LMFDB - Embedded newform 384.2.v.a.109.18

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			109.18
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.18

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.208677	−	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	−0.325342	−	0.945596i	$-0.605479\pi$
$5$	1.48823	−	1.81341i	0.665556	−	0.810982i	0.990898	+	0.134614i	$0.0429795\pi$
$6$	0.843395	−	1.13520i	0.344314	−	0.463445i
$7$	2.68193	+	1.79201i	1.01367	+	0.677315i	0.947256	−	0.320476i	$-0.103843\pi$
$7$	2.68193	+	1.79201i	1.01367	+	0.677315i	0.0664177	+	0.997792i	$0.478843\pi$
$8$	−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	0.187477	−	0.982269i	$-0.439969\pi$
$11$	−0.671156	−	0.203593i	−0.202361	−	0.0613856i	−0.389838	+	0.920883i	$0.627469\pi$
$12$	−1.41185	−	1.41657i	−0.407566	−	0.408930i
$13$	4.24699	−	3.48542i	1.17790	−	0.966681i	0.178054	−	0.984021i	$-0.443020\pi$
$13$	4.24699	−	3.48542i	1.17790	−	0.966681i	0.999850	+	0.0173397i	$0.00551967\pi$
$14$	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	−0.207532	−	0.978228i	$-0.566543\pi$
$17$	−4.31273	−	1.78639i	−1.04599	−	0.433264i	−0.838459	+	0.544965i	$0.816543\pi$
$18$	1.27894	−	0.603586i	0.301449	−	0.142267i
$19$	−0.0391274	+	0.397267i	−0.00897643	+	0.0911392i	−0.998629	−	0.0523447i	$-0.983331\pi$
$19$	−0.0391274	+	0.397267i	−0.00897643	+	0.0911392i	0.989653	+	0.143484i	$0.0458305\pi$
$20$	−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	−0.0706520	−	0.997501i	$-0.522508\pi$
$23$	−2.48258	−	0.493815i	−0.517653	−	0.102968i	−0.447001	+	0.894533i	$0.647508\pi$
$24$	−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	0.905280	−	0.424814i	$-0.139661\pi$
$29$	−0.449375	−	1.48139i	−0.0834469	−	0.275088i	−0.988727	+	0.149727i	$0.952161\pi$
$30$	−0.803426	−	3.21886i	−0.146685	−	0.587681i
$31$	−3.23930	+	3.23930i	−0.581795	+	0.581795i	−0.935396	−	0.353601i	$-0.884957\pi$
$31$	−3.23930	+	3.23930i	−0.581795	+	0.581795i	0.353601	+	0.935396i	$0.384957\pi$
$32$	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	−0.593975	−	0.804483i	$-0.702442\pi$
$37$	−6.20193	+	0.610836i	−1.01959	+	0.100421i	−0.425615	+	0.904904i	$0.639942\pi$
$38$	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	−0.759011	−	0.651078i	$-0.774317\pi$
$41$	1.22543	−	6.16066i	0.191380	−	0.962134i	0.950391	−	0.311056i	$-0.100683\pi$
$42$	4.29622	−	1.53316i	0.662921	−	0.236572i
$43$	10.2279	−	5.46694i	1.55974	−	0.833701i	0.559757	−	0.828657i	$-0.310895\pi$
$43$	10.2279	−	5.46694i	1.55974	−	0.833701i	0.999987	−	0.00504352i	$-0.00160541\pi$
$44$	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	0.440626	+	0.897691i	$0.354756\pi$
$47$	−3.46695	+	8.36996i	−0.505707	+	1.22088i	−0.946333	+	0.323193i	$0.895244\pi$
$48$	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	0.610204	+	0.792245i	$0.291088\pi$
$53$	−2.45565	+	8.09520i	−0.337310	+	1.11196i	−0.947513	+	0.319716i	$0.896412\pi$
$54$	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	0.782600	−	0.622525i	$-0.213893\pi$
$59$	2.49418	+	2.04692i	0.324715	+	0.266486i	−0.457885	+	0.889011i	$0.651393\pi$
$60$	−4.66999	+	0.452077i	−0.602893	+	0.0583629i
$61$	−5.58448	+	10.4478i	−0.715019	+	1.33771i	0.217312	+	0.976102i	$0.430271\pi$
$61$	−5.58448	+	10.4478i	−0.715019	+	1.33771i	−0.932332	+	0.361605i	$0.882229\pi$
$62$	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	−0.0121942	+	0.999926i	$0.503882\pi$
$67$	−6.84973	+	12.8149i	−0.836827	+	1.56559i	−0.824633	+	0.565668i	$0.808618\pi$
$68$	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	−0.100326	−	0.994955i	$-0.531989\pi$
$71$	7.22361	−	10.8109i	0.857285	−	1.28302i	0.957611	−	0.288063i	$-0.0930113\pi$
$72$	−2.79884	+	0.408004i	−0.329847	+	0.0480837i
$73$	−4.10328	+	2.74172i	−0.480252	+	0.320894i	−0.772024	−	0.635594i	$-0.780755\pi$
$73$	−4.10328	+	2.74172i	−0.480252	+	0.320894i	0.291771	+	0.956488i	$0.405755\pi$
$74$	−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	0.989355	+	0.145520i	$0.0464856\pi$
$79$	3.49016	+	8.42599i	0.392674	+	0.947998i	−0.596682	+	0.802478i	$0.703514\pi$
$80$	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	0.217219	−	0.976123i	$-0.430301\pi$
$83$	2.18497	+	0.215201i	0.239832	+	0.0236214i	0.0226128	+	0.999744i	$0.492801\pi$
$84$	−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	−0.195520	−	0.980700i	$-0.562639\pi$
$89$	−0.00810227	+	0.00161164i	−0.000858839	+	0.000170834i	0.194661	+	0.980871i	$0.437639\pi$
$90$	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	−0.558320	−	0.829626i	$-0.688554\pi$
$97$	2.67206	−	2.67206i	0.271306	−	0.271306i	0.829626	+	0.558320i	$0.188554\pi$
$98$	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	0.948679	+	0.316242i	$0.102421\pi$
$101$	0.803229	+	8.15532i	0.0799243	+	0.811485i	−0.868754	+	0.495243i	$0.835079\pi$
$102$	−5.66525	+	3.38919i	−0.560943	+	0.335580i
$103$	2.37877	+	11.9589i	0.234387	+	1.17834i	0.901296	+	0.433204i	$0.142617\pi$
$103$	2.37877	+	11.9589i	0.234387	+	1.17834i	−0.666909	+	0.745139i	$0.732383\pi$
$104$	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	0.894880	−	0.446307i	$-0.147261\pi$
$107$	0.275363	+	0.515168i	0.0266204	+	0.0498032i	−0.868259	+	0.496110i	$0.834761\pi$
$108$	0.393457	−	1.96092i	0.0378604	−	0.188689i
$109$	0.786655	−	7.98704i	0.0753479	−	0.765020i	−0.881064	−	0.472998i	$-0.843172\pi$
$109$	0.786655	−	7.98704i	0.0753479	−	0.765020i	0.956412	−	0.292022i	$-0.0943281\pi$
$110$	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	−0.619108	−	0.785306i	$-0.712506\pi$
$113$	−5.33195	+	2.20857i	−0.501588	+	0.207765i	0.117520	+	0.993071i	$0.462506\pi$
$114$	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	−0.501841	−	0.864960i	$-0.667344\pi$
$131$	−17.1664	−	9.17564i	−1.49984	−	0.801679i	−0.997996	+	0.0632805i	$0.979844\pi$
$132$	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	−0.845065	−	0.534664i	$-0.820438\pi$
$137$	−11.8877	−	17.7912i	−1.01564	−	1.52001i	−0.170573	−	0.985345i	$-0.554562\pi$
$138$	−2.65437	+	2.40175i	−0.225955	+	0.204450i
$139$	11.6699	+	3.54001i	0.989824	+	0.300260i	0.743360	−	0.668892i	$-0.233231\pi$
$139$	11.6699	+	3.54001i	0.989824	+	0.300260i	0.246464	+	0.969152i	$0.420731\pi$
$140$	−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	0.999678	+	0.0253923i	$0.00808349\pi$
$149$	5.68092	+	10.6283i	0.465399	+	0.870701i	−0.534278	+	0.845309i	$0.679417\pi$
$150$	−0.643163	−	0.304851i	−0.0525141	−	0.0248910i
$151$	−10.3138	−	2.05154i	−0.839326	−	0.166952i	−0.243334	−	0.969943i	$-0.578241\pi$
$151$	−10.3138	−	2.05154i	−0.839326	−	0.166952i	−0.595992	+	0.802990i	$0.703241\pi$
$152$	−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	−0.562843	−	0.826564i	$-0.690292\pi$
$157$	−6.94248	−	22.8863i	−0.554070	−	1.82653i	0.00877263	−	0.999962i	$-0.497208\pi$
$158$	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	0.685149	−	0.728403i	$-0.259737\pi$
$163$	21.1872	−	6.42706i	1.65951	−	0.503406i	0.974360	+	0.224997i	$0.0722371\pi$
$164$	−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	−0.544411	−	0.838819i	$-0.683247\pi$
$167$	−9.38689	+	1.86717i	−0.726379	+	0.144486i	−0.181968	+	0.983304i	$0.558247\pi$
$168$	−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	−0.100601	−	0.994927i	$-0.532077\pi$
$173$	−5.17396	−	0.509591i	−0.393369	−	0.0387435i	−0.292768	+	0.956183i	$0.594577\pi$
$174$	−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	0.826100	−	0.563524i	$-0.190555\pi$
$179$	1.50166	+	1.82978i	0.112239	+	0.136764i	−0.713860	+	0.700288i	$0.753055\pi$
$180$	−4.33167	−	1.80272i	−0.322863	−	0.134367i
$181$	2.98874	−	9.85255i	0.222151	−	0.732334i	−0.773038	−	0.634360i	$-0.781264\pi$
$181$	2.98874	−	9.85255i	0.222151	−	0.732334i	0.995189	−	0.0979744i	$-0.0312363\pi$
$182$	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	$-0.803154\pi$
$191$		−	16.0243i		−	1.15948i	0.814802	−	0.579739i	$-0.196846\pi$
$192$	−1.52138	−	7.85401i	−0.109796	−	0.566814i
$193$		−	17.2615i		−	1.24251i	−0.783608	−	0.621255i	$-0.786623\pi$
$193$		−	17.2615i		−	1.24251i	0.783608	−	0.621255i	$-0.213377\pi$
$194$	−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	0.971603	−	0.236618i	$-0.0760390\pi$
$197$	13.0403	+	10.7019i	0.929082	+	0.762478i	−0.0425212	+	0.999096i	$0.513539\pi$
$198$	−0.981253	+	0.144718i	−0.0697346	+	0.0102846i
$199$	−5.56652	+	8.33089i	−0.394600	+	0.590561i	−0.974572	−	0.224076i	$-0.928064\pi$
$199$	−5.56652	+	8.33089i	−0.394600	+	0.590561i	0.579971	+	0.814637i	$0.303064\pi$
$200$	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	0.0279799	−	0.999608i	$-0.491093\pi$
$211$	−2.02769	−	0.199710i	−0.139592	−	0.0137486i	−0.167572	+	0.985860i	$0.553593\pi$
$212$	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	0.507139	−	0.861864i	$-0.330703\pi$
$223$	−5.29718	−	5.29718i	−0.354726	−	0.354726i	−0.861864	+	0.507139i	$0.830703\pi$
$224$	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	0.976978	−	0.213339i	$-0.0684337\pi$
$227$	0.694958	+	2.29097i	0.0461260	+	0.152057i	−0.930852	+	0.365396i	$0.880934\pi$
$228$	0.618000	−	0.505454i	0.0409280	−	0.0334745i
$229$	1.11971	+	11.3686i	0.0739925	+	0.751258i	0.958568	+	0.284862i	$0.0919478\pi$
$229$	1.11971	+	11.3686i	0.0739925	+	0.751258i	−0.884576	+	0.466396i	$0.845552\pi$
$230$	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	0.361123	−	0.932518i	$-0.382393\pi$
$233$	5.15779	+	1.02595i	0.337898	+	0.0672121i	−0.0232250	+	0.999730i	$0.507393\pi$
$234$	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	−0.997822	−	0.0659662i	$-0.978987\pi$
$239$	−27.0549	−	11.2065i	−1.75003	−	0.724888i	−0.752212	−	0.658921i	$-0.771013\pi$
$240$	9.19716	+	1.86140i	0.593674	+	0.120153i
$241$	17.8857	−	7.40848i	1.15212	−	0.477222i	0.276874	−	0.960906i	$-0.410702\pi$
$241$	17.8857	−	7.40848i	1.15212	−	0.477222i	0.875243	+	0.483684i	$0.160702\pi$
$242$	−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	−0.930790	−	0.365556i	$-0.880879\pi$
$251$	−6.18938	+	7.54178i	−0.390670	+	0.476033i	0.540120	+	0.841588i	$0.318379\pi$
$252$	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	0.858345	−	0.513073i	$-0.171493\pi$
$263$	11.5597	+	7.72394i	0.712801	+	0.476279i	−0.145544	+	0.989352i	$0.546493\pi$
$264$	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	0.102118	−	0.994772i	$-0.467438\pi$
$269$	18.0036	−	14.7752i	1.09770	−	0.900857i	0.995580	+	0.0939150i	$0.0299382\pi$
$270$	2.23003	−	2.45633i	0.135715	−	0.149487i
$271$	−10.9674	+	4.54285i	−0.666223	+	0.275959i	−0.690055	−	0.723757i	$-0.742413\pi$
$271$	−10.9674	+	4.54285i	−0.666223	+	0.275959i	0.0238314	+	0.999716i	$0.492413\pi$
$272$	−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	0.970361	+	0.241659i	$0.0776916\pi$
$277$	10.5217	+	19.6848i	0.632190	+	1.18274i	−0.338172	+	0.941084i	$0.609808\pi$
$278$	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	0.827357	+	0.561676i	$0.189843\pi$
$281$	4.65884	+	23.4216i	0.277923	+	1.39721i	−0.549434	+	0.835537i	$0.685157\pi$
$282$	6.57759	+	10.9949i	0.391690	+	0.654735i
$283$	−2.33621	−	23.7199i	−0.138873	−	1.41000i	−0.771837	−	0.635821i	$-0.780662\pi$
$283$	−2.33621	−	23.7199i	−0.138873	−	1.41000i	0.632964	−	0.774181i	$-0.281838\pi$
$284$	−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	0.658164	−	0.752875i	$-0.271333\pi$
$293$	24.8296	−	2.44550i	1.45056	−	0.142868i	0.792396	+	0.610007i	$0.208833\pi$
$294$	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	0.325638	−	0.945494i	$-0.394421\pi$
$307$	−11.6556	−	14.2023i	−0.665218	−	0.810570i	−0.990856	+	0.134924i	$0.956921\pi$
$308$	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	−0.759237	−	0.650815i	$-0.774428\pi$
$311$	−7.90956	+	5.28500i	−0.448510	+	0.299685i	0.310727	+	0.950499i	$0.399428\pi$
$312$	−3.81359	+	15.0644i	−0.215902	+	0.852856i
$313$	−3.57046	+	5.34358i	−0.201815	+	0.302037i	−0.918547	−	0.395311i	$-0.870637\pi$
$313$	−3.57046	+	5.34358i	−0.201815	+	0.302037i	0.716733	+	0.697348i	$0.245637\pi$
$314$	−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	−0.0768174	−	0.997045i	$-0.524476\pi$
$317$	14.1523	−	26.4771i	0.794873	−	1.48710i	0.871690	−	0.490057i	$-0.163024\pi$
$318$	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	0.678344	+	0.734745i	$0.262698\pi$
$331$	−5.34669	+	17.6257i	−0.293881	+	0.968795i	−0.972224	+	0.234050i	$0.924802\pi$
$332$	−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	−0.543793	−	0.839219i	$-0.683012\pi$
$337$	7.96983	−	19.2409i	0.434144	−	1.04812i	0.977937	−	0.208898i	$-0.0669876\pi$
$338$	−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	−0.465330	−	0.885137i	$-0.654064\pi$
$347$	−13.9530	+	1.37425i	−0.749037	+	0.0737737i	−0.283707	+	0.958911i	$0.591564\pi$
$348$	−1.46405	+	2.72808i	−0.0784814	+	0.146240i
$349$	−26.9048	+	8.16147i	−1.44018	+	0.436874i	−0.911272	−	0.411806i	$-0.864898\pi$
$349$	−26.9048	+	8.16147i	−1.44018	+	0.436874i	−0.528908	+	0.848679i	$0.677398\pi$
$350$	−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	−0.0747341	−	0.997203i	$-0.523811\pi$
$353$	17.3316	−	17.3316i	0.922469	−	0.922469i	0.997203	+	0.0747341i	$0.0238108\pi$
$354$	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	−0.990127	−	0.140172i	$-0.955234\pi$
$359$	−2.44440	−	12.2888i	−0.129011	−	0.648580i	0.861117	−	0.508408i	$-0.169766\pi$
$360$	−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	0.781736	−	0.623609i	$-0.214334\pi$
$367$	17.1179	+	7.09048i	0.893549	+	0.370120i	0.111813	+	0.993729i	$0.464334\pi$
$368$	−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	0.661937	−	0.749560i	$-0.269735\pi$
$373$	15.3711	+	4.66276i	0.795883	+	0.241429i	0.133947	+	0.990989i	$0.457235\pi$
$374$	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	−0.278472	−	0.960444i	$-0.589828\pi$
$379$	13.9749	−	17.0285i	0.717845	−	0.874696i	0.996317	+	0.0857480i	$0.0273280\pi$
$380$	−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	−0.866055	−	0.499948i	$-0.833352\pi$
$389$	−4.07784	+	4.96886i	−0.206755	+	0.251931i	0.659301	+	0.751879i	$0.270852\pi$
$390$	−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	−0.202168	−	0.979351i	$-0.564799\pi$
$397$	14.3245	−	11.7558i	0.718925	−	0.590006i	0.921092	+	0.389345i	$0.127299\pi$
$398$	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	0.969934	−	0.243369i	$-0.0782526\pi$
$401$	29.7109	+	12.3067i	1.48369	+	0.614566i	0.513759	+	0.857935i	$0.328253\pi$
$402$	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	0.996637	+	0.0819425i	$0.0261124\pi$
$409$	2.16844	+	10.9015i	0.107223	+	0.539044i	−0.889415	+	0.457101i	$0.848888\pi$
$410$	−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	0.286490	−	0.958083i	$-0.407511\pi$
$419$	21.6359	−	6.56316i	1.05698	−	0.320632i	0.770490	+	0.637452i	$0.220011\pi$
$420$	−13.3347	−	7.15621i	−0.650667	−	0.349187i
$421$	−15.2268	+	1.49971i	−0.742110	+	0.0730915i	−0.462004	−	0.886878i	$-0.652870\pi$
$421$	−15.2268	+	1.49971i	−0.742110	+	0.0730915i	−0.280106	+	0.959969i	$0.590370\pi$
$422$	−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	0.258033	+	0.966136i	$0.416926\pi$
$431$	−12.6138	+	30.4524i	−0.607585	+	1.46684i	−0.865618	+	0.500704i	$0.833074\pi$
$432$	−1.89736	+	3.52137i	−0.0912869	+	0.169422i
$433$	−8.57242	−	20.6956i	−0.411964	−	0.994569i	−0.984610	−	0.174766i	$-0.944083\pi$
$433$	−8.57242	−	20.6956i	−0.411964	−	0.994569i	0.572646	−	0.819803i	$-0.305917\pi$
$434$	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	−0.641119	−	0.767442i	$-0.721529\pi$
$439$	−3.71779	+	2.48414i	−0.177440	+	0.118562i	0.463678	+	0.886004i	$0.346529\pi$
$440$	−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	0.304831	−	0.952407i	$-0.401400\pi$
$443$	−11.9930	−	9.84242i	−0.569806	−	0.467628i	−0.874637	+	0.484779i	$0.838900\pi$
$444$	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	$0.147695\pi$
$449$			18.9658i			0.895051i	−0.894271	+	0.447526i	$0.852305\pi$
$450$	−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	−0.122686	−	0.992446i	$-0.539151\pi$
$457$	15.9747	−	10.6739i	0.747265	−	0.499306i	0.869950	+	0.493139i	$0.164151\pi$
$458$	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	0.987281	+	0.158982i	$0.0508213\pi$
$461$	20.4102	+	24.8700i	0.950600	+	1.15831i	−0.0366816	+	0.999327i	$0.511679\pi$
$462$	−3.19557	+	0.154313i	−0.148672	+	0.00717928i
$463$	11.6610	+	28.1521i	0.541931	+	1.30834i	0.923359	+	0.383939i	$0.125433\pi$
$463$	11.6610	+	28.1521i	0.541931	+	1.30834i	−0.381428	+	0.924399i	$0.624567\pi$
$464$	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	−0.354975	−	0.934876i	$-0.615511\pi$
$467$	−19.1361	−	1.88474i	−0.885515	−	0.0872156i	−0.530539	+	0.847660i	$0.678011\pi$
$468$	−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	0.930942	−	0.365166i	$-0.118988\pi$
$479$	12.3826	+	12.3826i	0.565776	+	0.565776i	−0.365166	+	0.930942i	$0.618988\pi$
$480$	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	0.996178	−	0.0873413i	$-0.0278371\pi$
$487$	0.935808	+	4.70462i	0.0424055	+	0.213187i	−0.953773	+	0.300528i	$0.902837\pi$
$488$	−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	0.978117	+	0.208055i	$0.0667133\pi$
$491$	13.4656	+	25.1924i	0.607696	+	1.13692i	−0.370421	+	0.928864i	$0.620787\pi$
$492$	−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	−0.524902	−	0.851163i	$-0.675898\pi$
$499$	4.63527	−	3.80407i	0.207503	−	0.170293i	0.732405	+	0.680869i	$0.238398\pi$
$500$	−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	0.954472	−	0.298300i	$-0.0964195\pi$
$503$	7.03373	+	10.5267i	0.313619	+	0.469363i	−0.640854	+	0.767663i	$0.721419\pi$
$504$	−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	0.0267088	−	0.999643i	$-0.491497\pi$
$509$	−17.8148	−	9.52219i	−0.789626	−	0.422064i	−0.816334	+	0.577580i	$0.803997\pi$
$510$	−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	−0.999748	−	0.0224567i	$-0.992851\pi$
$521$	−14.5605	−	21.7914i	−0.637908	−	0.954697i	0.361840	−	0.932240i	$-0.382149\pi$
$522$	−1.46887	−	1.62337i	−0.0642908	−	0.0710531i
$523$	24.2559	+	7.35795i	1.06064	+	0.321741i	0.771950	−	0.635683i	$-0.219281\pi$
$523$	24.2559	+	7.35795i	1.06064	+	0.321741i	0.288687	+	0.957424i	$0.406781\pi$
$524$	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	−0.880744	−	0.473592i	$-0.842957\pi$
$541$	−9.57232	−	31.5557i	−0.411546	−	1.35669i	0.469198	−	0.883093i	$-0.344543\pi$
$542$	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	−0.278795	−	0.960351i	$-0.589935\pi$
$547$	0.536468	−	0.162736i	0.0229377	−	0.00695808i	0.301733	+	0.953393i	$0.402435\pi$
$548$	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	0.863572	−	0.504226i	$-0.168222\pi$
$557$	38.0488	+	3.74748i	1.61218	+	0.158786i	0.748609	+	0.663012i	$0.230722\pi$
$558$	−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	0.476289	−	0.879289i	$-0.341982\pi$
$563$	−11.3661	−	13.8496i	−0.479024	−	0.583692i	−0.955313	+	0.295597i	$0.904482\pi$
$564$	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	−0.0632580	−	0.997997i	$-0.520149\pi$
$569$	21.0623	−	31.5220i	0.882979	−	1.32147i	0.946237	−	0.323474i	$-0.104851\pi$
$570$	1.31018	−	0.193229i	0.0548775	−	0.00809347i
$571$	−0.0581427	−	0.0477165i	−0.00243320	−	0.00199687i	0.633176	−	0.774008i	$-0.281751\pi$
$571$	−0.0581427	−	0.0477165i	−0.00243320	−	0.00199687i	−0.635609	+	0.772011i	$0.719251\pi$
$572$	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	$-0.767263\pi$
$577$		−	32.0792i		−	1.33547i	0.744397	−	0.667737i	$-0.232737\pi$
$578$	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	−0.918504	−	0.395412i	$-0.870602\pi$
$587$	1.57200	−	5.18218i	0.0648833	−	0.213892i	0.983387	+	0.181520i	$0.0581018\pi$
$588$	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	0.669351	+	0.742946i	$0.266572\pi$
$593$	−8.01882	+	19.3592i	−0.329294	+	0.794985i	−0.998645	+	0.0520392i	$0.983428\pi$
$594$	−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	−0.860853	−	0.508854i	$-0.830069\pi$
$599$	3.16214	−	15.8971i	0.129201	−	0.649539i	0.990054	−	0.140685i	$-0.0449306\pi$
$600$	1.05235	+	0.958610i	0.0429620	+	0.0391351i
$601$	−21.9914	+	4.37437i	−0.897049	+	0.178434i	−0.622020	−	0.783002i	$-0.713688\pi$
$601$	−21.9914	+	4.37437i	−0.897049	+	0.178434i	−0.275030	+	0.961436i	$0.588688\pi$
$602$	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	0.429923	−	0.902866i	$-0.358541\pi$
$607$	−11.6521	−	11.6521i	−0.472943	−	0.472943i	−0.902866	+	0.429923i	$0.858541\pi$
$608$	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	−0.812890	−	0.582417i	$-0.802107\pi$
$613$	−3.19992	−	32.4893i	−0.129243	−	1.31223i	0.683647	−	0.729813i	$-0.260393\pi$
$614$	−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	−0.288961	−	0.957341i	$-0.593310\pi$
$617$	−22.9091	−	4.55690i	−0.922285	−	0.183454i	−0.633324	+	0.773887i	$0.718310\pi$
$618$	15.5820	+	7.38566i	0.626799	+	0.297095i
$619$	0.269130	+	0.503507i	0.0108172	+	0.0202376i	0.887272	−	0.461247i	$-0.152598\pi$
$619$	0.269130	+	0.503507i	0.0108172	+	0.0202376i	−0.876455	+	0.481485i	$0.840098\pi$
$620$	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	0.977178	−	0.212421i	$-0.0681349\pi$
$631$	10.2231	+	15.3000i	0.406977	+	0.609084i	−0.570202	+	0.821505i	$0.693135\pi$
$632$	−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	−0.0661376	−	0.997811i	$-0.521068\pi$
$643$	−23.6466	−	12.6394i	−0.932531	−	0.498448i	−0.866393	+	0.499362i	$0.833568\pi$
$644$	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	0.0358448	−	0.999357i	$-0.488588\pi$
$647$	−22.2242	−	14.8497i	−0.873724	−	0.583804i	−0.909569	+	0.415554i	$0.863588\pi$
$648$	−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	−0.631566	−	0.775322i	$-0.717587\pi$
$653$	0.144288	−	0.118414i	0.00564643	−	0.00463390i	0.637212	+	0.770688i	$0.280087\pi$
$654$	−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	−0.924733	−	0.380616i	$-0.875712\pi$
$659$	1.45005	−	14.7226i	0.0564859	−	0.573511i	0.981219	−	0.192896i	$-0.0617879\pi$
$660$	3.22633	+	0.647362i	0.125585	+	0.0251985i
$661$	−14.1375	−	26.4493i	−0.549884	−	1.02876i	−0.991320	−	0.131467i	$-0.958031\pi$
$661$	−14.1375	−	26.4493i	−0.549884	−	1.02876i	0.441437	−	0.897292i	$-0.354469\pi$
$662$	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	0.960264	−	0.279094i	$-0.0900341\pi$
$673$	17.6711	+	17.6711i	0.681170	+	0.681170i	−0.279094	+	0.960264i	$0.590034\pi$
$674$	−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	−0.0776014	−	0.996984i	$-0.524726\pi$
$677$	1.06133	−	0.104532i	0.0407903	−	0.00401750i	0.118392	+	0.992967i	$0.462226\pi$
$678$	−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	−0.198817	−	0.980037i	$-0.563710\pi$
$683$	13.2134	−	7.06272i	0.505598	−	0.270248i	0.704414	+	0.709789i	$0.251210\pi$
$684$	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	0.557343	−	0.830282i	$-0.311821\pi$
$691$	−9.61358	−	11.7142i	−0.365718	−	0.445628i	−0.923061	+	0.384654i	$0.874321\pi$
$692$	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	−0.995265	−	0.0972014i	$-0.969011\pi$
$701$	−9.57136	+	17.9068i	−0.361505	+	0.676329i	0.633759	+	0.773530i	$0.281511\pi$
$702$	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	0.452112	−	0.891961i	$-0.350671\pi$
$709$	−8.90694	−	7.30974i	−0.334507	−	0.274523i	−0.786619	+	0.617438i	$0.788171\pi$
$710$	−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	0.997852	−	0.0655149i	$-0.0208690\pi$
$719$	6.59462	+	15.9208i	0.245938	+	0.593747i	−0.751914	+	0.659262i	$0.770869\pi$
$720$	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	0.769835	+	0.638243i	$0.220339\pi$
$727$	−5.00553	+	25.1645i	−0.185645	+	0.933300i	−0.955480	+	0.295057i	$0.904661\pi$
$728$	−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	−0.101176	−	0.994869i	$-0.532260\pi$
$733$	9.94750	−	3.01754i	0.367419	−	0.111455i	0.468595	+	0.883413i	$0.344760\pi$
$734$	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	−0.836544	−	0.547899i	$-0.815428\pi$
$739$	−12.1074	−	39.9129i	−0.445380	−	1.46822i	0.391165	−	0.920321i	$-0.372072\pi$
$740$	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	0.999570	−	0.0293121i	$-0.00933166\pi$
$743$	1.76824	+	8.88955i	0.0648705	+	0.326126i	−0.934700	+	0.355438i	$0.884332\pi$
$744$	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	0.479126	−	0.877746i	$-0.340954\pi$
$751$	5.40575	+	2.23914i	0.197259	+	0.0817072i	−0.281867	+	0.959453i	$0.590954\pi$
$752$	−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	0.463789	−	0.885946i	$-0.346490\pi$
$757$	9.82816	+	2.98134i	0.357210	+	0.108359i	−0.106579	+	0.994304i	$0.533990\pi$
$758$	−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	0.174997	−	0.984569i	$-0.444008\pi$
$761$	−18.4181	−	12.3066i	−0.667657	−	0.446114i	−0.842654	+	0.538455i	$0.819008\pi$
$762$	−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

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

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Database

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