\pi$
$101$	0.803229	−	8.15532i	0.0799243	−	0.811485i	0.948679	−	0.316242i	$-0.102421\pi$
$102$	−5.66525	−	3.38919i	−0.560943	−	0.335580i
$103$	2.37877	−	11.9589i	0.234387	−	1.17834i	−0.666909	−	0.745139i	$-0.732383\pi$
$103$	2.37877	−	11.9589i	0.234387	−	1.17834i	0.901296	−	0.433204i	$-0.142617\pi$
$104$	3.73804	−	15.0834i	0.366545	−	1.47905i
$105$	7.42140	−	1.47621i	0.724255	−	0.144063i
$106$	10.8106	−	5.12408i	1.05002	−	0.497695i
$107$	0.275363	−	0.515168i	0.0266204	−	0.0498032i	−0.868259	−	0.496110i	$-0.834761\pi$
$107$	0.275363	−	0.515168i	0.0266204	−	0.0498032i	0.894880	+	0.446307i	$0.147261\pi$
$108$	0.393457	+	1.96092i	0.0378604	+	0.188689i
$109$	0.786655	+	7.98704i	0.0753479	+	0.765020i	0.956412	+	0.292022i	$0.0943281\pi$
$109$	0.786655	+	7.98704i	0.0753479	+	0.765020i	−0.881064	+	0.472998i	$0.843172\pi$
$110$	0.993091	−	2.10426i	0.0946875	−	0.200633i
$111$	−5.75756	+	2.38486i	−0.546483	+	0.226361i
$112$	4.89757	−	11.9364i	0.462777	−	1.12789i
$113$	−5.33195	−	2.20857i	−0.501588	−	0.207765i	0.117520	−	0.993071i	$-0.462506\pi$
$113$	−5.33195	−	2.20857i	−0.501588	−	0.207765i	−0.619108	+	0.785306i	$0.712506\pi$
$114$	0.417979	−	0.379470i	0.0391473	−	0.0355406i
$115$	−4.59013	−	3.76702i	−0.428032	−	0.351277i
$116$	−0.00517241	−	3.09610i	−0.000480247	−	0.287465i
$117$	5.25752	−	1.59485i	0.486058	−	0.147444i
$118$	3.38357	+	3.06155i	0.311483	+	0.281838i
$119$	−8.36521	+	12.5194i	−0.766838	+	1.14765i
$120$	−0.342182	−	6.62640i	−0.0312368	−	0.604905i
$121$	−8.73717	+	5.83799i	−0.794288	+	0.530726i
$122$	13.4484	−	9.99141i	1.21756	−	0.904580i
$123$	3.98485	+	4.85556i	0.359302	+	0.437811i
$124$	8.08748	+	4.30549i	0.726277	+	0.386644i
$125$	9.30328	−	4.97271i	0.832111	−	0.444772i
$126$	4.51165	−	0.673093i	0.401930	−	0.0599639i
$127$	−2.81335			−0.249645			−0.124822	−	0.992179i	$-0.539836\pi$
$127$	−2.81335			−0.249645			−0.124822	+	0.992179i	$0.539836\pi$
$128$	−9.73793	−	5.75957i	−0.860720	−	0.509079i
$129$	11.5973			1.02109
$130$	−18.0278	+	2.68956i	−1.58114	+	0.235890i
$131$	−17.1664	+	9.17564i	−1.49984	+	0.801679i	−0.997996	−	0.0632805i	$-0.979844\pi$
$131$	−17.1664	+	9.17564i	−1.49984	+	0.801679i	−0.501841	+	0.864960i	$0.667344\pi$
$132$	0.659166	−	1.23818i	0.0573731	−	0.107770i
$133$	−0.816842	−	0.995325i	−0.0708292	−	0.0863056i
$134$	16.4953	−	12.2551i	1.42498	−	1.05868i
$135$	1.95055	−	1.30332i	0.167877	−	0.112172i
$136$	9.80518	+	8.84224i	0.840787	+	0.758216i
$137$	−11.8877	+	17.7912i	−1.01564	+	1.52001i	−0.170573	+	0.985345i	$0.554562\pi$
$137$	−11.8877	+	17.7912i	−1.01564	+	1.52001i	−0.845065	+	0.534664i	$0.820438\pi$
$138$	−2.65437	−	2.40175i	−0.225955	−	0.204450i
$139$	11.6699	−	3.54001i	0.989824	−	0.300260i	0.246464	−	0.969152i	$-0.420731\pi$
$139$	11.6699	−	3.54001i	0.989824	−	0.300260i	0.743360	+	0.668892i	$0.233231\pi$
$140$	−15.1336	+	0.0252825i	−1.27902	+	0.00213676i
$141$	−7.00315	−	5.74733i	−0.589771	−	0.484013i
$142$	−13.6142	+	12.3599i	−1.14248	+	1.03722i
$143$	−3.56000	−	1.47460i	−0.297702	−	0.123312i
$144$	−0.0133650	−	3.99998i	−0.00111375	−	0.333331i
$145$	−3.35515	+	1.38975i	−0.278630	+	0.115412i
$146$	2.97868	−	6.31152i	0.246517	−	0.522345i
$147$	−0.333654	−	3.38765i	−0.0275194	−	0.279409i
$148$	12.2203	−	2.45200i	1.00450	−	0.201553i
$149$	5.68092	−	10.6283i	0.465399	−	0.870701i	−0.534278	−	0.845309i	$-0.679417\pi$
$149$	5.68092	−	10.6283i	0.465399	−	0.870701i	0.999678	−	0.0253923i	$-0.00808349\pi$
$150$	−0.643163	+	0.304851i	−0.0525141	+	0.0248910i
$151$	−10.3138	+	2.05154i	−0.839326	+	0.166952i	−0.595992	−	0.802990i	$-0.703241\pi$
$151$	−10.3138	+	2.05154i	−0.839326	+	0.166952i	−0.243334	+	0.969943i	$0.578241\pi$
$152$	−0.966984	+	0.582887i	−0.0784327	+	0.0472783i
$153$	−0.910695	+	4.57837i	−0.0736253	+	0.370139i
$154$	−2.74550	−	1.64247i	−0.221239	−	0.132354i
$155$	1.05337	−	10.6950i	0.0846084	−	0.859043i
$156$	−10.9335	+	1.09530i	−0.875378	+	0.0876941i
$157$	−6.94248	+	22.8863i	−0.554070	+	1.82653i	0.00877263	+	0.999962i	$0.497208\pi$
$157$	−6.94248	+	22.8863i	−0.554070	+	1.82653i	−0.562843	+	0.826564i	$0.690292\pi$
$158$	12.5140	+	3.12349i	0.995563	+	0.248492i
$159$	−5.98174	−	5.98174i	−0.474383	−	0.474383i
$160$	−1.89234	+	13.1348i	−0.149603	+	1.03840i
$161$	−5.77318	+	5.77318i	−0.454990	+	0.454990i
$162$	1.21240	−	0.728064i	0.0952554	−	0.0572021i
$163$	21.1872	+	6.42706i	1.65951	+	0.503406i	0.974360	−	0.224997i	$-0.0722371\pi$
$163$	21.1872	+	6.42706i	1.65951	+	0.503406i	0.685149	+	0.728403i	$0.259737\pi$
$164$	−5.94053	−	11.0694i	−0.463877	−	0.864376i
$165$	−1.63739	−	0.161269i	−0.127471	−	0.0125548i
$166$	0.756961	+	3.01128i	0.0587515	+	0.233721i
$167$	−9.38689	−	1.86717i	−0.726379	−	0.144486i	−0.181968	−	0.983304i	$-0.558247\pi$
$167$	−9.38689	−	1.86717i	−0.726379	−	0.144486i	−0.544411	+	0.838819i	$0.683247\pi$
$168$	−9.11328	−	0.424817i	−0.703105	−	0.0327754i
$169$	3.35265	+	16.8549i	0.257896	+	1.29653i
$170$	5.20518	−	14.5859i	0.399219	−	1.11869i
$171$	−0.352053	−	0.188176i	−0.0269222	−	0.0143902i
$172$	−22.7565	−	4.48704i	−1.73517	−	0.342134i
$173$	−5.17396	+	0.509591i	−0.393369	+	0.0387435i	−0.292768	−	0.956183i	$-0.594577\pi$
$173$	−5.17396	+	0.509591i	−0.393369	+	0.0387435i	−0.100601	+	0.994927i	$0.532077\pi$
$174$	−2.06068	+	0.739266i	−0.156220	+	0.0560436i
$175$	0.621235	+	1.49979i	0.0469609	+	0.113374i
$176$	−1.77249	+	2.17456i	−0.133606	+	0.163913i
$177$	1.23476	−	2.98097i	0.0928102	−	0.224064i
$178$	0.000563502	−	0.0116692i	4.22362e−5	−	0.000874645i
$179$	1.50166	−	1.82978i	0.112239	−	0.136764i	−0.713860	−	0.700288i	$-0.753055\pi$
$179$	1.50166	−	1.82978i	0.112239	−	0.136764i	0.826100	+	0.563524i	$0.190555\pi$
$180$	−4.33167	+	1.80272i	−0.322863	+	0.134367i
$181$	2.98874	+	9.85255i	0.222151	+	0.732334i	0.995189	+	0.0979744i	$0.0312363\pi$
$181$	2.98874	+	9.85255i	0.222151	+	0.732334i	−0.773038	+	0.634360i	$0.781264\pi$
$182$	1.25063	+	25.0306i	0.0927031	+	1.85539i
$183$	−9.85014	−	6.58165i	−0.728143	−	0.486530i
$184$	4.27922	+	5.73974i	0.315468	+	0.423139i
$185$	−8.12218	−	12.1557i	−0.597155	−	0.893705i
$186$	0.945255	−	6.40927i	0.0693094	−	0.469950i
$187$	2.53082	−	2.07699i	0.185072	−	0.151884i
$188$	11.5181	+	13.9871i	0.840040	+	1.02011i
$189$	−1.52050	−	2.84466i	−0.110600	−	0.206919i
$190$	1.06439	+	0.788029i	0.0772190	+	0.0571696i
$191$			16.0243i			1.15948i	0.814802	+	0.579739i	$0.196846\pi$
$191$			16.0243i			1.15948i	−0.814802	+	0.579739i	$0.803154\pi$
$192$	−1.52138	+	7.85401i	−0.109796	+	0.566814i
$193$			17.2615i			1.24251i	0.783608	+	0.621255i	$0.213377\pi$
$193$			17.2615i			1.24251i	−0.783608	+	0.621255i	$0.786623\pi$
$194$	−3.17990	+	4.29509i	−0.228303	+	0.308370i
$195$	6.07567	+	11.3668i	0.435087	+	0.813991i
$196$	−0.655989	+	6.77641i	−0.0468564	+	0.484029i
$197$	13.0403	−	10.7019i	0.929082	−	0.762478i	−0.0425212	−	0.999096i	$-0.513539\pi$
$197$	13.0403	−	10.7019i	0.929082	−	0.762478i	0.971603	+	0.236618i	$0.0760390\pi$
$198$	−0.981253	−	0.144718i	−0.0697346	−	0.0102846i
$199$	−5.56652	−	8.33089i	−0.394600	−	0.590561i	0.579971	−	0.814637i	$-0.303064\pi$
$199$	−5.56652	−	8.33089i	−0.394600	−	0.590561i	−0.974572	+	0.224076i	$0.928064\pi$
$200$	1.37998	−	0.349343i	0.0975790	−	0.0247023i
$201$	−12.0818	−	8.07283i	−0.852187	−	0.569413i
$202$	11.5747	−	0.578322i	0.814395	−	0.0406906i
$203$	1.44947	+	4.77828i	0.101733	+	0.335369i
$204$	3.55837	−	8.63142i	0.249136	−	0.604320i
$205$	−9.34810	+	11.3907i	−0.652899	+	0.795560i
$206$	17.2237	+	0.831723i	1.20003	+	0.0579489i
$207$	−0.968653	+	2.33854i	−0.0673261	+	0.162539i
$208$	21.8776	+	2.08098i	1.51694	+	0.144290i
$209$	0.107141	+	0.258662i	0.00741112	+	0.0178920i
$210$	3.61350	+	10.0725i	0.249355	+	0.695069i
$211$	−2.02769	+	0.199710i	−0.139592	+	0.0137486i	−0.167572	−	0.985860i	$-0.553593\pi$
$211$	−2.02769	+	0.199710i	−0.139592	+	0.0137486i	0.0279799	+	0.999608i	$0.491093\pi$
$212$	9.42314	+	14.0518i	0.647184	+	0.965085i
$213$	11.4669	+	6.12917i	0.785698	+	0.419964i
$214$	0.778045	+	0.277656i	0.0531861	+	0.0189802i
$215$	5.30768	+	26.6835i	0.361981	+	1.81980i
$216$	−2.66069	+	0.959539i	−0.181037	+	0.0652884i
$217$	−14.4924	−	2.88272i	−0.983810	−	0.195692i
$218$	−11.0076	+	2.76703i	−0.745528	+	0.187407i
$219$	−4.91121	−	0.483712i	−0.331869	−	0.0326862i
$220$	3.15053	+	0.949959i	0.212409	+	0.0640462i
$221$	−24.5425	−	7.44488i	−1.65090	−	0.500797i
$222$	−4.53725	−	7.55562i	−0.304520	−	0.507100i
$223$	−5.29718	+	5.29718i	−0.354726	+	0.354726i	−0.861864	−	0.507139i	$-0.830703\pi$
$223$	−5.29718	+	5.29718i	−0.354726	+	0.354726i	0.507139	+	0.861864i	$0.330703\pi$
$224$	17.7179	+	4.35954i	1.18383	+	0.291284i
$225$	0.355877	+	0.355877i	0.0237251	+	0.0237251i
$226$	1.97654	−	7.91886i	0.131478	−	0.526754i
$227$	0.694958	−	2.29097i	0.0461260	−	0.152057i	−0.930852	−	0.365396i	$-0.880934\pi$
$227$	0.694958	−	2.29097i	0.0461260	−	0.152057i	0.976978	+	0.213339i	$0.0684337\pi$
$228$	0.618000	+	0.505454i	0.0409280	+	0.0334745i
$229$	1.11971	−	11.3686i	0.0739925	−	0.751258i	−0.884576	−	0.466396i	$-0.845552\pi$
$229$	1.11971	−	11.3686i	0.0739925	−	0.751258i	0.958568	−	0.284862i	$-0.0919478\pi$
$230$	4.31121	−	7.20646i	0.284273	−	0.475180i
$231$	−0.441342	+	2.21878i	−0.0290382	+	0.145985i
$232$	4.32953	−	0.653318i	0.284248	−	0.0428924i
$233$	5.15779	−	1.02595i	0.337898	−	0.0672121i	−0.0232250	−	0.999730i	$-0.507393\pi$
$233$	5.15779	−	1.02595i	0.337898	−	0.0672121i	0.361123	+	0.932518i	$0.382393\pi$
$234$	3.32789	+	7.02106i	0.217551	+	0.458981i
$235$	10.0186	−	18.7434i	0.653539	−	1.22269i
$236$	−3.57622	+	5.37159i	−0.232792	+	0.349661i
$237$	−0.893939	−	9.07631i	−0.0580676	−	0.589570i
$238$	−19.2570	−	9.08819i	−1.24824	−	0.589100i
$239$	−27.0549	+	11.2065i	−1.75003	+	0.724888i	−0.752212	+	0.658921i	$0.771013\pi$
$239$	−27.0549	+	11.2065i	−1.75003	+	0.724888i	−0.997822	+	0.0659662i	$0.978987\pi$
$240$	9.19716	−	1.86140i	0.593674	−	0.120153i
$241$	17.8857	+	7.40848i	1.15212	+	0.477222i	0.875243	−	0.483684i	$-0.160702\pi$
$241$	17.8857	+	7.40848i	1.15212	+	0.477222i	0.276874	+	0.960906i	$0.410702\pi$
$242$	−9.98903	−	11.0027i	−0.642119	−	0.707281i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	16.7817	+	16.7257i	1.07434	+	1.07075i
$245$	7.64171	−	2.31809i	0.488211	−	0.148097i
$246$	−5.96008	+	6.58699i	−0.380001	+	0.419971i
$247$	1.21847	−	1.82356i	0.0775292	−	0.116031i
$248$	−4.33456	+	12.2107i	−0.275245	+	0.775379i
$249$	1.82553	−	1.21978i	0.115688	−	0.0773003i
$250$	8.89687	+	11.9751i	0.562687	+	0.757373i
$251$	−6.18938	−	7.54178i	−0.390670	−	0.476033i	0.540120	−	0.841588i	$-0.318379\pi$
$251$	−6.18938	−	7.54178i	−0.390670	−	0.476033i	−0.930790	+	0.365556i	$0.880879\pi$
$252$	1.88295	+	6.17014i	0.118615	+	0.388682i
$253$	1.56566	−	0.836862i	0.0984321	−	0.0526131i
$254$	−0.587081	−	3.93513i	−0.0368367	−	0.246912i
$255$	−10.9509			−0.685769
$256$	6.02402	−	14.8227i	0.376501	−	0.926416i
$257$	−12.1272			−0.756475			−0.378238	−	0.925709i	$-0.623470\pi$
$257$	−12.1272			−0.756475			−0.378238	+	0.925709i	$0.623470\pi$
$258$	2.42009	+	16.2216i	0.150668	+	1.00991i
$259$	−17.7278	+	9.47568i	−1.10155	+	0.588790i
$260$	−7.52395	−	24.6548i	−0.466616	−	1.52903i
$261$	0.982073	+	1.19666i	0.0607888	+	0.0740714i
$262$	−16.4165	−	22.0965i	−1.01421	−	1.36513i
$263$	11.5597	−	7.72394i	0.712801	−	0.476279i	−0.145544	−	0.989352i	$-0.546493\pi$
$263$	11.5597	−	7.72394i	0.712801	−	0.476279i	0.858345	+	0.513073i	$0.171493\pi$
$264$	1.86944	+	0.663617i	0.115056	+	0.0408428i
$265$	11.0254	−	16.5006i	0.677282	−	1.01362i
$266$	1.22174	−	1.35025i	0.0749096	−	0.0827888i
$267$	−0.00790529	+	0.00239804i	−0.000483796	+	0.000146758i
$268$	20.5838	+	20.5152i	1.25736	+	1.25316i
$269$	18.0036	+	14.7752i	1.09770	+	0.900857i	0.995580	−	0.0939150i	$-0.0299382\pi$
$269$	18.0036	+	14.7752i	1.09770	+	0.900857i	0.102118	+	0.994772i	$0.467438\pi$
$270$	2.23003	+	2.45633i	0.135715	+	0.149487i
$271$	−10.9674	−	4.54285i	−0.666223	−	0.275959i	0.0238314	−	0.999716i	$-0.492413\pi$
$271$	−10.9674	−	4.54285i	−0.666223	−	0.275959i	−0.690055	+	0.723757i	$0.742413\pi$
$272$	−10.3218	+	15.5600i	−0.625853	+	0.943463i
$273$	16.3724	−	6.78167i	0.990903	−	0.410446i
$274$	−27.3659	−	12.9151i	−1.65323	−	0.780232i
$275$	−0.0345984	−	0.351283i	−0.00208636	−	0.0211832i
$276$	2.80550	−	4.21395i	0.168871	−	0.253650i
$277$	10.5217	−	19.6848i	0.632190	−	1.18274i	−0.338172	−	0.941084i	$-0.609808\pi$
$277$	10.5217	−	19.6848i	0.632190	−	1.18274i	0.970361	−	0.241659i	$-0.0776916\pi$
$278$	7.38676	+	15.5843i	0.443028	+	0.934684i
$279$	−4.49304	+	0.893721i	−0.268991	+	0.0535057i
$280$	−3.19339	−	21.1626i	−0.190841	−	1.26470i
$281$	4.65884	−	23.4216i	0.277923	−	1.39721i	−0.549434	−	0.835537i	$-0.685157\pi$
$281$	4.65884	−	23.4216i	0.277923	−	1.39721i	0.827357	−	0.561676i	$-0.189843\pi$
$282$	6.57759	−	10.9949i	0.391690	−	0.654735i
$283$	−2.33621	+	23.7199i	−0.138873	+	1.41000i	0.632964	+	0.774181i	$0.281838\pi$
$283$	−2.33621	+	23.7199i	−0.138873	+	1.41000i	−0.771837	+	0.635821i	$0.780662\pi$
$284$	−20.1291	−	16.4634i	−1.19444	−	0.976921i
$285$	0.271840	−	0.896137i	0.0161024	−	0.0530826i
$286$	1.31968	−	5.28721i	0.0780345	−	0.312639i
$287$	14.3265	+	14.3265i	0.845666	+	0.845666i
$288$	5.59211	−	0.853396i	0.329518	−	0.0502868i
$289$	3.38764	−	3.38764i	0.199273	−	0.199273i
$290$	−2.64403	−	4.40295i	−0.155263	−	0.258550i
$291$	3.61614	+	1.09694i	0.211982	+	0.0643041i
$292$	9.44972	+	2.84931i	0.553003	+	0.166743i
$293$	24.8296	+	2.44550i	1.45056	+	0.142868i	0.792396	−	0.610007i	$-0.208833\pi$
$293$	24.8296	+	2.44550i	1.45056	+	0.142868i	0.658164	+	0.752875i	$0.271333\pi$
$294$	4.66879	−	1.17362i	0.272290	−	0.0684467i
$295$	7.42382	+	1.47669i	0.432232	+	0.0859762i
$296$	5.97978	+	16.5813i	0.347568	+	0.963766i
$297$	0.136828	+	0.687880i	0.00793955	+	0.0399148i
$298$	16.0516	+	5.72823i	0.929843	+	0.331827i
$299$	−12.2646	−	6.55559i	−0.709282	−	0.379119i
$300$	−0.560619	−	0.835999i	−0.0323673	−	0.0482664i
$301$	37.2274	−	3.66658i	2.14575	−	0.211338i
$302$	−5.02182	−	13.9982i	−0.288973	−	0.805504i
$303$	−3.13601	−	7.57099i	−0.180159	−	0.434942i
$304$	−1.01709	−	1.23092i	−0.0583341	−	0.0705980i
$305$	10.6352	−	25.6757i	0.608971	−	1.47019i
$306$	−6.59396	−	0.318419i	−0.376952	−	0.0182028i
$307$	−11.6556	+	14.2023i	−0.665218	+	0.810570i	−0.990856	−	0.134924i	$-0.956921\pi$
$307$	−11.6556	+	14.2023i	−0.665218	+	0.810570i	0.325638	+	0.945494i	$0.394421\pi$
$308$	1.72446	−	4.18297i	0.0982603	−	0.238347i
$309$	−3.53949	−	11.6681i	−0.201354	−	0.663776i
$310$	15.1793	−	0.758420i	0.862124	−	0.0430754i
$311$	−7.90956	−	5.28500i	−0.448510	−	0.299685i	0.310727	−	0.950499i	$-0.399428\pi$
$311$	−7.90956	−	5.28500i	−0.448510	−	0.299685i	−0.759237	+	0.650815i	$0.774428\pi$
$312$	−3.81359	−	15.0644i	−0.215902	−	0.852856i
$313$	−3.57046	−	5.34358i	−0.201815	−	0.302037i	0.716733	−	0.697348i	$-0.245637\pi$
$313$	−3.57046	−	5.34358i	−0.201815	−	0.302037i	−0.918547	+	0.395311i	$0.870637\pi$
$314$	−33.4606	−	4.93484i	−1.88829	−	0.278489i
$315$	5.84921	−	4.80033i	0.329566	−	0.270468i
$316$	−1.75755	+	18.1556i	−0.0988699	+	1.02133i
$317$	14.1523	+	26.4771i	0.794873	+	1.48710i	0.871690	+	0.490057i	$0.163024\pi$
$317$	14.1523	+	26.4771i	0.794873	+	1.48710i	−0.0768174	+	0.997045i	$0.524476\pi$
$318$	7.11861	−	9.61511i	0.399192	−	0.539189i
$319$		−	1.08573i		−	0.0607895i
$320$	−18.7670	+	0.0940586i	−1.04911	+	0.00525804i
$321$		−	0.584143i		−	0.0326037i
$322$	−9.27986	−	6.87040i	−0.517146	−	0.382873i
$323$	0.878420	+	1.64341i	0.0488766	+	0.0914417i
$324$	1.27137	+	1.54390i	0.0706315	+	0.0857722i
$325$	−2.13745	+	1.75416i	−0.118565	+	0.0973034i
$326$	−4.56847	+	30.9764i	−0.253024	+	1.71562i
$327$	4.45883	+	6.67312i	0.246574	+	0.369024i
$328$	14.2435	−	10.6191i	0.786466	−	0.586344i
$329$	−24.2972	−	16.2348i	−1.33955	−	0.895056i
$330$	−0.116113	−	2.32393i	−0.00639183	−	0.127928i
$331$	−5.34669	−	17.6257i	−0.293881	−	0.968795i	−0.972224	−	0.234050i	$-0.924802\pi$
$331$	−5.34669	−	17.6257i	−0.293881	−	0.968795i	0.678344	−	0.734745i	$-0.262698\pi$
$332$	−4.05402	+	1.68717i	−0.222493	+	0.0925955i
$333$	−3.95350	+	4.81735i	−0.216650	+	0.263989i
$334$	0.652845	−	13.5194i	0.0357221	−	0.739748i
$335$	13.0448	−	31.4929i	0.712713	−	1.72064i
$336$	−1.30752	−	12.8357i	−0.0713312	−	0.700245i
$337$	7.96983	+	19.2409i	0.434144	+	1.04812i	0.977937	+	0.208898i	$0.0669876\pi$
$337$	7.96983	+	19.2409i	0.434144	+	1.04812i	−0.543793	+	0.839219i	$0.683012\pi$
$338$	−22.8759	+	8.20668i	−1.24428	+	0.446384i
$339$	−5.74347	+	0.565683i	−0.311943	+	0.0307237i
$340$	21.4880	+	4.23692i	1.16535	+	0.229779i
$341$	2.83357	+	1.51458i	0.153447	+	0.0820189i
$342$	0.189743	−	0.531696i	0.0102601	−	0.0287509i
$343$	2.26283	+	11.3760i	0.122181	+	0.614246i
$344$	1.52742	−	32.7666i	0.0823530	−	1.76666i
$345$	−5.82390	−	1.15845i	−0.313548	−	0.0623686i
$346$	−1.79247	−	7.13066i	−0.0963637	−	0.383346i
$347$	−13.9530	−	1.37425i	−0.749037	−	0.0737737i	−0.283707	−	0.958911i	$-0.591564\pi$
$347$	−13.9530	−	1.37425i	−0.749037	−	0.0737737i	−0.465330	+	0.885137i	$0.654064\pi$
$348$	−1.46405	−	2.72808i	−0.0784814	−	0.146240i
$349$	−26.9048	−	8.16147i	−1.44018	−	0.436874i	−0.528908	−	0.848679i	$-0.677398\pi$
$349$	−26.9048	−	8.16147i	−1.44018	−	0.436874i	−0.911272	+	0.411806i	$0.864898\pi$
$350$	−1.96817	+	1.18191i	−0.105203	+	0.0631759i
$351$	3.88491	−	3.88491i	0.207361	−	0.207361i
$352$	−3.41150	−	2.02546i	−0.181834	−	0.107957i
$353$	17.3316	+	17.3316i	0.922469	+	0.922469i	0.997203	−	0.0747341i	$-0.0238108\pi$
$353$	17.3316	+	17.3316i	0.922469	+	0.922469i	−0.0747341	+	0.997203i	$0.523811\pi$
$354$	4.42725	+	1.10504i	0.235306	+	0.0587322i
$355$	−8.85423	+	29.1885i	−0.469934	+	1.54916i
$356$	0.0164397	−	0.00164691i	0.000871303	−	8.72859e-5i
$357$	−1.47584	+	14.9845i	−0.0781099	+	0.793063i
$358$	2.87274	+	1.71859i	0.151829	+	0.0908304i
$359$	−2.44440	+	12.2888i	−0.129011	+	0.648580i	0.861117	+	0.508408i	$0.169766\pi$
$359$	−2.44440	+	12.2888i	−0.129011	+	0.648580i	−0.990127	+	0.140172i	$0.955234\pi$
$360$	−3.42544	−	5.68266i	−0.180537	−	0.299503i
$361$	18.4786	−	3.67563i	0.972559	−	0.193454i
$362$	−13.1574	+	6.23645i	−0.691538	+	0.327780i
$363$	−4.95348	+	9.26732i	−0.259990	+	0.486408i
$364$	−34.7501	+	6.97260i	−1.82140	+	0.365464i
$365$	−1.13474	−	11.5212i	−0.0593952	−	0.603049i
$366$	7.15048	−	15.1512i	0.373762	−	0.791963i
$367$	17.1179	−	7.09048i	0.893549	−	0.370120i	0.111813	−	0.993729i	$-0.464334\pi$
$367$	17.1179	−	7.09048i	0.893549	−	0.370120i	0.781736	+	0.623609i	$0.214334\pi$
$368$	−7.13539	+	7.18323i	−0.371958	+	0.374452i
$369$	5.80322	+	2.40377i	0.302104	+	0.125135i
$370$	15.3077	−	13.8974i	0.795808	−	0.722490i
$371$	−21.0925	−	17.3102i	−1.09507	−	0.898701i
$372$	9.16211	−	0.0153064i	0.475033	−	0.000793602i
$373$	15.3711	−	4.66276i	0.795883	−	0.241429i	0.133947	−	0.990989i	$-0.457235\pi$
$373$	15.3711	−	4.66276i	0.795883	−	0.241429i	0.661937	+	0.749560i	$0.269735\pi$
$374$	3.43328	+	3.10652i	0.177530	+	0.160634i
$375$	5.86064	−	8.77107i	0.302642	−	0.452936i
$376$	−17.1606	+	19.0295i	−0.884992	+	0.981369i
$377$	−7.07177	+	4.72520i	−0.364214	+	0.243360i
$378$	3.66163	−	2.72039i	0.188334	−	0.139922i
$379$	13.9749	+	17.0285i	0.717845	+	0.874696i	0.996317	−	0.0857480i	$-0.0273280\pi$
$379$	13.9749	+	17.0285i	0.717845	+	0.874696i	−0.278472	+	0.960444i	$0.589828\pi$
$380$	−0.880128	+	1.65324i	−0.0451496	+	0.0848095i
$381$	−2.48116	+	1.32621i	−0.127113	+	0.0679436i
$382$	−22.4137	+	3.34390i	−1.14679	+	0.171089i
$383$	−0.700381			−0.0357878			−0.0178939	−	0.999840i	$-0.505696\pi$
$383$	−0.700381			−0.0357878			−0.0178939	+	0.999840i	$0.505696\pi$
$384$	−11.3031	−	0.489055i	−0.576811	−	0.0249570i
$385$	−5.30702			−0.270471
$386$	−24.1442	+	3.60207i	−1.22891	+	0.183341i
$387$	10.2279	−	5.46694i	0.519915	−	0.277900i
$388$	−6.67126	−	3.55154i	−0.338682	−	0.180302i
$389$	−4.07784	−	4.96886i	−0.206755	−	0.251931i	0.659301	−	0.751879i	$-0.270852\pi$
$389$	−4.07784	−	4.96886i	−0.206755	−	0.251931i	−0.866055	+	0.499948i	$0.833352\pi$
$390$	−14.6312	+	10.8702i	−0.740881	+	0.550435i
$391$	9.82454	−	6.56455i	0.496848	−	0.331983i
$392$	−9.61527	+	0.496524i	−0.485645	+	0.0250783i
$393$	−10.8141	+	16.1844i	−0.545497	+	0.816394i
$394$	17.6903	+	16.0066i	0.891223	+	0.806403i
$395$	20.4740	−	6.21071i	1.03016	−	0.312494i
$396$	−0.00234340	−	1.40271i	−0.000117760	−	0.0704888i
$397$	14.3245	+	11.7558i	0.718925	+	0.590006i	0.921092	−	0.389345i	$-0.127299\pi$
$397$	14.3245	+	11.7558i	0.718925	+	0.590006i	−0.202168	+	0.979351i	$0.564799\pi$
$398$	10.4911	−	9.52454i	0.525871	−	0.477422i
$399$	−1.18958	−	0.492742i	−0.0595537	−	0.0246679i
$400$	0.776607	+	1.85732i	0.0388303	+	0.0928659i
$401$	29.7109	−	12.3067i	1.48369	−	0.614566i	0.513759	−	0.857935i	$-0.328253\pi$
$401$	29.7109	−	12.3067i	1.48369	−	0.614566i	0.969934	+	0.243369i	$0.0782526\pi$
$402$	8.77053	−	18.5839i	0.437434	−	0.926880i
$403$	−2.46697	−	25.0476i	−0.122889	−	1.24771i
$404$	3.22429	+	16.0693i	0.160415	+	0.799476i
$405$	1.10585	−	2.06891i	0.0549503	−	0.102805i
$406$	−6.38106	+	3.02454i	−0.316687	+	0.150105i
$407$	4.28682	−	0.852702i	0.212490	−	0.0422669i
$408$	12.8156	+	3.17603i	0.634467	+	0.157237i
$409$	2.16844	−	10.9015i	0.107223	−	0.539044i	−0.889415	−	0.457101i	$-0.848888\pi$
$409$	2.16844	−	10.9015i	0.107223	−	0.539044i	0.996637	−	0.0819425i	$-0.0261124\pi$
$410$	−17.8833	−	10.6985i	−0.883191	−	0.528362i
$411$	−2.09731	+	21.2943i	−0.103453	+	1.05037i
$412$	2.43082	+	24.2649i	0.119758	+	1.19544i
$413$	3.02112	−	9.95929i	0.148660	−	0.490065i
$414$	−3.47312	−	0.866889i	−0.170695	−	0.0426053i
$415$	3.64198	+	3.64198i	0.178778	+	0.178778i
$416$	1.65462	+	31.0352i	0.0811246	+	1.52163i
$417$	8.62314	−	8.62314i	0.422277	−	0.422277i
$418$	−0.339441	+	0.203839i	−0.0166026	+	0.00997008i
$419$	21.6359	+	6.56316i	1.05698	+	0.320632i	0.770490	−	0.637452i	$-0.220011\pi$
$419$	21.6359	+	6.56316i	1.05698	+	0.320632i	0.286490	+	0.958083i	$0.407511\pi$
$420$	−13.3347	+	7.15621i	−0.650667	+	0.349187i
$421$	−15.2268	−	1.49971i	−0.742110	−	0.0730915i	−0.280106	−	0.959969i	$-0.590370\pi$
$421$	−15.2268	−	1.49971i	−0.742110	−	0.0730915i	−0.462004	+	0.886878i	$0.652870\pi$
$422$	−0.702472	−	2.79452i	−0.0341958	−	0.136035i
$423$	−8.88550	−	1.76744i	−0.432028	−	0.0859357i
$424$	−17.6884	+	16.1127i	−0.859024	+	0.782504i
$425$	−0.458340	−	2.30423i	−0.0222328	−	0.111772i
$426$	−6.18021	+	17.3181i	−0.299432	+	0.839066i
$427$	−33.6998	−	18.0129i	−1.63085	−	0.871705i
$428$	−0.226007	+	1.14622i	−0.0109245	+	0.0554045i
$429$	−3.83476	+	0.377691i	−0.185144	+	0.0182351i
$430$	−36.2155	+	12.9922i	−1.74647	+	0.626542i
$431$	−12.6138	−	30.4524i	−0.607585	−	1.46684i	−0.865618	−	0.500704i	$-0.833074\pi$
$431$	−12.6138	−	30.4524i	−0.607585	−	1.46684i	0.258033	−	0.966136i	$-0.416926\pi$
$432$	−1.89736	−	3.52137i	−0.0912869	−	0.169422i
$433$	−8.57242	+	20.6956i	−0.411964	+	0.994569i	0.572646	+	0.819803i	$0.305917\pi$
$433$	−8.57242	+	20.6956i	−0.411964	+	0.994569i	−0.984610	+	0.174766i	$0.944083\pi$
$434$	1.00793	−	20.8726i	0.0483821	−	1.00192i
$435$	−2.30385	+	2.80725i	−0.110461	+	0.134598i
$436$	−6.16736	−	14.8193i	−0.295363	−	0.709714i
$437$	0.293313	+	0.966923i	0.0140311	+	0.0462542i
$438$	−0.348271	−	6.97041i	−0.0166410	−	0.333059i
$439$	−3.71779	−	2.48414i	−0.177440	−	0.118562i	0.463678	−	0.886004i	$-0.346529\pi$
$439$	−3.71779	−	2.48414i	−0.177440	−	0.118562i	−0.641119	+	0.767442i	$0.721529\pi$
$440$	−0.671296	+	4.60499i	−0.0320028	+	0.219534i
$441$	−1.89118	−	2.83036i	−0.0900564	−	0.134779i
$442$	5.29195	−	35.8819i	0.251713	−	1.70673i
$443$	−11.9930	+	9.84242i	−0.569806	+	0.467628i	−0.874637	−	0.484779i	$-0.838900\pi$
$443$	−11.9930	+	9.84242i	−0.569806	+	0.467628i	0.304831	+	0.952407i	$0.401400\pi$
$444$	9.62148	−	7.92308i	0.456615	−	0.376013i
$445$	−0.00913546	−	0.0170912i	−0.000433062	−	0.000810203i
$446$	−8.51475	−	6.30395i	−0.403185	−	0.298501i
$447$		−	12.0513i		−	0.570005i
$448$	−2.40052	+	25.6923i	−0.113414	+	1.21385i
$449$		−	18.9658i		−	0.895051i	−0.894271	−	0.447526i	$-0.852305\pi$
$449$		−	18.9658i		−	0.895051i	0.894271	−	0.447526i	$-0.147695\pi$
$450$	−0.423514	+	0.572040i	−0.0199646	+	0.0269662i
$451$	−2.07672	−	3.88528i	−0.0977891	−	0.182951i
$452$	11.4888	+	1.11217i	0.540389	+	0.0523123i
$453$	−8.12888	+	6.67120i	−0.381928	+	0.313440i
$454$	3.34948	+	0.493989i	0.157199	+	0.0231841i
$455$	23.0966	+	34.5664i	1.08278	+	1.62050i
$456$	−0.578033	+	0.969893i	−0.0270689	+	0.0454194i
$457$	15.9747	+	10.6739i	0.747265	+	0.499306i	0.869950	−	0.493139i	$-0.164151\pi$
$457$	15.9747	+	10.6739i	0.747265	+	0.499306i	−0.122686	+	0.992446i	$0.539151\pi$
$458$	16.1353	−	0.806187i	0.753953	−	0.0376707i
$459$	1.35507	+	4.46706i	0.0632492	+	0.208505i
$460$	10.9796	+	4.52641i	0.511925	+	0.211045i
$461$	20.4102	−	24.8700i	0.950600	−	1.15831i	−0.0366816	−	0.999327i	$-0.511679\pi$
$461$	20.4102	−	24.8700i	0.950600	−	1.15831i	0.987281	−	0.158982i	$-0.0508213\pi$
$462$	−3.19557	−	0.154313i	−0.148672	−	0.00717928i
$463$	11.6610	−	28.1521i	0.541931	−	1.30834i	−0.381428	−	0.924399i	$-0.624567\pi$
$463$	11.6610	−	28.1521i	0.541931	−	1.30834i	0.923359	−	0.383939i	$-0.125433\pi$
$464$	1.81729	+	5.91953i	0.0843656	+	0.274807i
$465$	−4.11260	−	9.92870i	−0.190717	−	0.460433i
$466$	2.51134	+	7.00028i	0.116336	+	0.324282i
$467$	−19.1361	+	1.88474i	−0.885515	+	0.0872156i	−0.530539	−	0.847660i	$-0.678011\pi$
$467$	−19.1361	+	1.88474i	−0.885515	+	0.0872156i	−0.354975	+	0.934876i	$0.615511\pi$
$468$	−9.12614	+	6.11997i	−0.421856	+	0.282896i
$469$	−41.3350	−	22.0940i	−1.90867	−	1.02021i
$470$	28.3077	+	10.1020i	1.30574	+	0.465970i
$471$	4.66580	+	23.4566i	0.214989	+	1.08082i
$472$	−8.25969	−	3.88125i	−0.380183	−	0.178649i
$473$	−7.97756	−	1.58684i	−0.366809	−	0.0729628i
$474$	12.5088	−	3.14440i	0.574548	−	0.144427i
$475$	0.199939	+	0.0196923i	0.00917382	+	0.000903543i
$476$	8.69347	−	28.8318i	0.398465	−	1.32151i
$477$	−8.09520	−	2.45565i	−0.370654	−	0.112437i
$478$	−21.3206	−	35.5040i	−0.975182	−	1.62391i
$479$	12.3826	−	12.3826i	0.565776	−	0.565776i	−0.365166	−	0.930942i	$-0.618988\pi$
$479$	12.3826	−	12.3826i	0.565776	−	0.565776i	0.930942	+	0.365166i	$0.118988\pi$
$480$	4.52283	+	12.4759i	0.206438	+	0.569446i
$481$	−24.2105	−	24.2105i	−1.10390	−	1.10390i
$482$	−6.63017	+	26.5632i	−0.301996	+	1.20992i
$483$	−2.37003	+	7.81294i	−0.107840	+	0.355501i
$484$	13.3054	−	16.2680i	0.604790	−	0.739454i
$485$	−0.868908	+	8.82217i	−0.0394551	+	0.400594i
$486$	0.726038	−	1.21362i	0.0329337	−	0.0550508i
$487$	0.935808	−	4.70462i	0.0424055	−	0.213187i	−0.953773	−	0.300528i	$-0.902837\pi$
$487$	0.935808	−	4.70462i	0.0424055	−	0.213187i	0.996178	+	0.0873413i	$0.0278371\pi$
$488$	−19.8928	+	26.9633i	−0.900507	+	1.22057i
$489$	21.7151	−	4.31941i	0.981992	−	0.195330i
$490$	4.83703	+	10.2050i	0.218515	+	0.461014i
$491$	13.4656	−	25.1924i	0.607696	−	1.13692i	−0.370421	−	0.928864i	$-0.620787\pi$
$491$	13.4656	−	25.1924i	0.607696	−	1.13692i	0.978117	−	0.208055i	$-0.0667133\pi$
$492$	−10.4572	−	6.96201i	−0.471445	−	0.313872i
$493$	−0.708312	−	7.19161i	−0.0319008	−	0.323894i
$494$	2.80495	+	1.32377i	0.126200	+	0.0595594i
$495$	−1.52007	+	0.629636i	−0.0683223	+	0.0283000i
$496$	−17.9840	−	3.51481i	−0.807505	−	0.157820i
$497$	38.7464	+	16.0493i	1.73802	+	0.719910i
$498$	2.08709	+	2.29888i	0.0935247	+	0.103015i
$499$	4.63527	+	3.80407i	0.207503	+	0.170293i	0.732405	−	0.680869i	$-0.238398\pi$
$499$	4.63527	+	3.80407i	0.207503	+	0.170293i	−0.524902	+	0.851163i	$0.675898\pi$
$500$	−14.8934	+	14.9433i	−0.666054	+	0.668283i
$501$	−9.15867	+	2.77825i	−0.409179	+	0.124123i
$502$	9.25735	−	10.2311i	0.413176	−	0.456635i
$503$	7.03373	−	10.5267i	0.313619	−	0.469363i	−0.640854	−	0.767663i	$-0.721419\pi$
$503$	7.03373	−	10.5267i	0.313619	−	0.469363i	0.954472	+	0.298300i	$0.0964195\pi$
$504$	−8.23745	+	3.92132i	−0.366925	+	0.174669i
$505$	15.9843	−	10.6804i	0.711294	−	0.475271i
$506$	1.49726	+	2.01531i	0.0665615	+	0.0895912i
$507$	10.9021	+	13.2843i	0.484180	+	0.589975i
$508$	5.38169	−	1.64234i	0.238774	−	0.0728670i
$509$	−17.8148	+	9.52219i	−0.789626	+	0.422064i	−0.816334	−	0.577580i	$-0.803997\pi$
$509$	−17.8148	+	9.52219i	−0.789626	+	0.422064i	0.0267088	+	0.999643i	$0.491497\pi$
$510$	−2.28519	−	15.3173i	−0.101190	−	0.678263i
$511$	−15.9179			−0.704166
$512$	21.9900	+	5.33285i	0.971831	+	0.235681i
$513$	−0.399189			−0.0176246
$514$	−2.53067	−	16.9627i	−0.111623	−	0.748194i
$515$	25.2265	−	13.4838i	1.11161	−	0.594169i
$516$	−22.1846	+	6.77012i	−0.976623	+	0.298038i
$517$	4.03093	+	4.91170i	0.177280	+	0.216016i
$518$	−16.9533	−	22.8190i	−0.744886	−	1.00261i
$519$	−4.32281	+	2.88841i	−0.189750	+	0.126787i
$520$	32.9154	−	15.6689i	1.44344	−	0.687126i
$521$	−14.5605	+	21.7914i	−0.637908	+	0.954697i	0.361840	+	0.932240i	$0.382149\pi$
$521$	−14.5605	+	21.7914i	−0.637908	+	0.954697i	−0.999748	+	0.0224567i	$0.992851\pi$
$522$	−1.46887	+	1.62337i	−0.0642908	+	0.0710531i
$523$	24.2559	−	7.35795i	1.06064	−	0.321741i	0.288687	−	0.957424i	$-0.406781\pi$
$523$	24.2559	−	7.35795i	1.06064	−	0.321741i	0.771950	+	0.635683i	$0.219281\pi$
$524$	27.4813	−	27.5733i	1.20053	−	1.20455i
$525$	1.25488	+	1.02985i	0.0547673	+	0.0449464i
$526$	13.2160	+	14.5571i	0.576244	+	0.634721i
$527$	19.7569	+	8.18357i	0.860624	+	0.356482i
$528$	−0.538115	+	2.75333i	−0.0234184	+	0.119823i
$529$	−15.3299	+	6.34985i	−0.666517	+	0.276080i
$530$	25.3807	+	11.9782i	1.10247	+	0.520301i
$531$	−0.316260	−	3.21104i	−0.0137245	−	0.139347i
$532$	2.14358	+	1.42712i	0.0929360	+	0.0618735i
$533$	−16.2681	+	30.4354i	−0.704649	+	1.31831i
$534$	−0.00500387	−	0.0105570i	−0.000216539	−	0.000456845i
$535$	1.34402	−	0.267341i	0.0581069	−	0.0115582i
$536$	−24.3999	+	33.0723i	−1.05391	+	1.42851i
$537$	0.461795	−	2.32160i	0.0199279	−	0.100184i
$538$	−16.9096	+	28.2654i	−0.729024	+	1.21861i
$539$	−0.234011	+	2.37595i	−0.0100795	+	0.102339i
$540$	−2.97039	+	3.63179i	−0.127825	+	0.156287i
$541$	−9.57232	+	31.5557i	−0.411546	+	1.35669i	0.469198	+	0.883093i	$0.344543\pi$
$541$	−9.57232	+	31.5557i	−0.411546	+	1.35669i	−0.880744	+	0.473592i	$0.842957\pi$
$542$	4.06559	−	16.2885i	0.174632	−	0.699650i
$543$	7.28029	+	7.28029i	0.312427	+	0.312427i
$544$	−23.9182	−	11.1905i	−1.02548	−	0.479787i
$545$	−13.3131	+	13.3131i	−0.570269	+	0.570269i
$546$	12.9023	+	21.4855i	0.552167	+	0.919493i
$547$	0.536468	+	0.162736i	0.0229377	+	0.00695808i	0.301733	−	0.953393i	$-0.402435\pi$
$547$	0.536468	+	0.162736i	0.0229377	+	0.00695808i	−0.278795	+	0.960351i	$0.589935\pi$
$548$	12.3542	−	40.9727i	0.527746	−	1.75027i
$549$	−11.7896	−	1.16118i	−0.503169	−	0.0495578i
$550$	0.484131	−	0.121698i	0.0206434	−	0.00518924i
$551$	0.606091	+	0.120559i	0.0258203	+	0.00513598i
$552$	6.47963	+	3.04479i	0.275791	+	0.129595i
$553$	−5.73908	−	28.8523i	−0.244051	−	1.22693i
$554$	29.7294	+	10.6093i	1.26308	+	0.450748i
$555$	−12.8933	−	6.89161i	−0.547290	−	0.292532i
$556$	−20.2568	+	13.5842i	−0.859080	+	0.576097i
$557$	38.0488	−	3.74748i	1.61218	−	0.158786i	0.748609	−	0.663012i	$-0.230722\pi$
$557$	38.0488	−	3.74748i	1.61218	−	0.158786i	0.863572	+	0.504226i	$0.168222\pi$
$558$	−2.18767	−	6.09806i	−0.0926114	−	0.258152i
$559$	24.3834	+	58.8667i	1.03131	+	2.48979i
$560$	28.9344	−	8.88283i	1.22270	−	0.375368i
$561$	1.25290	−	3.02476i	0.0528973	−	0.127705i
$562$	33.7327	+	1.62894i	1.42293	+	0.0687126i
$563$	−11.3661	+	13.8496i	−0.479024	+	0.583692i	−0.955313	−	0.295597i	$-0.904482\pi$
$563$	−11.3661	+	13.8496i	−0.479024	+	0.583692i	0.476289	+	0.879289i	$0.341982\pi$
$564$	16.7515	+	6.90592i	0.705364	+	0.290792i
$565$	−3.93012	−	12.9559i	−0.165342	−	0.545058i
$566$	−33.6653	+	1.68206i	−1.41506	+	0.0707023i
$567$	−2.68193	−	1.79201i	−0.112630	−	0.0752573i
$568$	18.8274	−	31.5908i	0.789979	−	1.32552i
$569$	21.0623	+	31.5220i	0.882979	+	1.32147i	0.946237	+	0.323474i	$0.104851\pi$
$569$	21.0623	+	31.5220i	0.882979	+	1.32147i	−0.0632580	+	0.997997i	$0.520149\pi$
$570$	1.31018	+	0.193229i	0.0548775	+	0.00809347i
$571$	−0.0581427	+	0.0477165i	−0.00243320	+	0.00199687i	−0.635609	−	0.772011i	$-0.719251\pi$
$571$	−0.0581427	+	0.0477165i	−0.00243320	+	0.00199687i	0.633176	+	0.774008i	$0.281751\pi$
$572$	7.67078	+	0.742568i	0.320731	+	0.0310483i
$573$	7.55381	+	14.1322i	0.315565	+	0.590380i
$574$	−17.0493	+	23.0285i	−0.711625	+	0.961192i
$575$		−	1.27392i		−	0.0531263i
$576$	2.36062	+	7.64379i	0.0983590	+	0.318491i
$577$			32.0792i			1.33547i	0.744397	+	0.667737i	$0.232737\pi$
$577$			32.0792i			1.33547i	−0.744397	+	0.667737i	$0.767263\pi$
$578$	5.44533	+	4.03148i	0.226496	+	0.167688i
$579$	8.13702	+	15.2233i	0.338163	+	0.632658i
$580$	5.60680	−	4.61708i	0.232810	−	0.191714i
$581$	5.47429	−	4.49264i	0.227112	−	0.186386i
$582$	−0.779728	+	5.28693i	−0.0323208	+	0.219150i
$583$	3.29625	+	4.93319i	0.136517	+	0.204312i
$584$	−2.01349	+	13.8122i	−0.0833187	+	0.571553i
$585$	10.7165	+	7.16055i	0.443073	+	0.296052i
$586$	1.76075	+	35.2403i	0.0727360	+	1.45576i
$587$	1.57200	+	5.18218i	0.0648833	+	0.213892i	0.983387	−	0.181520i	$-0.0581018\pi$
$587$	1.57200	+	5.18218i	0.0648833	+	0.213892i	−0.918504	+	0.395412i	$0.870602\pi$
$588$	2.61585	+	6.28549i	0.107876	+	0.259209i
$589$	−1.16012	+	1.41361i	−0.0478019	+	0.0582468i
$590$	−0.516317	+	10.6921i	−0.0212564	+	0.440187i
$591$	6.45567	−	15.5854i	0.265551	−	0.641096i
$592$	−21.9449	+	11.8242i	−0.901930	+	0.485973i
$593$	−8.01882	−	19.3592i	−0.329294	−	0.794985i	−0.998645	−	0.0520392i	$-0.983428\pi$
$593$	−8.01882	−	19.3592i	−0.329294	−	0.794985i	0.669351	−	0.742946i	$-0.266572\pi$
$594$	−0.933607	+	0.334930i	−0.0383064	+	0.0137423i
$595$	−35.1522	+	3.46219i	−1.44110	+	0.141936i
$596$	−4.66267	+	23.6472i	−0.190990	+	0.968628i
$597$	−8.83639	−	4.72315i	−0.361649	−	0.193306i
$598$	6.61017	−	18.5230i	0.270310	−	0.757460i
$599$	3.16214	+	15.8971i	0.129201	+	0.649539i	0.990054	+	0.140685i	$0.0449306\pi$
$599$	3.16214	+	15.8971i	0.129201	+	0.649539i	−0.860853	+	0.508854i	$0.830069\pi$
$600$	1.05235	−	0.958610i	0.0429620	−	0.0391351i
$601$	−21.9914	−	4.37437i	−0.897049	−	0.178434i	−0.275030	−	0.961436i	$-0.588688\pi$
$601$	−21.9914	−	4.37437i	−0.897049	−	0.178434i	−0.622020	+	0.783002i	$0.713688\pi$
$602$	12.8970	+	51.3060i	0.525644	+	2.09108i
$603$	−14.4607	−	1.42426i	−0.588887	−	0.0580003i
$604$	18.5318	−	9.94527i	0.754046	−	0.404667i
$605$	−23.5896	−	7.15582i	−0.959053	−	0.290925i
$606$	9.93538	−	5.96632i	0.403597	−	0.242365i
$607$	−11.6521	+	11.6521i	−0.472943	+	0.472943i	−0.902866	−	0.429923i	$-0.858541\pi$
$607$	−11.6521	+	11.6521i	−0.472943	+	0.472943i	0.429923	+	0.902866i	$0.358541\pi$
$608$	1.50948	−	1.67950i	0.0612176	−	0.0681127i
$609$	3.53079	+	3.53079i	0.143075	+	0.143075i
$610$	38.1328	+	9.51792i	1.54395	+	0.385369i
$611$	14.4487	−	47.6309i	0.584531	−	1.92694i
$612$	−0.930622	−	9.28964i	−0.0376182	−	0.375511i
$613$	−3.19992	+	32.4893i	−0.129243	+	1.31223i	0.683647	+	0.729813i	$0.260393\pi$
$613$	−3.19992	+	32.4893i	−0.129243	+	1.31223i	−0.812890	+	0.582417i	$0.802107\pi$
$614$	−22.2975	−	13.3393i	−0.899855	−	0.538331i
$615$	−2.87475	+	14.4524i	−0.115921	+	0.582775i
$616$	6.21071	+	1.53917i	0.250237	+	0.0620150i
$617$	−22.9091	+	4.55690i	−0.922285	+	0.183454i	−0.633324	−	0.773887i	$-0.718310\pi$
$617$	−22.9091	+	4.55690i	−0.922285	+	0.183454i	−0.288961	+	0.957341i	$0.593310\pi$
$618$	15.5820	−	7.38566i	0.626799	−	0.297095i
$619$	0.269130	−	0.503507i	0.0108172	−	0.0202376i	−0.876455	−	0.481485i	$-0.840098\pi$
$619$	0.269130	−	0.503507i	0.0108172	−	0.0202376i	0.887272	+	0.461247i	$0.152598\pi$
$620$	4.22839	+	21.0735i	0.169816	+	0.846331i
$621$	0.248102	+	2.51902i	0.00995600	+	0.101085i
$622$	5.74176	−	12.1662i	0.230224	−	0.487821i
$623$	−0.0246178	+	0.0101970i	−0.000986291	+	0.000408535i
$624$	20.2753	−	8.47779i	0.811662	−	0.339383i
$625$	25.1879	+	10.4331i	1.00751	+	0.417326i
$626$	6.72917	−	6.10921i	0.268952	−	0.244173i
$627$	0.216423	+	0.177613i	0.00864308	+	0.00709319i
$628$	−0.0799096	−	47.8322i	−0.00318874	−	1.90871i
$629$	27.8384	−	8.44470i	1.10999	−	0.336712i
$630$	7.93497	+	7.17977i	0.316137	+	0.286049i
$631$	10.2231	−	15.3000i	0.406977	−	0.609084i	−0.570202	−	0.821505i	$-0.693135\pi$
$631$	10.2231	−	15.3000i	0.406977	−	0.609084i	0.977178	+	0.212421i	$0.0681349\pi$
$632$	−25.7616	+	1.33031i	−1.02474	+	0.0529167i
$633$	−1.69412	+	1.13197i	−0.0673352	+	0.0449919i
$634$	−34.0811	+	25.3205i	−1.35354	+	1.00560i
$635$	−4.18691	−	5.10177i	−0.166153	−	0.202457i
$636$	14.9345	+	7.95059i	0.592190	+	0.315261i
$637$	16.4938	−	8.81612i	0.653508	−	0.349308i
$638$	1.51865	−	0.226568i	0.0601241	−	0.00896990i
$639$	13.0022			0.514357
$640$	−4.04780	−	26.2304i	−0.160004	−	1.03685i
$641$	−35.0911			−1.38601			−0.693007	−	0.720931i	$-0.743715\pi$
$641$	−35.0911			−1.38601			−0.693007	+	0.720931i	$0.743715\pi$
$642$	0.817061	−	0.121897i	0.0322468	−	0.00481089i
$643$	−23.6466	+	12.6394i	−0.932531	+	0.498448i	−0.866393	−	0.499362i	$-0.833568\pi$
$643$	−23.6466	+	12.6394i	−0.932531	+	0.498448i	−0.0661376	+	0.997811i	$0.521068\pi$
$644$	7.67337	−	14.4137i	0.302373	−	0.567981i
$645$	17.2595	+	21.0307i	0.679591	+	0.828084i
$646$	−2.11538	+	1.57162i	−0.0832286	+	0.0618344i
$647$	−22.2242	+	14.8497i	−0.873724	+	0.583804i	−0.909569	−	0.415554i	$-0.863588\pi$
$647$	−22.2242	+	14.8497i	−0.873724	+	0.583804i	0.0358448	+	0.999357i	$0.488588\pi$
$648$	−1.89420	+	2.10048i	−0.0744111	+	0.0825146i
$649$	−1.25725	+	1.88160i	−0.0493512	+	0.0738593i
$650$	−2.89964	−	2.62367i	−0.113733	−	0.102909i
$651$	−14.1401	+	4.28935i	−0.554194	+	0.168113i
$652$	−44.2810	+	0.0739770i	−1.73418	+	0.00289716i
$653$	0.144288	+	0.118414i	0.00564643	+	0.00463390i	0.637212	−	0.770688i	$-0.280087\pi$
$653$	0.144288	+	0.118414i	0.00564643	+	0.00463390i	−0.631566	+	0.775322i	$0.717587\pi$
$654$	−8.40345	+	7.62924i	−0.328601	+	0.298327i
$655$	−42.1868	−	17.4743i	−1.64837	−	0.682779i
$656$	17.8256	+	17.7069i	0.695974	+	0.691338i
$657$	−4.55932	+	1.88853i	−0.177876	+	0.0736786i
$658$	17.6380	−	37.3731i	0.687599	−	1.45695i
$659$	1.45005	+	14.7226i	0.0564859	+	0.573511i	0.981219	+	0.192896i	$0.0617879\pi$
$659$	1.45005	+	14.7226i	0.0564859	+	0.573511i	−0.924733	+	0.380616i	$0.875712\pi$
$660$	3.22633	−	0.647362i	0.125585	−	0.0251985i
$661$	−14.1375	+	26.4493i	−0.549884	+	1.02876i	0.441437	+	0.897292i	$0.354469\pi$
$661$	−14.1375	+	26.4493i	−0.549884	+	1.02876i	−0.991320	+	0.131467i	$0.958031\pi$
$662$	23.5379	−	11.1567i	0.914826	−	0.433616i
$663$	−25.1540	+	5.00344i	−0.976901	+	0.194318i
$664$	−3.20588	−	5.31842i	−0.124412	−	0.206395i
$665$	0.589286	−	2.96254i	0.0228515	−	0.114882i
$666$	−7.56319	−	4.52462i	−0.293068	−	0.175325i
$667$	0.384075	−	3.89958i	0.0148714	−	0.150992i
$668$	19.0462	−	1.90802i	0.736921	−	0.0738237i
$669$	−2.17462	+	7.16877i	−0.0840758	+	0.277161i
$670$	46.7723	+	11.6743i	1.80697	+	0.451019i
$671$	5.87516	+	5.87516i	0.226808	+	0.226808i
$672$	17.6809	−	4.50739i	0.682054	−	0.173876i
$673$	17.6711	−	17.6711i	0.681170	−	0.681170i	−0.279094	−	0.960264i	$-0.590034\pi$
$673$	17.6711	−	17.6711i	0.681170	−	0.681170i	0.960264	+	0.279094i	$0.0900341\pi$
$674$	−25.2497	+	15.1628i	−0.972583	+	0.584049i
$675$	0.481615	+	0.146096i	0.0185374	+	0.00562325i
$676$	−16.2526	−	30.2847i	−0.625100	−	1.16480i
$677$	1.06133	+	0.104532i	0.0407903	+	0.00401750i	0.118392	−	0.992967i	$-0.462226\pi$
$677$	1.06133	+	0.104532i	0.0407903	+	0.00401750i	−0.0776014	+	0.996984i	$0.524726\pi$
$678$	−1.98977	−	7.91554i	−0.0764166	−	0.303995i
$679$	11.9546	+	2.37792i	0.458776	+	0.0912562i
$680$	−1.44228	+	30.9401i	−0.0553088	+	1.18650i
$681$	−0.467058	−	2.34806i	−0.0178977	−	0.0899777i
$682$	−1.52719	+	4.27947i	−0.0584790	+	0.163869i
$683$	13.2134	+	7.06272i	0.505598	+	0.270248i	0.704414	−	0.709789i	$-0.251210\pi$
$683$	13.2134	+	7.06272i	0.505598	+	0.270248i	−0.198817	+	0.980037i	$0.563710\pi$
$684$	0.783296	+	0.154447i	0.0299501	+	0.00590544i
$685$	−49.9545	+	4.92009i	−1.90866	+	0.187987i
$686$	−15.4398	+	5.53900i	−0.589494	+	0.211480i
$687$	−4.37162	−	10.5540i	−0.166788	−	0.402662i
$688$	46.1505	−	4.70117i	1.75947	−	0.179230i
$689$	17.7860	−	42.9392i	0.677593	−	1.63585i
$690$	0.405044	−	8.38782i	0.0154198	−	0.319319i
$691$	−9.61358	+	11.7142i	−0.365718	+	0.445628i	−0.923061	−	0.384654i	$-0.874321\pi$
$691$	−9.61358	+	11.7142i	−0.365718	+	0.445628i	0.557343	+	0.830282i	$0.311821\pi$
$692$	9.59984	−	3.99519i	0.364931	−	0.151874i
$693$	0.656695	+	2.16483i	0.0249458	+	0.0822352i
$694$	−0.989457	−	19.8033i	−0.0375593	−	0.751724i
$695$	23.7869	+	15.8939i	0.902289	+	0.602890i
$696$	3.51034	−	2.61710i	0.133059	−	0.0992011i
$697$	−16.2903	−	24.3802i	−0.617040	−	0.923465i
$698$	5.80132	−	39.3357i	0.219583	−	1.48888i
$699$	4.06514	−	3.33617i	0.153758	−	0.126186i
$700$	−2.06389	−	2.50631i	−0.0780078	−	0.0947296i
$701$	−9.57136	−	17.9068i	−0.361505	−	0.676329i	0.633759	−	0.773530i	$-0.281511\pi$
$701$	−9.57136	−	17.9068i	−0.361505	−	0.676329i	−0.995265	+	0.0972014i	$0.969011\pi$
$702$	6.24465	+	4.62326i	0.235689	+	0.174494i
$703$			2.48772i			0.0938261i
$704$	2.12117	−	5.19444i	0.0799447	−	0.195773i
$705$		−	21.2529i		−	0.800432i
$706$	−20.6256	+	27.8590i	−0.776255	+	1.04849i
$707$	−12.4602	−	23.3114i	−0.468614	−	0.876715i
$708$	−0.621791	+	6.42314i	−0.0233683	+	0.241396i
$709$	−8.90694	+	7.30974i	−0.334507	+	0.274523i	−0.786619	−	0.617438i	$-0.788171\pi$
$709$	−8.90694	+	7.30974i	−0.334507	+	0.274523i	0.452112	+	0.891961i	$0.350671\pi$
$710$	−42.6745	−	6.29374i	−1.60155	−	0.236200i
$711$	−5.06693	−	7.58319i	−0.190025	−	0.284392i
$712$	0.00573417	+	0.0226511i	0.000214897	+	0.000848886i
$713$	9.64143	+	6.44219i	0.361074	+	0.241262i
$714$	−21.2673	+	1.06260i	−0.795907	+	0.0397669i
$715$	−2.62404	−	8.65029i	−0.0981334	−	0.323503i
$716$	−1.80438	+	4.37682i	−0.0674328	+	0.163569i
$717$	−18.5776	+	22.6368i	−0.693792	+	0.845387i
$718$	−17.6989	−	0.854672i	−0.660517	−	0.0318961i
$719$	6.59462	−	15.9208i	0.245938	−	0.593747i	−0.751914	−	0.659262i	$-0.770869\pi$
$719$	6.59462	−	15.9208i	0.245938	−	0.593747i	0.997852	+	0.0655149i	$0.0208690\pi$
$720$	7.23372	−	5.97712i	0.269585	−	0.222754i
$721$	−15.0507	−	36.3356i	−0.560518	−	1.35321i
$722$	8.99728	+	25.0797i	0.334844	+	0.933368i
$723$	19.2661	−	1.89754i	0.716513	−	0.0705704i
$724$	−11.4688	−	17.1023i	−0.426233	−	0.635602i
$725$	−0.687116	−	0.367271i	−0.0255188	−	0.0136401i
$726$	−13.9962	−	4.99473i	−0.519447	−	0.185372i
$727$	−5.00553	−	25.1645i	−0.185645	−	0.933300i	−0.955480	−	0.295057i	$-0.904661\pi$
$727$	−5.00553	−	25.1645i	−0.185645	−	0.933300i	0.769835	−	0.638243i	$-0.220339\pi$
$728$	−17.0043	−	47.1511i	−0.630223	−	1.74754i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	15.8783	−	3.99142i	0.587684	−	0.147729i
$731$	−53.8764	−	5.30636i	−1.99269	−	0.196263i
$732$	22.6846	+	6.83992i	0.838445	+	0.252811i
$733$	9.94750	+	3.01754i	0.367419	+	0.111455i	0.468595	−	0.883413i	$-0.344760\pi$
$733$	9.94750	+	3.01754i	0.367419	+	0.111455i	−0.101176	+	0.994869i	$0.532260\pi$
$734$	13.4898	+	22.4638i	0.497918	+	0.829154i
$735$	5.64665	−	5.64665i	0.208280	−	0.208280i
$736$	−11.5364	−	8.48153i	−0.425238	−	0.312633i
$737$	7.20626	+	7.20626i	0.265446	+	0.265446i
$738$	−2.15124	+	8.61876i	−0.0791882	+	0.317261i
$739$	−12.1074	+	39.9129i	−0.445380	+	1.46822i	0.391165	+	0.920321i	$0.372072\pi$
$739$	−12.1074	+	39.9129i	−0.445380	+	1.46822i	−0.836544	+	0.547899i	$0.815428\pi$
$740$	22.6331	+	18.5113i	0.832009	+	0.680489i
$741$	0.214969	−	2.18262i	0.00789710	−	0.0801806i
$742$	19.8108	−	33.1151i	0.727279	−	1.21569i
$743$	1.76824	−	8.88955i	0.0648705	−	0.326126i	−0.934700	−	0.355438i	$-0.884332\pi$
$743$	1.76824	−	8.88955i	0.0648705	−	0.326126i	0.999570	+	0.0293121i	$0.00933166\pi$
$744$	1.93333	+	12.8122i	0.0708793	+	0.469716i
$745$	27.7279	−	5.51543i	1.01587	−	0.202070i
$746$	9.72954	+	20.5270i	0.356224	+	0.751547i
$747$	1.03497	−	1.93630i	0.0378676	−	0.0708453i
$748$	−3.62875	+	5.45049i	−0.132680	+	0.199290i
$749$	−0.184681	−	1.87510i	−0.00674810	−	0.0685146i
$750$	13.4914	+	6.36716i	0.492635	+	0.232496i
$751$	5.40575	−	2.23914i	0.197259	−	0.0817072i	−0.281867	−	0.959453i	$-0.590954\pi$
$751$	5.40575	−	2.23914i	0.197259	−	0.0817072i	0.479126	+	0.877746i	$0.340954\pi$
$752$	−30.1982	−	20.0321i	−1.10121	−	0.730497i
$753$	−9.01371	−	3.73360i	−0.328478	−	0.136060i
$754$	−8.08501	−	8.90547i	−0.294439	−	0.324318i
$755$	−19.0696	−	15.6500i	−0.694014	−	0.569563i
$756$	4.56920	+	4.55396i	0.166180	+	0.165626i
$757$	9.82816	−	2.98134i	0.357210	−	0.108359i	−0.106579	−	0.994304i	$-0.533990\pi$
$757$	9.82816	−	2.98134i	0.357210	−	0.108359i	0.463789	+	0.885946i	$0.346490\pi$
$758$	−20.9021	+	23.1007i	−0.759199	+	0.839054i
$759$	0.986294	−	1.47609i	0.0358002	−	0.0535788i
$760$	−2.49611	−	0.886072i	−0.0905433	−	0.0321412i
$761$	−18.4181	+	12.3066i	−0.667657	+	0.446114i	−0.842654	−	0.538455i	$-0.819008\pi$
$761$	−18.4181	+	12.3066i	−0.667657	+	0.446114i	0.174997	+	0.984569i	$0.444008\pi$
$762$	−2.37277	−	3.19373i	−0.0859563	−	0.115696i
$763$	16.4226	+	20.0110i	0.594538	+	0.724447i
$764$	−9.35445	−	30.6530i	−0.338432	−	1.10899i
$765$	−9.65779	+	5.16220i	−0.349178	+	0.186640i
$766$	−0.146153	−	0.979646i	−0.00528073	−	0.0353960i
$767$	17.7271			0.640090
$768$	−1.67464	−	15.9121i	−0.0604285	−	0.574179i
$769$	−26.2913			−0.948089			−0.474044	−	0.880501i	$-0.657206\pi$
$769$	−26.2913			−0.948089			−0.474044	+	0.880501i	$0.657206\pi$
$770$	−1.10745	−	7.42310i	−0.0399098	−	0.267510i
$771$	−10.6953	+	5.71673i	−0.385180	+	0.205883i
$772$	−10.0767	−	33.0197i	−0.362668	−	1.18840i
$773$	32.9821	+	40.1888i	1.18628	+	1.44549i	0.867340	+	0.497715i	$0.165828\pi$
$773$	32.9821	+	40.1888i	1.18628	+	1.44549i	0.318942	+	0.947774i	$0.396672\pi$
$774$	9.78112	+	13.1653i	0.351575	+	0.473217i
$775$	1.91702	−	1.28091i	0.0688615	−	0.0460118i
$776$	3.57553	−	10.0724i	0.128354	−	0.361579i
$777$	−11.1677	+	16.7136i	−0.400638	+	0.599597i
$778$	6.09916	−	6.74070i	0.218666	−	0.241666i
$779$	2.39948	−	0.727874i	0.0859703	−	0.0260788i
$780$	−18.2577	−	18.1968i	−0.653731	−	0.651551i
$781$	−7.04919	−	5.78512i	−0.252240	−	0.207008i
$782$	11.2322	+	12.3720i	0.401663	+	0.442423i
$783$	1.43021	+	0.592413i	0.0511116	+	0.0211711i
$784$	−2.70099	−	13.3456i	−0.0964639	−	0.476628i
$785$	−51.8343	+	21.4705i	−1.85004	+	0.766314i
$786$	−24.8943	−	11.7487i	−0.887949	−	0.419062i
$787$	−2.10233	−	21.3454i	−0.0749401	−	0.760880i	−0.957067	−	0.289867i	$-0.906389\pi$
$787$	−2.10233	−	21.3454i	−0.0749401	−	0.760880i	0.882127	−	0.471012i	$-0.156111\pi$
$788$	−18.6975	+	28.0842i	−0.666070	+	1.00046i
$789$	6.55370	−	12.2611i	0.233318	−	0.436507i
$790$	12.9596	+	27.3416i	0.461080	+	0.972769i
$791$	−18.2577	+	3.63168i	−0.649169	+	0.129128i
$792$	1.96153	−	0.295991i	0.0696999	−	0.0105176i
$793$	12.6978	−	63.8361i	0.450912	−	2.26689i
$794$	−13.4540	+	22.4893i	−0.477466	+	0.798114i
$795$	1.94516	−	19.7496i	0.0689878	−	0.700445i
$796$	15.5115	+	12.6867i	0.549792	+	0.449668i
$797$	6.49890	−	21.4240i	0.230203	−	0.758877i	−0.763398	−	0.645928i	$-0.776470\pi$
$797$	6.49890	−	21.4240i	0.230203	−	0.758877i	0.993601	−	0.112949i	$-0.0360296\pi$
$798$	0.440976	−	1.76673i	0.0156104	−	0.0625417i
$799$	29.9040	+	29.9040i	1.05793	+	1.05793i
$800$	−2.43583	+	1.47384i	−0.0861197	+	0.0521083i
$801$	−0.00584141	+	0.00584141i	−0.000206396	+	0.000206396i
$802$	23.4137	+	38.9895i	0.826767	+	1.37677i
$803$	3.31213	+	1.00472i	0.116883	+	0.0354560i
$804$	27.8241	+	8.38961i	0.981280	+	0.295879i
$805$	−19.0609	−	1.87734i	−0.671810	−	0.0661675i
$806$	34.5201	−	8.67749i	1.21592	−	0.305651i
$807$	22.8427	+	4.54370i	0.804101	+	0.159946i
$808$	−21.8038	+	7.86321i	−0.767055	+	0.276627i
$809$	−0.452021	−	2.27246i	−0.0158922	−	0.0798955i	0.972025	−	0.234876i	$-0.0754685\pi$
$809$	−0.452021	−	2.27246i	−0.0158922	−	0.0798955i	−0.987917	+	0.154981i	$0.950468\pi$
$810$	3.12461	+	1.11506i	0.109788	+	0.0391793i
$811$	26.0914	+	13.9462i	0.916195	+	0.489716i	0.860912	−	0.508754i	$-0.169894\pi$
$811$	26.0914	+	13.9462i	0.916195	+	0.489716i	0.0552830	+	0.998471i	$0.482394\pi$
$812$	−5.56210	−	8.29425i	−0.195192	−	0.291071i
$813$	−11.8139	+	1.16357i	−0.414331	+	0.0408080i
$814$	2.08726	+	5.81818i	0.0731585	+	0.203927i
$815$	19.8765	+	47.9860i	0.696242	+	1.68088i
$816$	−1.76810	+	18.5884i	−0.0618960	+	0.650723i
$817$	1.77164	−	4.27712i	0.0619819	−	0.149638i
$818$	15.7008	+	0.758183i	0.548965	+	0.0265093i
$819$	11.2423	−	13.6988i	0.392838	−	0.478675i
$820$	11.2326	−	27.2464i	0.392258	−	0.951487i
$821$	−14.6807	−	48.3958i	−0.512360	−	1.68902i	−0.706218	−	0.707995i	$-0.749600\pi$
$821$	−14.6807	−	48.3958i	−0.512360	−	1.68902i	0.193858	−	0.981030i	$-0.437900\pi$
$822$	−30.2227	+	1.51005i	−1.05414	+	0.0526692i
$823$	10.3680	+	6.92766i	0.361405	+	0.241483i	0.722994	−	0.690855i	$-0.242766\pi$
$823$	10.3680	+	6.92766i	0.361405	+	0.241483i	−0.361589	+	0.932338i	$0.617766\pi$
$824$	−33.4328	+	8.46358i	−1.16469	+	0.294843i
$825$	−0.196107	−	0.293494i	−0.00682756	−	0.0102182i
$826$	14.5608	+	2.14747i	0.506636	+	0.0747199i
$827$	22.2233	−	18.2382i	0.772780	−	0.634204i	−0.163065	−	0.986615i	$-0.552138\pi$
$827$	22.2233	−	18.2382i	0.772780	−	0.634204i	0.935845	+	0.352411i	$0.114638\pi$
$828$	0.487787	−	5.03887i	0.0169518	−	0.175113i
$829$	21.4062	+	40.0483i	0.743469	+	1.39093i	0.914055	+	0.405591i	$0.132934\pi$
$829$	21.4062	+	40.0483i	0.743469	+	1.39093i	−0.170585	+	0.985343i	$0.554566\pi$
$830$	−4.33416	+	5.85416i	−0.150441	+	0.203201i
$831$		−	22.3203i		−	0.774284i
$832$	−43.0647	+	8.79070i	−1.49300	+	0.304763i
$833$			15.8903i			0.550566i
$834$	13.8609	+	10.2620i	0.479964	+	0.355345i
$835$	−10.5839	−	19.8011i	−0.366271	−	0.685244i
$836$	−0.355949	−	0.432251i	−0.0123108	−	0.0149497i
$837$	−3.54121	+	2.90619i	−0.122402	+	0.100453i
$838$	−4.66522	+	31.6324i	−0.161157	+	1.09272i
$839$	−11.3391	−	16.9701i	−0.391468	−	0.585873i	0.582424	−	0.812885i	$-0.302104\pi$
$839$	−11.3391	−	16.9701i	−0.391468	−	0.585873i	−0.973892	+	0.227012i	$0.927104\pi$
$840$	−12.7923	−	17.1584i	−0.441375	−	0.592019i
$841$	22.1200	+	14.7801i	0.762760	+	0.509660i
$842$	−1.07979	−	21.6112i	−0.0372119	−	0.744772i
$843$	−6.93212	−	22.8521i	−0.238755	−	0.787069i
$844$	3.76220	−	1.56572i	0.129500	−	0.0538944i
$845$	−25.5753	+	31.1636i	−0.879819	+	1.07206i
$846$	0.617974	−	12.7973i	0.0212464	−	0.439979i
$847$	−12.9707	+	31.3141i	−0.445680	+	1.07597i
$848$	−26.2286	−	21.3790i	−0.900693	−	0.734157i
$849$	9.12114	+	22.0204i	0.313037	+	0.755737i
$850$	3.12736	−	1.12193i	0.107267	−	0.0384820i
$851$	15.6984	−	1.54616i	0.538134	−	0.0530016i
$852$	−25.5131	−	5.03057i	−0.874064	−	0.172345i
$853$	−14.1542	−	7.56560i	−0.484632	−	0.259041i	0.210938	−	0.977499i	$-0.432348\pi$
$853$	−14.1542	−	7.56560i	−0.484632	−	0.259041i	−0.695570	+	0.718458i	$0.744848\pi$
$854$	18.1629	−	50.8958i	0.621521	−	1.74162i
$855$	−0.182694	−	0.918467i	−0.00624802	−	0.0314109i
$856$	−1.65041	−	0.0769344i	−0.0564100	−	0.00262956i
$857$	−36.5094	−	7.26217i	−1.24714	−	0.248071i	−0.472985	−	0.881070i	$-0.656824\pi$
$857$	−36.5094	−	7.26217i	−1.24714	−	0.248071i	−0.774152	+	0.632999i	$0.781824\pi$
$858$	−1.32851	−	5.28499i	−0.0453547	−	0.180427i
$859$	−23.7078	−	2.33502i	−0.808901	−	0.0796698i	−0.314893	−	0.949127i	$-0.601969\pi$
$859$	−23.7078	−	2.33502i	−0.808901	−	0.0796698i	−0.494008	+	0.869457i	$0.664469\pi$
$860$	−25.7300	−	47.9446i	−0.877386	−	1.63490i
$861$	19.3883	+	5.88137i	0.660751	+	0.200437i
$862$	39.9626	−	23.9980i	1.36113	−	0.817376i
$863$	11.2373	−	11.2373i	0.382522	−	0.382522i	−0.489488	−	0.872010i	$-0.662816\pi$
$863$	11.2373	−	11.2373i	0.382522	−	0.382522i	0.872010	+	0.489488i	$0.162816\pi$
$864$	4.52951	−	3.38873i	0.154097	−	0.115287i
$865$	−8.62414	−	8.62414i	−0.293230	−	0.293230i
$866$	−30.7365	−	7.67182i	−1.04447	−	0.260699i
$867$	1.39071	−	4.58456i	0.0472310	−	0.155700i
$868$	29.4055	−	2.94580i	0.998088	−	0.0999870i
$869$	−0.626969	+	6.36573i	−0.0212685	+	0.215943i
$870$	−4.40736	−	2.63667i	−0.149423	−	0.0893914i
$871$	15.5747	−	78.2991i	0.527727	−	2.65306i
$872$	19.4412	−	11.7189i	0.658362	−	0.396853i
$873$	3.70625	−	0.737219i	0.125438	−	0.0249511i
$874$	−1.29126	+	0.612041i	−0.0436775	+	0.0207026i
$875$	16.0396	−	30.0080i	0.542238	−	1.01446i
$876$	9.67706	−	1.94170i	0.326958	−	0.0656039i
$877$	1.31090	+	13.3097i	0.0442658	+	0.449438i	0.991614	+	0.129233i	$0.0412517\pi$
$877$	1.31090	+	13.3097i	0.0442658	+	0.449438i	−0.947348	+	0.320205i	$0.896248\pi$
$878$	2.69884	−	5.71857i	0.0910814	−	0.192992i
$879$	23.0505	−	9.54785i	0.777476	−	0.322041i
$880$	−6.58123	+	0.0219896i	−0.221853	+	0.000741269i
$881$	−3.70441	−	1.53442i	−0.124805	−	0.0516959i	0.319407	−	0.947618i	$-0.396516\pi$
$881$	−3.70441	−	1.53442i	−0.124805	−	0.0516959i	−0.444212	+	0.895922i	$0.646516\pi$
$882$	3.56427	−	3.23589i	0.120015	−	0.108958i
$883$	3.74588	+	3.07417i	0.126059	+	0.103454i	0.695310	−	0.718710i	$-0.255267\pi$
$883$	3.74588	+	3.07417i	0.126059	+	0.103454i	−0.569251	+	0.822164i	$0.692767\pi$
$884$	51.2935	−	0.0856922i	1.72519	−	0.00288214i
$885$	7.24333	−	2.19724i	0.243482	−	0.0738595i
$886$	−16.2696	−	14.7212i	−0.546587	−	0.494567i
$887$	26.0759	−	39.0253i	0.875542	−	1.31034i	−0.0741788	−	0.997245i	$-0.523634\pi$
$887$	26.0759	−	39.0253i	0.875542	−	1.31034i	0.949721	−	0.313097i	$-0.101366\pi$
$888$	13.0901	+	11.8045i	0.439273	+	0.396134i
$889$	−7.54521	+	5.04155i	−0.253058	+	0.169088i
$890$	0.0219997	−	0.0163446i	0.000737433	−	0.000547873i
$891$	0.444936	+	0.542156i	0.0149059	+	0.0181629i
$892$	7.04071	−	13.2253i	0.235740	−	0.442817i
$893$	−3.18945	+	1.70480i	−0.106731	+	0.0570489i
$894$	16.8565	−	2.51482i	0.563765	−	0.0841080i
$895$	5.55296			0.185615
$896$	−36.4377	+	2.00370i	−1.21730	+	0.0669390i
$897$	−13.9067			−0.464332
$898$	26.5281	−	3.95772i	0.885254	−	0.132071i
$899$	6.25434	−	3.34301i	0.208594	−	0.111496i
$900$	−0.888509	−	0.473011i	−0.0296170	−	0.0157670i
$901$	25.0518	+	30.5257i	0.834595	+	1.01696i
$902$	5.00110	−	3.71555i	0.166518	−	0.123714i
$903$	31.1032	−	20.7825i	1.03505	−	0.691598i
$904$	0.841815	+	16.3019i	0.0279984	+	0.542193i
$905$	−13.4188	+	20.0827i	−0.446056	+	0.667570i
$906$	−11.0275	−	9.97801i	−0.366365	−	0.331497i
$907$	31.6576	−	9.60323i	1.05117	−	0.318870i	0.283006	−	0.959118i	$-0.408668\pi$
$907$	31.6576	−	9.60323i	1.05117	−	0.318870i	0.768168	+	0.640248i	$0.221168\pi$
$908$	0.00799913	+	4.78811i	0.000265460	+	0.158899i
$909$	−6.33465	−	5.19871i	−0.210107	−	0.172430i
$910$	−43.5295	+	39.5191i	−1.44299	+	1.31005i
$911$	−29.8828	−	12.3778i	−0.990060	−	0.410096i	−0.171917	−	0.985111i	$-0.554996\pi$
$911$	−29.8828	−	12.3778i	−0.990060	−	0.410096i	−0.818143	+	0.575015i	$0.804996\pi$
$912$	−1.47724	−	0.606120i	−0.0489164	−	0.0200706i
$913$	−1.42264	+	0.589278i	−0.0470826	+	0.0195022i
$914$	−11.5965	+	24.5717i	−0.383577	+	0.812761i
$915$	−2.72401	−	27.6574i	−0.0900531	−	0.914324i
$916$	4.49470	+	22.4007i	0.148509	+	0.740141i
$917$	−29.5963	+	55.3708i	−0.977356	+	1.82850i
$918$	−5.96546	+	2.82755i	−0.196889	+	0.0933231i
$919$	−51.8160	+	10.3069i	−1.70925	+	0.339992i	−0.950343	−	0.311203i	$-0.899268\pi$
$919$	−51.8160	+	10.3069i	−1.70925	+	0.339992i	−0.758910	+	0.651195i	$0.774268\pi$
$920$	−4.04006	+	16.3020i	−0.133197	+	0.537462i
$921$	−3.58435	+	18.0197i	−0.118108	+	0.593770i
$922$	39.0456	+	23.3587i	1.28590	+	0.769278i
$923$	−7.00186	+	71.0911i	−0.230469	+	2.33999i
$924$	−0.450999	−	4.50196i	−0.0148368	−	0.148103i
$925$	0.910462	−	3.00139i	0.0299358	−	0.0986851i
$926$	41.8106	+	10.4359i	1.37398	+	0.342945i
$927$	−8.62187	−	8.62187i	−0.283179	−	0.283179i
$928$	−7.90062	+	3.77717i	−0.259350	+	0.123992i
$929$	14.1377	−	14.1377i	0.463842	−	0.463842i	−0.436070	−	0.899913i	$-0.643630\pi$
$929$	14.1377	−	14.1377i	0.463842	−	0.463842i	0.899913	+	0.436070i	$0.143630\pi$
$930$	13.0294	−	7.82432i	0.427251	−	0.256570i
$931$	−1.30034	−	0.394455i	−0.0426171	−	0.0129277i
$932$	−9.26747	+	4.97349i	−0.303566	+	0.162912i
$933$	−9.46694	−	0.932412i	−0.309934	−	0.0305258i
$934$	−6.62952	−	26.3730i	−0.216924	−	0.862952i
$935$	7.53287	+	1.49838i	0.246351	+	0.0490023i
$936$	−10.4646	−	11.4879i	−0.342047	−	0.375495i
$937$	6.26562	+	31.4994i	0.204689	+	1.02904i	0.937335	+	0.348430i	$0.113285\pi$
$937$	6.26562	+	31.4994i	0.204689	+	1.02904i	−0.732646	+	0.680610i	$0.761715\pi$
$938$	22.2780	−	62.4271i	0.727401	−	2.03832i
$939$	−5.66781	−	3.02951i	−0.184962	−	0.0988643i
$940$	−8.22283	+	41.7029i	−0.268199	+	1.36020i
$941$	−19.3251	+	1.90336i	−0.629982	+	0.0620478i	−0.407969	−	0.912996i	$-0.633763\pi$
$941$	−19.3251	+	1.90336i	−0.629982	+	0.0620478i	−0.222013	+	0.975044i	$0.571263\pi$
$942$	−31.8358	+	11.4211i	−1.03727	+	0.372118i
$943$	−6.08446	−	14.6892i	−0.198137	−	0.478346i
$944$	3.70522	−	12.3630i	0.120595	−	0.402382i
$945$	2.89569	−	6.99081i	0.0941967	−	0.227411i
$946$	0.554828	−	11.4896i	0.0180390	−	0.373560i
$947$	−32.0456	+	39.0477i	−1.04134	+	1.26888i	−0.0790462	+	0.996871i	$0.525187\pi$
$947$	−32.0456	+	39.0477i	−1.04134	+	1.26888i	−0.962295	+	0.272007i	$0.912313\pi$
$948$	7.00846	+	16.8403i	0.227624	+	0.546948i
$949$	−7.87055	−	25.9457i	−0.255489	−	0.842233i
$950$	0.0141784	+	0.283770i	0.000460007	+	0.00920672i
$951$	24.9624	+	16.6794i	0.809463	+	0.540866i
$952$	42.1422	+	6.14331i	1.36584	+	0.199106i
$953$	8.05260	+	12.0516i	0.260849	+	0.390389i	0.938658	−	0.344850i	$-0.112070\pi$
$953$	8.05260	+	12.0516i	0.260849	+	0.390389i	−0.677809	+	0.735238i	$0.737070\pi$
$954$	1.74552	−	11.8355i	0.0565134	−	0.383187i
$955$	−29.0587	+	23.8478i	−0.940317	+	0.771698i
$956$	45.2115	−	37.2307i	1.46224	−	1.20413i
$957$	−0.511812	−	0.957533i	−0.0165445	−	0.0309526i
$958$	19.9039	+	14.7360i	0.643067	+	0.476099i
$959$			69.0178i			2.22870i
$960$	−16.5067	+	8.92967i	−0.532752	+	0.288204i
$961$		−	10.0139i		−	0.323028i
$962$	28.8119	−	38.9162i	0.928932	−	1.25471i
$963$	−0.275363	−	0.515168i	−0.00887346	−	0.0166011i
$964$	−38.5384	−	3.73071i	−1.24124	−	0.120158i
$965$	−31.3022	+	25.6891i	−1.00765	+	0.826960i
$966$	−11.4228	−	1.68466i	−0.367522	−	0.0542031i
$967$	16.5998	+	24.8433i	0.533813	+	0.798907i	0.996138	−	0.0878035i	$-0.0279848\pi$
$967$	16.5998	+	24.8433i	0.533813	+	0.798907i	−0.462325	+	0.886710i	$0.652985\pi$
$968$	25.5311	+	15.2159i	0.820601	+	0.489058i
$969$	1.54939	+	1.03527i	0.0497737	+	0.0332577i
$970$	−12.5212	+	0.625611i	−0.402031	+	0.0200872i
$971$	13.2994	+	43.8423i	0.426798	+	1.40697i	0.862126	+	0.506694i	$0.169132\pi$
$971$	13.2994	+	43.8423i	0.426798	+	1.40697i	−0.435328	+	0.900272i	$0.643368\pi$
$972$	1.84904	+	0.762279i	0.0593078	+	0.0244501i
$973$	24.9540	−	30.4065i	0.799988	−	0.974789i
$974$	6.77579	+	0.327200i	0.217110	+	0.0104842i
$975$	−1.05816	+	2.55462i	−0.0338882	+	0.0818133i
$976$	−41.8657	−	22.1982i	−1.34009	−	0.710546i
$977$	−15.2020	−	36.7010i	−0.486356	−	1.17417i	−0.956540	−	0.291600i	$-0.905813\pi$
$977$	−15.2020	−	36.7010i	−0.486356	−	1.17417i	0.470184	−	0.882568i	$-0.344187\pi$
$978$	10.5731	+	29.4723i	0.338092	+	0.942420i
$979$	0.00576601		0.000567902i	0.000184282		1.81502e-5i
$980$	−13.2647	+	8.89526i	−0.423725	+	0.284149i
$981$	7.07802	+	3.78328i	0.225984	+	0.120791i
$982$	38.0475	+	13.5778i	1.21414	+	0.433284i
$983$	−8.14356	−	40.9404i	−0.259739	−	1.30580i	−0.861760	−	0.507316i	$-0.830638\pi$
$983$	−8.14356	−	40.9404i	−0.259739	−	1.30580i	0.602021	−	0.798481i	$-0.294362\pi$
$984$	7.55583	−	16.0796i	0.240871	−	0.512599i
$985$	38.8138	+	7.72055i	1.23671	+	0.245997i
$986$	9.91133	−	2.49146i	0.315641	−	0.0793442i
$987$	−29.0812	−	2.86425i	−0.925666	−	0.0911701i
$988$	−1.26628	+	4.19961i	−0.0402857	+	0.133607i
$989$	−28.0913	−	8.52139i	−0.893250	−	0.270965i
$990$	−1.19790	−	1.99479i	−0.0380716	−	0.0633985i
$991$	20.7717	−	20.7717i	0.659834	−	0.659834i	−0.295506	−	0.955341i	$-0.595488\pi$
$991$	20.7717	−	20.7717i	0.659834	−	0.659834i	0.955341	+	0.295506i	$0.0954884\pi$
$992$	1.16345	−	25.8883i	0.0369394	−	0.821953i
$993$	−13.0241	−	13.0241i	−0.413306	−	0.413306i
$994$	−14.3632	+	57.5450i	−0.455573	+	1.82522i
$995$	6.82308	−	22.4927i	0.216306	−	0.713066i
$996$	−2.78000	+	3.39900i	−0.0880877	+	0.107702i
$997$	1.39910	−	14.2053i	0.0443099	−	0.449886i	−0.947274	−	0.320423i	$-0.896175\pi$
$997$	1.39910	−	14.2053i	0.0443099	−	0.449886i	0.991584	−	0.129463i	$-0.0413252\pi$
$998$	−4.35360	+	7.27733i	−0.137811	+	0.230360i
$999$	−1.21579	+	6.11219i	−0.0384659	+	0.193381i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.18	yes	512
128.109	even	32	inner	384.2.v.a.109.18	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.18	✓	512	128.109	even	32	inner
384.2.v.a.229.18	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)

\(f(q)\)	\(=\)	\(q+(0.208677 + 1.39873i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.91291 + 0.583766i) q^{4} +(1.48823 + 1.81341i) q^{5} +(0.843395 + 1.13520i) q^{6} +(2.68193 - 1.79201i) q^{7} +(-1.21571 - 2.55383i) q^{8} +(0.555570 - 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.208677 + 1.39873i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.91291 + 0.583766i) q^{4} +(1.48823 + 1.81341i) q^{5} +(0.843395 + 1.13520i) q^{6} +(2.68193 - 1.79201i) q^{7} +(-1.21571 - 2.55383i) q^{8} +(0.555570 - 0.831470i) q^{9} +(-2.22592 + 2.46005i) q^{10} +(-0.671156 + 0.203593i) q^{11} +(-1.41185 + 1.41657i) q^{12} +(4.24699 + 3.48542i) q^{13} +(3.06620 + 3.37735i) q^{14} +(2.16734 + 0.897740i) q^{15} +(3.31843 - 2.23338i) q^{16} +(-4.31273 + 1.78639i) q^{17} +(1.27894 + 0.603586i) q^{18} +(-0.0391274 - 0.397267i) q^{19} +(-3.90545 - 2.60011i) q^{20} +(1.52050 - 2.84466i) q^{21} +(-0.424827 - 0.896283i) q^{22} +(-2.48258 + 0.493815i) q^{23} +(-2.27603 - 1.67919i) q^{24} +(-0.0981862 + 0.493616i) q^{25} +(-3.98892 + 6.66774i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-4.08417 + 4.99357i) q^{28} +(-0.449375 + 1.48139i) q^{29} +(-0.803426 + 3.21886i) q^{30} +(-3.23930 - 3.23930i) q^{31} +(3.81638 + 4.17555i) q^{32} +(-0.495934 + 0.495934i) q^{33} +(-3.39865 - 5.65958i) q^{34} +(7.24097 + 2.19653i) q^{35} +(-0.577371 + 1.91485i) q^{36} +(-6.20193 - 0.610836i) q^{37} +(0.547505 - 0.137629i) q^{38} +(5.38853 + 1.07184i) q^{39} +(2.82189 - 6.00527i) q^{40} +(1.22543 + 6.16066i) q^{41} +(4.29622 + 1.53316i) q^{42} +(10.2279 + 5.46694i) q^{43} +(1.16501 - 0.781253i) q^{44} +(2.33461 - 0.229939i) q^{45} +(-1.20877 - 3.36941i) q^{46} +(-3.46695 - 8.36996i) q^{47} +(1.87379 - 3.53397i) q^{48} +(1.30267 - 3.14492i) q^{49} +(-0.710925 - 0.0343303i) q^{50} +(-2.96139 + 3.60846i) q^{51} +(-10.1588 - 4.18803i) q^{52} +(-2.45565 - 8.09520i) q^{53} +(1.41245 - 0.0705720i) q^{54} +(-1.36803 - 0.914089i) q^{55} +(-7.83694 - 4.67063i) q^{56} +(-0.221777 - 0.331913i) q^{57} +(-2.16585 - 0.319424i) q^{58} +(2.49418 - 2.04692i) q^{59} +(-4.66999 - 0.452077i) q^{60} +(-5.58448 - 10.4478i) q^{61} +(3.85495 - 5.20688i) q^{62} -3.22553i q^{63} +(-5.04409 + 6.20944i) q^{64} +12.8886i q^{65} +(-0.797169 - 0.590189i) q^{66} +(-6.84973 - 12.8149i) q^{67} +(7.20702 - 5.93483i) q^{68} +(-1.95665 + 1.60578i) q^{69} +(-1.56133 + 10.5866i) q^{70} +(7.22361 + 10.8109i) q^{71} +(-2.79884 - 0.408004i) q^{72} +(-4.10328 - 2.74172i) q^{73} +(-0.439800 - 8.80231i) q^{74} +(0.146096 + 0.481615i) q^{75} +(0.306758 + 0.737094i) q^{76} +(-1.43515 + 1.74874i) q^{77} +(-0.374765 + 7.76078i) q^{78} +(3.49016 - 8.42599i) q^{79} +(8.98863 + 2.69391i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-8.36141 + 2.99964i) q^{82} +(2.18497 - 0.215201i) q^{83} +(-1.24797 + 6.32920i) q^{84} +(-9.65779 - 5.16220i) q^{85} +(-5.51246 + 15.4470i) q^{86} +(0.302010 + 1.51831i) q^{87} +(1.33587 + 1.46651i) q^{88} +(-0.00810227 - 0.00161164i) q^{89} +(0.808803 + 3.21752i) q^{90} +(17.6360 + 1.73700i) q^{91} +(4.46067 - 2.39387i) q^{92} +(-4.38380 - 1.32981i) q^{93} +(10.9839 - 6.59595i) q^{94} +(0.662178 - 0.662178i) q^{95} +(5.33409 + 1.88348i) q^{96} +(2.67206 + 2.67206i) q^{97} +(4.67075 + 1.16582i) q^{98} +(-0.203593 + 0.671156i) 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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