LMFDB - Embedded newform 820.2.s.c.583.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [820,2,Mod(583,820)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(820, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("820.583"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 820 = 2^{2} \cdot 5 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	820.s (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [240,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.54773296574$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$120$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			583.6
Character	$\chi$	$=$	820.583
Dual form			820.2.s.c.647.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.39711 - 0.219268i) q^{2} -2.16299 q^{3} +(1.90384 + 0.612684i) q^{4} +(-0.498284 + 2.17984i) q^{5} +(3.02194 + 0.474275i) q^{6} +0.295068i q^{7} +(-2.52554 - 1.27344i) q^{8} +1.67853 q^{9} +(1.17413 - 2.93623i) q^{10} +(0.592458 - 0.592458i) q^{11} +(-4.11800 - 1.32523i) q^{12} +5.60783i q^{13} +(0.0646989 - 0.412242i) q^{14} +(1.07778 - 4.71498i) q^{15} +(3.24924 + 2.33291i) q^{16} +5.37402i q^{17} +(-2.34510 - 0.368048i) q^{18} +(2.97295 - 2.97295i) q^{19} +(-2.28421 + 3.84479i) q^{20} -0.638229i q^{21} +(-0.957637 + 0.697823i) q^{22} +(-0.212568 + 0.212568i) q^{23} +(5.46272 + 2.75444i) q^{24} +(-4.50343 - 2.17236i) q^{25} +(1.22962 - 7.83477i) q^{26} +2.85832 q^{27} +(-0.180783 + 0.561762i) q^{28} +(2.66637 - 2.66637i) q^{29} +(-2.53963 + 6.35103i) q^{30} +4.70570i q^{31} +(-4.02802 - 3.97179i) q^{32} +(-1.28148 + 1.28148i) q^{33} +(1.17835 - 7.50810i) q^{34} +(-0.643201 - 0.147028i) q^{35} +(3.19566 + 1.02841i) q^{36} +(2.69046 - 2.69046i) q^{37} +(-4.80541 + 3.50167i) q^{38} -12.1297i q^{39} +(4.03433 - 4.87074i) q^{40} +(-4.98535 + 4.01824i) q^{41} +(-0.139943 + 0.891677i) q^{42} +(-2.01035 - 2.01035i) q^{43} +(1.49094 - 0.764957i) q^{44} +(-0.836386 + 3.65894i) q^{45} +(0.343591 - 0.250372i) q^{46} -10.3048 q^{47} +(-7.02807 - 5.04606i) q^{48} +6.91294 q^{49} +(5.81546 + 4.02249i) q^{50} -11.6240i q^{51} +(-3.43583 + 10.6764i) q^{52} -3.29257i q^{53} +(-3.99340 - 0.626739i) q^{54} +(0.996252 + 1.58668i) q^{55} +(0.375751 - 0.745205i) q^{56} +(-6.43046 + 6.43046i) q^{57} +(-4.30987 + 3.14057i) q^{58} -14.2604 q^{59} +(4.94073 - 8.31624i) q^{60} +2.98490i q^{61} +(1.03181 - 6.57439i) q^{62} +0.495280i q^{63} +(4.75670 + 6.43225i) q^{64} +(-12.2242 - 2.79430i) q^{65} +(2.07136 - 1.50938i) q^{66} -3.44881 q^{67} +(-3.29257 + 10.2313i) q^{68} +(0.459783 - 0.459783i) q^{69} +(0.866385 + 0.346447i) q^{70} +(-5.63883 + 5.63883i) q^{71} +(-4.23920 - 2.13751i) q^{72} +(-3.86014 + 3.86014i) q^{73} +(-4.34880 + 3.16894i) q^{74} +(9.74087 + 4.69880i) q^{75} +(7.48150 - 3.83855i) q^{76} +(0.174815 + 0.174815i) q^{77} +(-2.65965 + 16.9465i) q^{78} +(-1.35423 - 1.35423i) q^{79} +(-6.70442 + 5.92037i) q^{80} -11.2181 q^{81} +(7.84617 - 4.52080i) q^{82} +(-1.25094 + 1.25094i) q^{83} +(0.391032 - 1.21509i) q^{84} +(-11.7145 - 2.67779i) q^{85} +(2.36787 + 3.24948i) q^{86} +(-5.76734 + 5.76734i) q^{87} +(-2.25073 + 0.741816i) q^{88} +(-10.3994 + 10.3994i) q^{89} +(1.97081 - 4.92855i) q^{90} -1.65469 q^{91} +(-0.534934 + 0.274460i) q^{92} -10.1784i q^{93} +(14.3969 + 2.25951i) q^{94} +(4.99919 + 7.96193i) q^{95} +(8.71256 + 8.59094i) q^{96} -13.1496i q^{97} +(-9.65814 - 1.51579i) q^{98} +(0.994459 - 0.994459i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) $ 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/820\mathbb{Z}\right)^\times$.

$n$	$411$	$621$	$657$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	−1.39711	−	0.219268i	−0.987907	−	0.155046i
$2$	−1.39711	−	0.219268i	−0.987907	−	0.155046i
$3$	−2.16299			−1.24880			−0.624402	−	0.781103i	$-0.714657\pi$
$3$	−2.16299			−1.24880			−0.624402	+	0.781103i	$0.714657\pi$
$4$	1.90384	+	0.612684i	0.951922	+	0.306342i
$5$	−0.498284	+	2.17984i	−0.222839	+	0.974855i
$5$	−0.498284	+	2.17984i	−0.222839	+	0.974855i
$6$	3.02194	+	0.474275i	1.23370	+	0.193622i
$7$			0.295068i			0.111525i	0.998444	+	0.0557625i	$0.0177590\pi$
$7$			0.295068i			0.111525i	−0.998444	+	0.0557625i	$0.982241\pi$
$8$	−2.52554	−	1.27344i	−0.892913	−	0.450229i
$9$	1.67853			0.559511
$10$	1.17413	−	2.93623i	0.371292	−	0.928516i
$11$	0.592458	−	0.592458i	0.178633	−	0.178633i	−0.612127	−	0.790760i	$-0.709686\pi$
$11$	0.592458	−	0.592458i	0.178633	−	0.178633i	0.790760	+	0.612127i	$0.209686\pi$
$12$	−4.11800	−	1.32523i	−1.18876	−	0.382561i
$13$			5.60783i			1.55533i	0.628677	+	0.777667i	$0.283597\pi$
$13$			5.60783i			1.55533i	−0.628677	+	0.777667i	$0.716403\pi$
$14$	0.0646989	−	0.412242i	0.0172915	−	0.110176i
$15$	1.07778	−	4.71498i	0.278283	−	1.21740i
$16$	3.24924	+	2.33291i	0.812309	+	0.583227i
$17$			5.37402i			1.30339i	0.758481	+	0.651695i	$0.225942\pi$
$17$			5.37402i			1.30339i	−0.758481	+	0.651695i	$0.774058\pi$
$18$	−2.34510	−	0.368048i	−0.552745	−	0.0867498i
$19$	2.97295	−	2.97295i	0.682041	−	0.682041i	−0.278419	−	0.960460i	$-0.589810\pi$
$19$	2.97295	−	2.97295i	0.682041	−	0.682041i	0.960460	+	0.278419i	$0.0898103\pi$
$20$	−2.28421	+	3.84479i	−0.510765	+	0.859721i
$21$		−	0.638229i		−	0.139273i
$22$	−0.957637	+	0.697823i	−0.204169	+	0.148776i
$23$	−0.212568	+	0.212568i	−0.0443236	+	0.0443236i	−0.728921	−	0.684598i	$-0.759978\pi$
$23$	−0.212568	+	0.212568i	−0.0443236	+	0.0443236i	0.684598	+	0.728921i	$0.259978\pi$
$24$	5.46272	+	2.75444i	1.11507	+	0.562248i
$25$	−4.50343	−	2.17236i	−0.900685	−	0.434472i
$26$	1.22962	−	7.83477i	0.241148	−	1.53652i
$27$	2.85832			0.550085
$28$	−0.180783	+	0.561762i	−0.0341648	+	0.106163i
$29$	2.66637	−	2.66637i	0.495132	−	0.495132i	−0.414786	−	0.909919i	$-0.636144\pi$
$29$	2.66637	−	2.66637i	0.495132	−	0.495132i	0.909919	+	0.414786i	$0.136144\pi$
$30$	−2.53963	+	6.35103i	−0.463671	+	1.15953i
$31$			4.70570i			0.845169i	0.906323	+	0.422585i	$0.138877\pi$
$31$			4.70570i			0.845169i	−0.906323	+	0.422585i	$0.861123\pi$
$32$	−4.02802	−	3.97179i	−0.712059	−	0.702119i
$33$	−1.28148	+	1.28148i	−0.223077	+	0.223077i
$34$	1.17835	−	7.50810i	0.202085	−	1.28763i
$35$	−0.643201	−	0.147028i	−0.108721	−	0.0248522i
$36$	3.19566	+	1.02841i	0.532610	+	0.171402i
$37$	2.69046	−	2.69046i	0.442308	−	0.442308i	−0.450479	−	0.892787i	$-0.648747\pi$
$37$	2.69046	−	2.69046i	0.442308	−	0.442308i	0.892787	+	0.450479i	$0.148747\pi$
$38$	−4.80541	+	3.50167i	−0.779541	+	0.568046i
$39$		−	12.1297i		−	1.94231i
$40$	4.03433	−	4.87074i	0.637884	−	0.770132i
$41$	−4.98535	+	4.01824i	−0.778581	+	0.627544i
$41$	−4.98535	+	4.01824i	−0.778581	+	0.627544i
$42$	−0.139943	+	0.891677i	−0.0215937	+	0.137589i
$43$	−2.01035	−	2.01035i	−0.306575	−	0.306575i	0.537004	−	0.843579i	$-0.319556\pi$
$43$	−2.01035	−	2.01035i	−0.306575	−	0.306575i	−0.843579	+	0.537004i	$0.819556\pi$
$44$	1.49094	−	0.764957i	0.224767	−	0.115322i
$45$	−0.836386	+	3.65894i	−0.124681	+	0.545442i
$46$	0.343591	−	0.250372i	0.0506598	−	0.0369154i
$47$	−10.3048			−1.50311			−0.751554	−	0.659672i	$-0.770695\pi$
$47$	−10.3048			−1.50311			−0.751554	+	0.659672i	$0.770695\pi$
$48$	−7.02807	−	5.04606i	−1.01441	−	0.728336i
$49$	6.91294			0.987562
$50$	5.81546	+	4.02249i	0.822430	+	0.568866i
$51$		−	11.6240i		−	1.62768i
$52$	−3.43583	+	10.6764i	−0.476464	+	1.48056i
$53$		−	3.29257i		−	0.452269i	−0.974096	−	0.226135i	$-0.927391\pi$
$53$		−	3.29257i		−	0.452269i	0.974096	−	0.226135i	$-0.0726089\pi$
$54$	−3.99340	−	0.626739i	−0.543433	−	0.0852884i
$55$	0.996252	+	1.58668i	0.134335	+	0.213947i
$56$	0.375751	−	0.745205i	0.0502118	−	0.0995822i
$57$	−6.43046	+	6.43046i	−0.851735	+	0.851735i
$58$	−4.30987	+	3.14057i	−0.565913	+	0.412377i
$59$	−14.2604			−1.85655			−0.928275	−	0.371893i	$-0.878709\pi$
$59$	−14.2604			−1.85655			−0.928275	+	0.371893i	$0.878709\pi$
$60$	4.94073	−	8.31624i	0.637845	−	1.07362i
$61$			2.98490i			0.382177i	0.981573	+	0.191089i	$0.0612018\pi$
$61$			2.98490i			0.382177i	−0.981573	+	0.191089i	$0.938798\pi$
$62$	1.03181	−	6.57439i	0.131040	−	0.834949i
$63$			0.495280i			0.0623995i
$64$	4.75670	+	6.43225i	0.594588	+	0.804031i
$65$	−12.2242	−	2.79430i	−1.51622	−	0.346590i
$66$	2.07136	−	1.50938i	0.254967	−	0.185792i
$67$	−3.44881			−0.421339			−0.210670	−	0.977557i	$-0.567564\pi$
$67$	−3.44881			−0.421339			−0.210670	+	0.977557i	$0.567564\pi$
$68$	−3.29257	+	10.2313i	−0.399283	+	1.24073i
$69$	0.459783	−	0.459783i	0.0553514	−	0.0553514i
$70$	0.866385	+	0.346447i	0.103553	+	0.0414084i
$71$	−5.63883	+	5.63883i	−0.669206	+	0.669206i	−0.957532	−	0.288326i	$-0.906901\pi$
$71$	−5.63883	+	5.63883i	−0.669206	+	0.669206i	0.288326	+	0.957532i	$0.406901\pi$
$72$	−4.23920	−	2.13751i	−0.499595	−	0.251908i
$73$	−3.86014	+	3.86014i	−0.451795	+	0.451795i	−0.895950	−	0.444155i	$-0.853504\pi$
$73$	−3.86014	+	3.86014i	−0.451795	+	0.451795i	0.444155	+	0.895950i	$0.353504\pi$
$74$	−4.34880	+	3.16894i	−0.505538	+	0.368382i
$75$	9.74087	+	4.69880i	1.12478	+	0.542571i
$76$	7.48150	−	3.83855i	0.858187	−	0.440312i
$77$	0.174815	+	0.174815i	0.0199220	+	0.0199220i
$78$	−2.65965	+	16.9465i	−0.301147	+	1.91882i
$79$	−1.35423	−	1.35423i	−0.152363	−	0.152363i	0.626810	−	0.779173i	$-0.284360\pi$
$79$	−1.35423	−	1.35423i	−0.152363	−	0.152363i	−0.779173	+	0.626810i	$0.784360\pi$
$80$	−6.70442	+	5.92037i	−0.749576	+	0.661918i
$81$	−11.2181			−1.24646
$82$	7.84617	−	4.52080i	0.866464	−	0.499239i
$83$	−1.25094	+	1.25094i	−0.137309	+	0.137309i	−0.772420	−	0.635112i	$-0.780954\pi$
$83$	−1.25094	+	1.25094i	−0.137309	+	0.137309i	0.635112	+	0.772420i	$0.280954\pi$
$84$	0.391032	−	1.21509i	0.0426651	−	0.132577i
$85$	−11.7145	−	2.67779i	−1.27062	−	0.290447i
$86$	2.36787	+	3.24948i	0.255334	+	0.350401i
$87$	−5.76734	+	5.76734i	−0.618323	+	0.618323i
$88$	−2.25073	+	0.741816i	−0.239929	+	0.0790779i
$89$	−10.3994	+	10.3994i	−1.10234	+	1.10234i	−0.108209	+	0.994128i	$0.534512\pi$
$89$	−10.3994	+	10.3994i	−1.10234	+	1.10234i	−0.994128	+	0.108209i	$0.965488\pi$
$90$	1.97081	−	4.92855i	0.207742	−	0.519515i
$91$	−1.65469			−0.173459
$92$	−0.534934	+	0.274460i	−0.0557707	+	0.0286144i
$93$		−	10.1784i		−	1.05545i
$94$	14.3969	+	2.25951i	1.48493	+	0.233051i
$95$	4.99919	+	7.96193i	0.512906	+	0.816877i
$96$	8.71256	+	8.59094i	0.889222	+	0.876809i
$97$		−	13.1496i		−	1.33514i	−0.744549	−	0.667568i	$-0.767335\pi$
$97$		−	13.1496i		−	1.33514i	0.744549	−	0.667568i	$-0.232665\pi$
$98$	−9.65814	−	1.51579i	−0.975620	−	0.153117i
$99$	0.994459	−	0.994459i	0.0999469	−	0.0999469i
$100$	−7.24284	−	6.89501i	−0.724284	−	0.689501i
$101$	6.43682	−	6.43682i	0.640487	−	0.640487i	−0.310188	−	0.950675i	$-0.600392\pi$
$101$	6.43682	−	6.43682i	0.640487	−	0.640487i	0.950675	+	0.310188i	$0.100392\pi$
$102$	−2.54876	+	16.2400i	−0.252365	+	1.60800i
$103$	6.32443	+	6.32443i	0.623165	+	0.623165i	0.946339	−	0.323175i	$-0.104750\pi$
$103$	6.32443	+	6.32443i	0.623165	+	0.623165i	−0.323175	+	0.946339i	$0.604750\pi$
$104$	7.14124	−	14.1628i	0.700256	−	1.38878i
$105$	1.39124	+	0.318019i	0.135771	+	0.0310355i
$106$	−0.721955	+	4.60009i	−0.0701225	+	0.446800i
$107$	−6.55946	−	6.55946i	−0.634127	−	0.634127i	0.314973	−	0.949101i	$-0.398004\pi$
$107$	−6.55946	−	6.55946i	−0.634127	−	0.634127i	−0.949101	+	0.314973i	$0.898004\pi$
$108$	5.44180	+	1.75125i	0.523637	+	0.168514i
$109$	−6.36154	−	6.36154i	−0.609325	−	0.609325i	0.333445	−	0.942770i	$-0.391789\pi$
$109$	−6.36154	−	6.36154i	−0.609325	−	0.609325i	−0.942770	+	0.333445i	$0.891789\pi$
$110$	−1.04397	−	2.43521i	−0.0995385	−	0.232188i
$111$	−5.81944	+	5.81944i	−0.552356	+	0.552356i
$112$	−0.688365	+	0.958744i	−0.0650444	+	0.0905928i
$113$	−5.99373	−	5.99373i	−0.563843	−	0.563843i	0.366554	−	0.930397i	$-0.380538\pi$
$113$	−5.99373	−	5.99373i	−0.563843	−	0.563843i	−0.930397	+	0.366554i	$0.880538\pi$
$114$	10.3941	−	7.57408i	0.973494	−	0.709378i
$115$	−0.357446	−	0.569285i	−0.0333320	−	0.0530861i
$116$	6.70999	−	3.44271i	0.623007	−	0.319647i
$117$			9.41293i			0.870226i
$118$	19.9234	+	3.12686i	1.83410	+	0.287851i
$119$	−1.58570			−0.145361
$120$	−8.72623	+	10.5354i	−0.796592	+	0.961744i
$121$			10.2980i			0.936181i
$122$	0.654493	−	4.17024i	0.0592550	−	0.377556i
$123$	10.7833	−	8.69142i	0.972295	−	0.783679i
$124$	−2.88311	+	8.95892i	−0.258911	+	0.804535i
$125$	6.97939	−	8.73430i	0.624256	−	0.781220i
$126$	0.108599	−	0.691962i	0.00967478	−	0.0616449i
$127$	−9.71448	−	9.71448i	−0.862020	−	0.862020i	0.129552	−	0.991573i	$-0.458646\pi$
$127$	−9.71448	−	9.71448i	−0.862020	−	0.862020i	−0.991573	+	0.129552i	$0.958646\pi$
$128$	−5.23526	−	10.0296i	−0.462736	−	0.886496i
$129$	4.34836	+	4.34836i	0.382852	+	0.382852i
$130$	16.4659	+	6.58432i	1.44415	+	0.577483i
$131$	7.66395			0.669603			0.334801	−	0.942289i	$-0.391331\pi$
$131$	7.66395			0.669603			0.334801	+	0.942289i	$0.391331\pi$
$132$	−3.22488	+	1.65460i	−0.280690	+	0.144014i
$133$	0.877221	+	0.877221i	0.0760647	+	0.0760647i
$134$	4.81837	+	0.756213i	0.416244	+	0.0653269i
$135$	−1.42426	+	6.23069i	−0.122581	+	0.536253i
$136$	6.84349	−	13.5723i	0.586824	−	1.16381i
$137$		−	10.8159i		−	0.924062i	−0.886864	−	0.462031i	$-0.847121\pi$
$137$		−	10.8159i		−	0.924062i	0.886864	−	0.462031i	$-0.152879\pi$
$138$	−0.743185	+	0.541553i	−0.0632641	+	0.0461001i
$139$	−5.79546			−0.491565			−0.245782	−	0.969325i	$-0.579045\pi$
$139$	−5.79546			−0.491565			−0.245782	+	0.969325i	$0.579045\pi$
$140$	−1.13447	−	0.673996i	−0.0958804	−	0.0569631i
$141$	22.2892			1.87709
$142$	9.11449	−	6.64166i	0.764871	−	0.557356i
$143$	3.32240	+	3.32240i	0.277833	+	0.277833i
$144$	5.45395	+	3.91586i	0.454496	+	0.326322i
$145$	4.48366	+	7.14088i	0.372347	+	0.593017i
$146$	6.23945	−	4.54664i	0.516381	−	0.376283i
$147$	−14.9526			−1.23327
$148$	6.77061	−	3.47381i	0.556541	−	0.285545i
$149$	−0.492775	−	0.492775i	−0.0403697	−	0.0403697i	0.686634	−	0.727003i	$-0.259088\pi$
$149$	−0.492775	−	0.492775i	−0.0403697	−	0.0403697i	−0.727003	+	0.686634i	$0.759088\pi$
$150$	−12.5788	−	8.70061i	−1.02705	−	0.710402i
$151$	3.76361	−	3.76361i	0.306279	−	0.306279i	−0.537186	−	0.843464i	$-0.680513\pi$
$151$	3.76361	−	3.76361i	0.306279	−	0.306279i	0.843464	+	0.537186i	$0.180513\pi$
$152$	−11.2942	+	3.72243i	−0.916078	+	0.301929i
$153$			9.02046i			0.729261i
$154$	−0.205905	−	0.282568i	−0.0165923	−	0.0227699i
$155$	−10.2577	−	2.34478i	−0.823918	−	0.188337i
$156$	7.43167	−	23.0930i	0.595010	−	1.84892i
$157$	−0.485792			−0.0387704			−0.0193852	−	0.999812i	$-0.506171\pi$
$157$	−0.485792			−0.0387704			−0.0193852	+	0.999812i	$0.506171\pi$
$158$	1.59507	+	2.18895i	0.126897	+	0.174144i
$159$			7.12180i			0.564795i
$160$	10.6650	−	6.80136i	0.843140	−	0.537695i
$161$	−0.0627220	−	0.0627220i	−0.00494319	−	0.00494319i
$162$	15.6730	+	2.45978i	1.23139	+	0.193258i
$163$	13.5914	−	13.5914i	1.06456	−	1.06456i	0.0667960	−	0.997767i	$-0.478722\pi$
$163$	13.5914	−	13.5914i	1.06456	−	1.06456i	0.997767	−	0.0667960i	$-0.0212777\pi$
$164$	−11.9532	+	4.59565i	−0.933391	+	0.358860i
$165$	−2.15488	−	3.43197i	−0.167758	−	0.267178i
$166$	2.02200	−	1.47341i	0.156937	−	0.114359i
$167$			11.5521i			0.893929i	0.894552	+	0.446964i	$0.147495\pi$
$167$			11.5521i			0.893929i	−0.894552	+	0.446964i	$0.852505\pi$
$168$	−0.812746	+	1.61187i	−0.0627047	+	0.124359i
$169$	−18.4478			−1.41906
$170$	15.7793	+	6.30979i	1.21022	+	0.483938i
$171$	4.99019	−	4.99019i	0.381609	−	0.381609i
$172$	−2.59568	−	5.05909i	−0.197919	−	0.385752i
$173$	11.4707	−	11.4707i	0.872101	−	0.872101i	−0.120600	−	0.992701i	$-0.538482\pi$
$173$	11.4707	−	11.4707i	0.872101	−	0.872101i	0.992701	+	0.120600i	$0.0384819\pi$
$174$	9.32220	−	6.79302i	0.706715	−	0.514978i
$175$	0.640994	−	1.32881i	0.0484546	−	0.100449i
$176$	3.30718	−	0.542886i	0.249288	−	0.0409216i
$177$	30.8452			2.31847
$178$	16.8094	−	12.2489i	1.25992	−	0.918094i
$179$	−3.60813	+	3.60813i	−0.269684	+	0.269684i	−0.828973	−	0.559289i	$-0.811074\pi$
$179$	−3.60813	+	3.60813i	−0.269684	+	0.269684i	0.559289	+	0.828973i	$0.311074\pi$
$180$	−3.83412	+	6.45360i	−0.285778	+	0.481023i
$181$	−7.71931	+	7.71931i	−0.573772	+	0.573772i	−0.933180	−	0.359409i	$-0.882978\pi$
$181$	−7.71931	+	7.71931i	−0.573772	+	0.573772i	0.359409	+	0.933180i	$0.382978\pi$
$182$	2.31179	+	0.362820i	0.171361	+	0.0268940i
$183$		−	6.45631i		−	0.477264i
$184$	0.807543	−	0.266157i	0.0595328	−	0.0196213i
$185$	4.52416	+	7.20539i	0.332623	+	0.529750i
$186$	−2.23180	+	14.2204i	−0.163643	+	1.04269i
$187$	3.18388	+	3.18388i	0.232828	+	0.232828i
$188$	−19.6187	−	6.31357i	−1.43084	−	0.460465i
$189$			0.843398i			0.0613482i
$190$	−5.23862	−	12.2199i	−0.380050	−	0.886523i
$191$	15.8707	+	15.8707i	1.14836	+	1.14836i	0.986875	+	0.161488i	$0.0516293\pi$
$191$	15.8707	+	15.8707i	1.14836	+	1.14836i	0.161488	+	0.986875i	$0.448371\pi$
$192$	−10.2887	−	13.9129i	−0.742523	−	1.00408i
$193$			11.8917i			0.855982i	0.903783	+	0.427991i	$0.140779\pi$
$193$			11.8917i			0.855982i	−0.903783	+	0.427991i	$0.859221\pi$
$194$	−2.88328	+	18.3714i	−0.207007	+	1.31899i
$195$	26.4408	+	6.04404i	1.89347	+	0.432822i
$196$	13.1611	+	4.23544i	0.940082	+	0.302532i
$197$	18.9229	+	18.9229i	1.34820	+	1.34820i	0.887617	+	0.460583i	$0.152360\pi$
$197$	18.9229	+	18.9229i	1.34820	+	1.34820i	0.460583	+	0.887617i	$0.347640\pi$
$198$	−1.60742	+	1.17132i	−0.114235	+	0.0832419i
$199$	13.1786	−	13.1786i	0.934207	−	0.934207i	−0.0637586	−	0.997965i	$-0.520309\pi$
$199$	13.1786	−	13.1786i	0.934207	−	0.934207i	0.997965	+	0.0637586i	$0.0203088\pi$
$200$	8.60721	+	11.2212i	0.608622	+	0.793461i
$201$	7.45974			0.526170
$202$	−10.4043	+	7.58157i	−0.732047	+	0.533437i
$203$	0.786759	+	0.786759i	0.0552197	+	0.0552197i
$204$	7.12181	−	22.1302i	0.498626	−	1.54942i
$205$	−6.27501	−	12.8695i	−0.438266	−	0.898846i
$206$	−7.44919	−	10.2227i	−0.519010	−	0.712248i
$207$	−0.356803	+	0.356803i	−0.0247995	+	0.0247995i
$208$	−13.0826	+	18.2212i	−0.907112	+	1.26341i
$209$		−	3.52269i		−	0.243670i
$210$	−1.87398	−	0.749362i	−0.129317	−	0.0517109i
$211$	15.3564	+	15.3564i	1.05718	+	1.05718i	0.998263	+	0.0589138i	$0.0187637\pi$
$211$	15.3564	+	15.3564i	1.05718	+	1.05718i	0.0589138	+	0.998263i	$0.481236\pi$
$212$	2.01730	−	6.26854i	0.138549	−	0.430525i
$213$	12.1967	−	12.1967i	0.835707	−	0.835707i
$214$	7.72603	+	10.6026i	0.528140	+	0.724778i
$215$	5.38396	−	3.38051i	0.367183	−	0.230549i
$216$	−7.21881	−	3.63990i	−0.491178	−	0.247664i
$217$	−1.38850			−0.0942576
$218$	7.49290	+	10.2827i	0.507483	+	0.696430i
$219$	8.34945	−	8.34945i	0.564204	−	0.564204i
$220$	0.924576	+	3.63117i	0.0623349	+	0.244814i
$221$	−30.1366			−2.02721
$222$	9.40642	−	6.85439i	0.631318	−	0.460036i
$223$	−6.06023	+	6.06023i	−0.405823	+	0.405823i	−0.880279	−	0.474456i	$-0.842645\pi$
$223$	−6.06023	+	6.06023i	−0.405823	+	0.405823i	0.474456	+	0.880279i	$0.342645\pi$
$224$	1.17195	−	1.18854i	0.0783039	−	0.0794124i
$225$	−7.55915	−	3.64638i	−0.503943	−	0.243092i
$226$	7.05968	+	9.68815i	0.469603	+	0.644446i
$227$	−22.9523			−1.52340			−0.761698	−	0.647933i	$-0.775634\pi$
$227$	−22.9523			−1.52340			−0.761698	+	0.647933i	$0.775634\pi$
$228$	−16.1824	+	8.30275i	−1.07171	+	0.549863i
$229$	−8.25822	−	8.25822i	−0.545719	−	0.545719i	0.379481	−	0.925200i	$-0.376103\pi$
$229$	−8.25822	−	8.25822i	−0.545719	−	0.545719i	−0.925200	+	0.379481i	$0.876103\pi$
$230$	0.374566	+	0.873731i	0.0246982	+	0.0576121i
$231$	−0.378123	−	0.378123i	−0.0248787	−	0.0248787i
$232$	−10.1295	+	3.33856i	−0.665033	+	0.219187i
$233$			1.24661i			0.0816681i	0.999166	+	0.0408341i	$0.0130015\pi$
$233$			1.24661i			0.0816681i	−0.999166	+	0.0408341i	$0.986998\pi$
$234$	2.06395	−	13.1509i	0.134925	−	0.859702i
$235$	5.13471	−	22.4628i	0.334952	−	1.46531i
$236$	−27.1496	−	8.73714i	−1.76729	−	0.568739i
$237$	2.92919	+	2.92919i	0.190271	+	0.190271i
$238$	2.21540	+	0.347693i	0.143603	+	0.0225376i
$239$	−16.3808	−	16.3808i	−1.05959	−	1.05959i	−0.998108	−	0.0614786i	$-0.980418\pi$
$239$	−16.3808	−	16.3808i	−1.05959	−	1.05959i	−0.0614786	−	0.998108i	$-0.519582\pi$
$240$	14.5016	−	12.8057i	0.936074	−	0.826605i
$241$		−	0.184499i		−	0.0118846i	−0.999982	−	0.00594232i	$-0.998108\pi$
$241$		−	0.184499i		−	0.0118846i	0.999982	−	0.00594232i	$-0.00189151\pi$
$242$	2.25802	−	14.3874i	0.145151	−	0.924860i
$243$	15.6897			1.00650
$244$	−1.82880	+	5.68278i	−0.117077	+	0.363803i
$245$	−3.44461	+	15.0691i	−0.220068	+	0.962730i
$246$	−16.9712	+	9.77846i	−1.08204	+	0.623452i
$247$	16.6718	+	16.6718i	1.06080	+	1.06080i
$248$	5.99243	−	11.8844i	0.380520	−	0.754663i
$249$	2.70578	−	2.70578i	0.171472	−	0.171472i
$250$	−11.6661	+	10.6724i	−0.737832	+	0.674984i
$251$	−22.1113			−1.39566			−0.697828	−	0.716265i	$-0.745850\pi$
$251$	−22.1113			−1.39566			−0.697828	+	0.716265i	$0.745850\pi$
$252$	−0.303450	+	0.942936i	−0.0191156	+	0.0593994i
$253$			0.251875i			0.0158353i
$254$	11.4421	+	15.7023i	0.717944	+	0.985249i
$255$	25.3384	+	5.79203i	1.58675	+	0.362711i
$256$	5.11508	+	15.1603i	0.319693	+	0.947521i
$257$	−12.2412			−0.763582			−0.381791	−	0.924249i	$-0.624693\pi$
$257$	−12.2412			−0.763582			−0.381791	+	0.924249i	$0.624693\pi$
$258$	−5.12169	−	7.02860i	−0.318863	−	0.437582i
$259$	0.793867	+	0.793867i	0.0493285	+	0.0493285i
$260$	−21.5609	−	12.8095i	−1.33715	−	0.794409i
$261$	4.47559	−	4.47559i	0.277032	−	0.277032i
$262$	−10.7074	−	1.68046i	−0.661505	−	0.103819i
$263$			11.8229i			0.729030i	0.931197	+	0.364515i	$0.118765\pi$
$263$			11.8229i			0.729030i	−0.931197	+	0.364515i	$0.881235\pi$
$264$	4.86832	−	1.60454i	0.299624	−	0.0987528i
$265$	7.17728	+	1.64064i	0.440897	+	0.100783i
$266$	−1.03323	−	1.41792i	−0.0633513	−	0.0869384i
$267$	22.4939	−	22.4939i	1.37660	−	1.37660i
$268$	−6.56599	−	2.11303i	−0.401082	−	0.129074i
$269$			8.55896i			0.521849i	0.965359	+	0.260925i	$0.0840274\pi$
$269$			8.55896i			0.521849i	−0.965359	+	0.260925i	$0.915973\pi$
$270$	3.35604	−	8.39268i	0.204242	−	0.510762i
$271$			12.5928i			0.764957i	0.923964	+	0.382479i	$0.124929\pi$
$271$			12.5928i			0.764957i	−0.923964	+	0.382479i	$0.875071\pi$
$272$	−12.5371	+	17.4615i	−0.760172	+	1.05876i
$273$	3.57908			0.216616
$274$	−2.37157	+	15.1110i	−0.143272	+	0.912887i
$275$	−3.95512	+	1.38106i	−0.238503	+	0.0832808i
$276$	1.15706	−	0.593654i	0.0696467	−	0.0357338i
$277$	−9.15817	+	9.15817i	−0.550261	+	0.550261i	−0.926516	−	0.376255i	$-0.877212\pi$
$277$	−9.15817	+	9.15817i	−0.550261	+	0.550261i	0.376255	+	0.926516i	$0.377212\pi$
$278$	8.09691	+	1.27076i	0.485620	+	0.0762151i
$279$			7.89868i			0.472881i
$280$	1.43720	+	1.19040i	0.0858890	+	0.0711401i
$281$	21.4286	−	21.4286i	1.27832	−	1.27832i	0.336716	−	0.941606i	$-0.390684\pi$
$281$	21.4286	−	21.4286i	1.27832	−	1.27832i	0.941606	−	0.336716i	$-0.109316\pi$
$282$	−31.1404	−	4.88730i	−1.85439	−	0.291034i
$283$	−11.0847	+	11.0847i	−0.658917	+	0.658917i	−0.955124	−	0.296207i	$-0.904278\pi$
$283$	−11.0847	+	11.0847i	−0.658917	+	0.658917i	0.296207	+	0.955124i	$0.404278\pi$
$284$	−14.1903	+	7.28063i	−0.842037	+	0.432026i
$285$	−10.8132	−	17.2216i	−0.640518	−	1.02012i
$286$	−3.91327	−	5.37027i	−0.231397	−	0.317551i
$287$	−1.18565	−	1.47102i	−0.0699868	−	0.0868313i
$288$	−6.76115	−	6.66677i	−0.398405	−	0.392843i
$289$	−11.8800			−0.698826
$290$	−4.69840	−	10.9597i	−0.275900	−	0.643577i
$291$			28.4424i			1.66732i
$292$	−9.71415	+	4.98406i	−0.568477	+	0.291670i
$293$	24.2894			1.41900			0.709501	−	0.704705i	$-0.248921\pi$
$293$	24.2894			1.41900			0.709501	+	0.704705i	$0.248921\pi$
$294$	20.8905	+	3.27863i	1.21836	+	0.191214i
$295$	7.10575	−	31.0855i	0.413713	−	1.80987i
$296$	−10.2210	+	3.36872i	−0.594083	+	0.195803i
$297$	1.69344	−	1.69344i	0.0982631	−	0.0982631i
$298$	0.580412	+	0.796511i	0.0336223	+	0.0461406i
$299$	−1.19205	−	1.19205i	−0.0689379	−	0.0689379i
$300$	15.6662	+	14.9139i	0.904489	+	0.861052i
$301$	0.593188	−	0.593188i	0.0341908	−	0.0341908i
$302$	−6.08343	+	4.43295i	−0.350062	+	0.255088i
$303$	−13.9228	+	13.9228i	−0.799843	+	0.799843i
$304$	16.5954	−	2.72420i	0.951813	−	0.156244i
$305$	−6.50661	−	1.48733i	−0.372567	−	0.0851641i
$306$	1.97790	−	12.6026i	0.113069	−	0.720442i
$307$	10.1386	−	10.1386i	0.578638	−	0.578638i	−0.355890	−	0.934528i	$-0.615822\pi$
$307$	10.1386	−	10.1386i	0.578638	−	0.578638i	0.934528	+	0.355890i	$0.115822\pi$
$308$	0.225714	+	0.439927i	0.0128613	+	0.0250672i
$309$	−13.6797	−	13.6797i	−0.778210	−	0.778210i
$310$	13.8170	+	5.52510i	0.784753	+	0.313805i
$311$	−16.2293	−	16.2293i	−0.920279	−	0.920279i	0.0767695	−	0.997049i	$-0.475539\pi$
$311$	−16.2293	−	16.2293i	−0.920279	−	0.920279i	−0.997049	+	0.0767695i	$0.975539\pi$
$312$	−15.4464	+	30.6340i	−0.874482	+	1.73431i
$313$	10.5559			0.596657			0.298328	−	0.954463i	$-0.403571\pi$
$313$	10.5559			0.596657			0.298328	+	0.954463i	$0.403571\pi$
$314$	0.678706	+	0.106519i	0.0383016	+	0.00601119i
$315$	−1.07963	−	0.246790i	−0.0608304	−	0.0139051i
$316$	−1.74853	−	3.40796i	−0.0983624	−	0.191713i
$317$	8.92147			0.501080			0.250540	−	0.968106i	$-0.419392\pi$
$317$	8.92147			0.501080			0.250540	+	0.968106i	$0.419392\pi$
$318$	1.56158	−	9.94995i	0.0875692	−	0.557966i
$319$		−	3.15942i		−	0.176894i
$320$	−16.3915	+	7.16377i	−0.916311	+	0.400467i
$321$	14.1881	+	14.1881i	0.791901	+	0.791901i
$322$	0.0738767	+	0.101383i	0.00411699	+	0.00564983i
$323$	15.9767	+	15.9767i	0.888966	+	0.888966i
$324$	−21.3576	−	6.87316i	−1.18653	−	0.381842i
$325$	12.1822	−	25.2545i	0.675749	−	1.40087i
$326$	−21.9689	+	16.0086i	−1.21675	+	0.886633i
$327$	13.7600	+	13.7600i	0.760927	+	0.760927i
$328$	17.7077	−	3.79968i	0.977744	−	0.209802i
$329$		−	3.04061i		−	0.167634i
$330$	2.25809	+	5.26734i	0.124304	+	0.289958i
$331$	14.1620	−	14.1620i	0.778415	−	0.778415i	−0.201146	−	0.979561i	$-0.564467\pi$
$331$	14.1620	−	14.1620i	0.778415	−	0.778415i	0.979561	+	0.201146i	$0.0644666\pi$
$332$	−3.14803	+	1.61517i	−0.172771	+	0.0886437i
$333$	4.51602	−	4.51602i	0.247476	−	0.247476i
$334$	2.53301	−	16.1396i	0.138600	−	0.883119i
$335$	1.71849	−	7.51786i	0.0938910	−	0.410745i
$336$	1.48893	−	2.07376i	0.0812277	−	0.113133i
$337$	−9.81602	−	9.81602i	−0.534713	−	0.534713i	0.387258	−	0.921971i	$-0.373422\pi$
$337$	−9.81602	−	9.81602i	−0.534713	−	0.534713i	−0.921971	+	0.387258i	$0.873422\pi$
$338$	25.7736	+	4.04501i	1.40190	+	0.220020i
$339$	12.9644	+	12.9644i	0.704129	+	0.704129i
$340$	−20.6619	−	12.2754i	−1.12055	−	0.665726i
$341$	2.78793	+	2.78793i	0.150975	+	0.150975i
$342$	−8.06604	+	5.87766i	−0.436162	+	0.317828i
$343$			4.10526i			0.221663i
$344$	2.51715	+	7.63726i	0.135716	+	0.411774i
$345$	0.773153	+	1.23136i	0.0416251	+	0.0662941i
$346$	−18.5410	+	13.5107i	−0.996771	+	0.726339i
$347$	−29.6855			−1.59360			−0.796801	−	0.604241i	$-0.793476\pi$
$347$	−29.6855			−1.59360			−0.796801	+	0.604241i	$0.793476\pi$
$348$	−14.5137	+	7.44655i	−0.778014	+	0.399177i
$349$	−11.0175			−0.589753			−0.294876	−	0.955535i	$-0.595278\pi$
$349$	−11.0175			−0.589753			−0.294876	+	0.955535i	$0.595278\pi$
$350$	−1.18691	+	1.71595i	−0.0634428	+	0.0917216i
$351$			16.0290i			0.855565i
$352$	−4.73954	+	0.0333130i	−0.252619	+	0.00177559i
$353$	11.9989	+	11.9989i	0.638635	+	0.638635i	0.950219	−	0.311584i	$-0.100859\pi$
$353$	11.9989	+	11.9989i	0.638635	+	0.638635i	−0.311584	+	0.950219i	$0.600859\pi$
$354$	−43.0942	−	6.76337i	−2.29043	−	0.359469i
$355$	−9.48202	−	15.1015i	−0.503253	−	0.801504i
$356$	−26.1704	+	13.4273i	−1.38703	+	0.711647i
$357$	3.42985			0.181527
$358$	5.83211	−	4.24981i	0.308236	−	0.224610i
$359$	29.8748			1.57673			0.788367	−	0.615206i	$-0.210927\pi$
$359$	29.8748			1.57673			0.788367	+	0.615206i	$0.210927\pi$
$360$	6.77176	−	8.17570i	0.356903	−	0.430897i
$361$			1.32316i			0.0696398i
$362$	12.4773	−	9.09214i	0.655794	−	0.477872i
$363$		−	22.2745i		−	1.16911i
$364$	−3.15027	−	1.01380i	−0.165119	−	0.0531376i
$365$	−6.49105	−	10.3379i	−0.339757	−	0.541113i
$366$	−1.41566	+	9.02019i	−0.0739978	+	0.471493i
$367$	−3.28211	+	3.28211i	−0.171324	+	0.171324i	−0.787561	−	0.616237i	$-0.788657\pi$
$367$	−3.28211	+	3.28211i	−0.171324	+	0.171324i	0.616237	+	0.787561i	$0.288657\pi$
$368$	−1.18659	+	0.194783i	−0.0618551	+	0.0101537i
$369$	−8.36808	+	6.74475i	−0.435625	+	0.351117i
$370$	−4.74085	−	11.0587i	−0.246465	−	0.574916i
$371$	0.971530			0.0504393
$372$	6.23614	−	19.3781i	0.323329	−	1.00471i
$373$	0.510894	+	0.510894i	0.0264531	+	0.0264531i	0.720210	−	0.693757i	$-0.244046\pi$
$373$	0.510894	+	0.510894i	0.0264531	+	0.0264531i	−0.693757	+	0.720210i	$0.744046\pi$
$374$	−3.75011	−	5.14636i	−0.193914	−	0.266112i
$375$	−15.0964	+	18.8922i	−0.779573	+	0.975590i
$376$	26.0251	+	13.1225i	1.34214	+	0.676742i
$377$	14.9526	+	14.9526i	0.770096	+	0.770096i
$378$	0.184930	−	1.17832i	0.00951179	−	0.0606063i
$379$	−32.1666			−1.65229			−0.826144	−	0.563459i	$-0.809470\pi$
$379$	−32.1666			−1.65229			−0.826144	+	0.563459i	$0.809470\pi$
$380$	4.63952	+	18.2212i	0.238002	+	0.934727i
$381$	21.0123	+	21.0123i	1.07649	+	1.07649i
$382$	−18.6932	−	25.6531i	−0.956427	−	1.31252i
$383$			12.3819i			0.632684i	0.948645	+	0.316342i	$0.102455\pi$
$383$			12.3819i			0.632684i	−0.948645	+	0.316342i	$0.897545\pi$
$384$	11.3238	+	21.6939i	0.577866	+	1.10706i
$385$	−0.468177	+	0.293962i	−0.0238605	+	0.0149817i
$386$	2.60747	−	16.6140i	0.132717	−	0.845631i
$387$	−3.37443	−	3.37443i	−0.171532	−	0.171532i
$388$	8.05653	−	25.0347i	0.409008	−	1.27094i
$389$	−4.79811			−0.243274			−0.121637	−	0.992575i	$-0.538814\pi$
$389$	−4.79811			−0.243274			−0.121637	+	0.992575i	$0.538814\pi$
$390$	−35.6155	−	14.2418i	−1.80346	−	0.721163i
$391$	−1.14235	−	1.14235i	−0.0577709	−	0.0577709i
$392$	−17.4589	−	8.80321i	−0.881807	−	0.444629i
$393$	−16.5771			−0.836202
$394$	−22.2882	−	30.5866i	−1.12286	−	1.54093i
$395$	3.62680	−	2.27722i	0.182484	−	0.114579i
$396$	2.50258	−	1.28401i	0.125760	−	0.0645237i
$397$	12.9178			0.648327			0.324163	−	0.946001i	$-0.394917\pi$
$397$	12.9178			0.648327			0.324163	+	0.946001i	$0.394917\pi$
$398$	−21.3016	+	15.5223i	−1.06775	+	0.778065i
$399$	−1.89742	−	1.89742i	−0.0949898	−	0.0949898i
$400$	−9.56478	−	17.5646i	−0.478239	−	0.878230i
$401$			35.5877i			1.77716i	0.458719	+	0.888581i	$0.348309\pi$
$401$			35.5877i			1.77716i	−0.458719	+	0.888581i	$0.651691\pi$
$402$	−10.4221	−	1.63568i	−0.519807	−	0.0815805i
$403$	−26.3888			−1.31452
$404$	16.1984	−	8.31096i	0.805902	−	0.413486i
$405$	5.58982	−	24.4537i	0.277760	−	1.21512i
$406$	−0.926679	−	1.27170i	−0.0459903	−	0.0631135i
$407$		−	3.18796i		−	0.158022i
$408$	−14.8024	+	29.3568i	−0.732828	+	1.45338i
$409$			28.3999i			1.40429i	0.712036	+	0.702143i	$0.247773\pi$
$409$			28.3999i			1.40429i	−0.712036	+	0.702143i	$0.752227\pi$
$410$	5.94502	+	19.3561i	0.293603	+	0.955927i
$411$			23.3946i			1.15397i
$412$	8.16585	+	15.9156i	0.402302	+	0.784105i
$413$		−	4.20779i		−	0.207052i
$414$	0.576729	−	0.420258i	0.0283447	−	0.0206546i
$415$	−2.10353	−	3.35018i	−0.103258	−	0.164454i
$416$	22.2731	−	22.5884i	1.09203	−	1.10749i
$417$	12.5355			0.613868
$418$	−0.772414	+	4.92160i	−0.0377800	+	0.240723i
$419$		−	19.6389i		−	0.959424i	−0.877426	−	0.479712i	$-0.840741\pi$
$419$		−	19.6389i		−	0.959424i	0.877426	−	0.479712i	$-0.159259\pi$
$420$	2.45385	+	1.45785i	0.119736	+	0.0711357i
$421$	−13.1860	−	13.1860i	−0.642647	−	0.642647i	0.308558	−	0.951205i	$-0.400154\pi$
$421$	−13.1860	−	13.1860i	−0.642647	−	0.642647i	−0.951205	+	0.308558i	$0.900154\pi$
$422$	−18.0874	−	24.8217i	−0.880482	−	1.20830i
$423$	−17.2969			−0.841005
$424$	−4.19289	+	8.31552i	−0.203625	+	0.403837i
$425$	11.6743	−	24.2015i	0.566287	−	1.17394i
$426$	−19.7146	+	14.3659i	−0.955174	+	0.696028i
$427$	−0.880747			−0.0426223
$428$	−8.46931	−	16.5071i	−0.409380	−	0.797899i
$429$	−7.18633	−	7.18633i	−0.346959	−	0.346959i
$430$	−8.26324	+	3.54243i	−0.398489	+	0.170831i
$431$	−35.2396			−1.69743			−0.848716	−	0.528850i	$-0.822624\pi$
$431$	−35.2396			−1.69743			−0.848716	+	0.528850i	$0.822624\pi$
$432$	9.28737	+	6.66821i	0.446839	+	0.320824i
$433$	0.610511	+	0.610511i	0.0293393	+	0.0293393i	0.721624	−	0.692285i	$-0.243396\pi$
$433$	0.610511	+	0.610511i	0.0293393	+	0.0293393i	−0.692285	+	0.721624i	$0.743396\pi$
$434$	1.93989	+	0.304454i	0.0931177	+	0.0146142i
$435$	−9.69811	−	15.4457i	−0.464989	−	0.740562i
$436$	−8.21376	−	16.0090i	−0.393368	−	0.766691i
$437$			1.26391i			0.0604610i
$438$	−13.4959	+	9.83435i	−0.644858	+	0.469903i
$439$	−22.5528	−	22.5528i	−1.07639	−	1.07639i	−0.996830	−	0.0795578i	$-0.974649\pi$
$439$	−22.5528	−	22.5528i	−1.07639	−	1.07639i	−0.0795578	−	0.996830i	$-0.525351\pi$
$440$	−0.495537	−	5.27588i	−0.0236238	−	0.251518i
$441$	11.6036			0.552552
$442$	42.1042	+	6.60799i	2.00269	+	0.314310i
$443$	16.8925	+	16.8925i	0.802587	+	0.802587i	0.983499	−	0.180913i	$-0.0579051\pi$
$443$	16.8925	+	16.8925i	0.802587	+	0.802587i	−0.180913	+	0.983499i	$0.557905\pi$
$444$	−14.6448	+	7.51382i	−0.695010	+	0.356590i
$445$	−17.4872	−	27.8510i	−0.828975	−	1.32026i
$446$	9.79564	−	7.13801i	0.463837	−	0.337994i
$447$	1.06587	+	1.06587i	0.0504138	+	0.0504138i
$448$	−1.89795	+	1.40355i	−0.0896696	+	0.0663114i
$449$	8.55502			0.403736			0.201868	−	0.979413i	$-0.435299\pi$
$449$	8.55502			0.403736			0.201868	+	0.979413i	$0.435299\pi$
$450$	9.76144	+	6.75188i	0.460159	+	0.318287i
$451$	−0.572973	+	5.33425i	−0.0269802	+	0.251180i
$452$	−7.73886	−	15.0834i	−0.364006	−	0.709463i
$453$	−8.14066	+	8.14066i	−0.382482	+	0.382482i
$454$	32.0669	+	5.03270i	1.50497	+	0.236196i
$455$	0.824506	−	3.60696i	0.0386534	−	0.169097i
$456$	24.4292	−	8.05158i	1.14400	−	0.377050i
$457$		−	28.2440i		−	1.32120i	−0.750739	−	0.660599i	$-0.770303\pi$
$457$		−	28.2440i		−	1.32120i	0.750739	−	0.660599i	$-0.229697\pi$
$458$	9.72690	+	13.3484i	0.454508	+	0.623731i
$459$			15.3607i			0.716975i
$460$	−0.331729	−	1.30283i	−0.0154670	−	0.0607448i
$461$	26.8598			1.25098			0.625492	−	0.780231i	$-0.284898\pi$
$461$	26.8598			1.25098			0.625492	+	0.780231i	$0.284898\pi$
$462$	0.445370	+	0.611191i	0.0207205	+	0.0284352i
$463$	−18.4162			−0.855873			−0.427936	−	0.903809i	$-0.640759\pi$
$463$	−18.4162			−0.855873			−0.427936	+	0.903809i	$0.640759\pi$
$464$	14.8841	−	2.44327i	0.690975	−	0.113426i
$465$	22.1873	+	5.07174i	1.02891	+	0.235196i
$466$	0.273342	−	1.74165i	0.0126623	−	0.0806806i
$467$	23.2022	+	23.2022i	1.07367	+	1.07367i	0.997061	+	0.0766098i	$0.0244096\pi$
$467$	23.2022	+	23.2022i	1.07367	+	1.07367i	0.0766098	+	0.997061i	$0.475590\pi$
$468$	−5.76715	+	17.9207i	−0.266587	+	0.828387i
$469$		−	1.01763i		−	0.0469899i
$470$	−12.0991	+	30.2572i	−0.558092	+	1.39566i
$471$	1.05076			0.0484166
$472$	36.0153	+	18.1598i	1.65774	+	0.835873i
$473$	−2.38209			−0.109529
$474$	−3.45013	−	4.73469i	−0.158470	−	0.217471i
$475$	−19.8468	+	6.93013i	−0.910632	+	0.317976i
$476$	−3.01892	−	0.971531i	−0.138372	−	0.0445301i
$477$		−	5.52668i		−	0.253049i
$478$	19.2940	+	26.4776i	0.882489	+	1.21106i
$479$	−5.93689	−	5.93689i	−0.271264	−	0.271264i	0.558345	−	0.829609i	$-0.311436\pi$
$479$	−5.93689	−	5.93689i	−0.271264	−	0.271264i	−0.829609	+	0.558345i	$0.811436\pi$
$480$	−23.0682	+	14.7113i	−1.05292	+	0.671475i
$481$	15.0876	+	15.0876i	0.687937	+	0.687937i
$482$	−0.0404548	+	0.257766i	−0.00184266	+	0.0117409i
$483$	0.135667	+	0.135667i	0.00617307	+	0.00617307i
$484$	−6.30941	+	19.6058i	−0.286791	+	0.891171i
$485$	28.6640	+	6.55222i	1.30156	+	0.297521i
$486$	−21.9203	−	3.44026i	−0.994326	−	0.156053i
$487$	−15.9947	+	15.9947i	−0.724790	+	0.724790i	−0.969577	−	0.244787i	$-0.921282\pi$
$487$	−15.9947	+	15.9947i	−0.724790	+	0.724790i	0.244787	+	0.969577i	$0.421282\pi$
$488$	3.80109	−	7.53848i	0.172067	−	0.341251i
$489$	−29.3981	+	29.3981i	−1.32943	+	1.32943i
$490$	8.11667	−	20.2979i	0.366674	−	0.916967i
$491$			14.0574i			0.634404i	0.948358	+	0.317202i	$0.102743\pi$
$491$			14.0574i			0.634404i	−0.948358	+	0.317202i	$0.897257\pi$
$492$	25.8548	−	9.94036i	1.16562	−	0.448146i
$493$	14.3291	+	14.3291i	0.645351	+	0.645351i
$494$	−19.6368	−	26.9480i	−0.883500	−	1.21245i
$495$	1.67224	+	2.66329i	0.0751617	+	0.119706i
$496$	−10.9780	+	15.2899i	−0.492926	+	0.686539i
$497$	−1.66384	−	1.66384i	−0.0746332	−	0.0746332i
$498$	−4.37356	+	3.18698i	−0.195984	+	0.142812i
$499$	28.5996	+	28.5996i	1.28029	+	1.28029i	0.940499	+	0.339796i	$0.110358\pi$
$499$	28.5996	+	28.5996i	1.28029	+	1.28029i	0.339796	+	0.940499i	$0.389642\pi$
$500$	18.6390	−	12.3526i	0.833563	−	0.552424i
$501$		−	24.9871i		−	1.11634i
$502$	30.8920	+	4.84831i	1.37878	+	0.216391i
$503$	14.2373			0.634808			0.317404	−	0.948290i	$-0.397189\pi$
$503$	14.2373			0.634808			0.317404	+	0.948290i	$0.397189\pi$
$504$	0.630710	−	1.25085i	0.0280940	−	0.0557173i
$505$	10.8239	+	17.2386i	0.481657	+	0.767108i
$506$	0.0552282	−	0.351898i	0.00245519	−	0.0156438i
$507$	39.9024			1.77213
$508$	−12.5429	−	24.4467i	−0.556503	−	1.08465i
$509$	13.8837	+	13.8837i	0.615384	+	0.615384i	0.944344	−	0.328960i	$-0.106698\pi$
$509$	13.8837	+	13.8837i	0.615384	+	0.615384i	−0.328960	+	0.944344i	$0.606698\pi$
$510$	−34.1305	−	13.6480i	−1.51133	−	0.604344i
$511$	−1.13900	−	1.13900i	−0.0503865	−	0.0503865i
$512$	−3.82216	−	22.3023i	−0.168917	−	0.985630i
$513$	8.49765	−	8.49765i	0.375180	−	0.375180i
$514$	17.1023	+	2.68409i	0.754348	+	0.118390i
$515$	−16.9376	+	10.6349i	−0.746361	+	0.468630i
$516$	5.61443	+	10.9428i	0.247161	+	0.481729i
$517$	−6.10515	+	6.10515i	−0.268504	+	0.268504i
$518$	−0.935051	−	1.28319i	−0.0410838	−	0.0563801i
$519$	−24.8110	+	24.8110i	−1.08908	+	1.08908i
$520$	27.3143	+	22.6239i	1.19781	+	0.992123i
$521$	−27.1602	−	27.1602i	−1.18991	−	1.18991i	−0.977091	−	0.212821i	$-0.931735\pi$
$521$	−27.1602	−	27.1602i	−1.18991	−	1.18991i	−0.212821	−	0.977091i	$-0.568265\pi$
$522$	−7.23425	+	5.27154i	−0.316635	+	0.230729i
$523$	−12.5127	+	12.5127i	−0.547141	+	0.547141i	−0.925613	−	0.378472i	$-0.876450\pi$
$523$	−12.5127	+	12.5127i	−0.547141	+	0.547141i	0.378472	+	0.925613i	$0.376450\pi$
$524$	14.5910	+	4.69558i	0.637409	+	0.205127i
$525$	−1.38646	+	2.87421i	−0.0605102	+	0.125441i
$526$	2.59238	−	16.5179i	0.113033	−	0.720214i
$527$	−25.2885			−1.10159
$528$	−7.15341	+	1.17426i	−0.311312	+	0.0511030i
$529$			22.9096i			0.996071i
$530$	−9.66773	−	3.86590i	−0.419939	−	0.167924i
$531$	−23.9366			−1.03876
$532$	1.13263	+	2.20755i	0.0491058	+	0.0957094i
$533$	−22.5336	−	27.9570i	−0.976040	−	1.21095i
$534$	−36.3587	+	26.4943i	−1.57339	+	1.14652i
$535$	17.5671	−	11.0301i	0.759491	−	0.476874i
$536$	8.71010	+	4.39185i	0.376219	+	0.189699i
$537$	7.80435	−	7.80435i	0.336783	−	0.336783i
$538$	1.87671	−	11.9578i	0.0809106	−	0.515539i
$539$	4.09562	−	4.09562i	0.176411	−	0.176411i
$540$	−6.52901	+	10.9896i	−0.280964	+	0.472919i
$541$			10.8226i			0.465301i	0.972560	+	0.232650i	$0.0747397\pi$
$541$			10.8226i			0.465301i	−0.972560	+	0.232650i	$0.925260\pi$
$542$	2.76119	−	17.5935i	0.118603	−	0.755707i
$543$	16.6968	−	16.6968i	0.716528	−	0.716528i
$544$	21.3444	−	21.6466i	0.915136	−	0.928091i
$545$	17.0370	−	10.6973i	0.729785	−	0.458222i
$546$	−5.00037	−	0.784778i	−0.213996	−	0.0335854i
$547$	39.0177			1.66828			0.834139	−	0.551554i	$-0.185965\pi$
$547$	39.0177			1.66828			0.834139	+	0.551554i	$0.185965\pi$
$548$	6.62671	−	20.5917i	0.283079	−	0.879634i
$549$			5.01025i			0.213832i
$550$	5.82857	−	1.06226i	0.248531	−	0.0452949i
$551$		−	15.8540i		−	0.675401i
$552$	−1.74671	+	0.575695i	−0.0743448	+	0.0245032i
$553$	0.399590	−	0.399590i	0.0169923	−	0.0169923i
$554$	14.8031	−	10.7869i	0.628922	−	0.458291i
$555$	−9.78572	−	15.5852i	−0.415381	−	0.661554i
$556$	−11.0336	−	3.55079i	−0.467931	−	0.150587i
$557$		−	35.3386i		−	1.49734i	−0.662941	−	0.748672i	$-0.730692\pi$
$557$		−	35.3386i		−	1.49734i	0.662941	−	0.748672i	$-0.269308\pi$
$558$	1.73193	−	11.0353i	0.0733183	−	0.467163i
$559$	11.2737	−	11.2737i	0.476826	−	0.476826i
$560$	−1.74691	−	1.97826i	−0.0738204	−	0.0835965i
$561$	−6.88670	−	6.88670i	−0.290757	−	0.290757i
$562$	−34.6367	+	25.2395i	−1.46106	+	1.06467i
$563$	−12.9105			−0.544114			−0.272057	−	0.962281i	$-0.587704\pi$
$563$	−12.9105			−0.544114			−0.272057	+	0.962281i	$0.587704\pi$
$564$	42.4351	+	13.6562i	1.78684	+	0.575030i
$565$	16.0520	−	10.0788i	0.675312	−	0.424019i
$566$	17.9171	−	13.0560i	0.753111	−	0.548786i
$567$		−	3.31010i		−	0.139011i
$568$	21.4218	−	7.06038i	0.898839	−	0.296247i
$569$	−25.8383			−1.08320			−0.541599	−	0.840637i	$-0.682181\pi$
$569$	−25.8383			−1.08320			−0.541599	+	0.840637i	$0.682181\pi$
$570$	11.3311	+	26.4315i	0.474608	+	1.10709i
$571$	−6.86766	+	6.86766i	−0.287403	+	0.287403i	−0.836052	−	0.548650i	$-0.815142\pi$
$571$	−6.86766	+	6.86766i	−0.287403	+	0.287403i	0.548650	+	0.836052i	$0.315142\pi$
$572$	4.28975	+	8.36092i	0.179364	+	0.349588i
$573$	−34.3282	−	34.3282i	−1.43408	−	1.43408i
$574$	1.33394	+	2.31515i	0.0556777	+	0.0966325i
$575$	1.41906	−	0.495510i	0.0591789	−	0.0206642i
$576$	7.98428	+	10.7967i	0.332678	+	0.449864i
$577$	−24.7568			−1.03064			−0.515320	−	0.856998i	$-0.672327\pi$
$577$	−24.7568			−1.03064			−0.515320	+	0.856998i	$0.672327\pi$
$578$	16.5978	+	2.60491i	0.690376	+	0.108350i
$579$		−	25.7216i		−	1.06895i
$580$	4.16108	+	16.3422i	0.172779	+	0.678572i
$581$	−0.369112	−	0.369112i	−0.0153134	−	0.0153134i
$582$	6.23651	−	39.7372i	0.258512	−	1.64716i
$583$	−1.95071	−	1.95071i	−0.0807901	−	0.0807901i
$584$	14.6646	−	4.83328i	0.606825	−	0.200003i
$585$	−20.5187	−	4.69031i	−0.848344	−	0.193921i
$586$	−33.9350	−	5.32589i	−1.40184	−	0.220010i
$587$			15.4873i			0.639230i	0.947548	+	0.319615i	$0.103553\pi$
$587$			15.4873i			0.639230i	−0.947548	+	0.319615i	$0.896447\pi$
$588$	−28.4674	−	9.16123i	−1.17398	−	0.377803i
$589$	13.9898	+	13.9898i	0.576440	+	0.576440i
$590$	−16.7436	+	41.8719i	−0.689323	+	1.72384i
$591$	−40.9300	−	40.9300i	−1.68364	−	1.68364i
$592$	15.0185	−	2.46534i	0.617257	−	0.101325i
$593$	−11.8002			−0.484577			−0.242289	−	0.970204i	$-0.577898\pi$
$593$	−11.8002			−0.484577			−0.242289	+	0.970204i	$0.577898\pi$
$594$	−2.73724	+	1.99460i	−0.112310	+	0.0818396i
$595$	0.790128	−	3.45657i	0.0323921	−	0.141706i
$596$	−0.636251	−	1.24008i	−0.0260618	−	0.0507957i
$597$	−28.5052	+	28.5052i	−1.16664	+	1.16664i
$598$	1.40405	+	1.92680i	0.0574157	+	0.0787928i
$599$	30.5031			1.24632			0.623162	−	0.782093i	$-0.285848\pi$
$599$	30.5031			1.24632			0.623162	+	0.782093i	$0.285848\pi$
$600$	−18.6173	−	24.2714i	−0.760049	−	0.990877i
$601$	6.76101	−	6.76101i	0.275787	−	0.275787i	−0.555637	−	0.831425i	$-0.687526\pi$
$601$	6.76101	−	6.76101i	0.275787	−	0.275787i	0.831425	+	0.555637i	$0.187526\pi$
$602$	−0.958817	+	0.698683i	−0.0390785	+	0.0284762i
$603$	−5.78894			−0.235744
$604$	9.47124	−	4.85942i	0.385379	−	0.197727i
$605$	−22.4480	−	5.13133i	−0.912641	−	0.208618i
$606$	22.5045	−	16.3989i	0.914183	−	0.666158i
$607$	−11.3825	+	11.3825i	−0.462002	+	0.462002i	−0.899311	−	0.437309i	$-0.855932\pi$
$607$	−11.3825	+	11.3825i	−0.462002	+	0.462002i	0.437309	+	0.899311i	$0.355932\pi$
$608$	−23.7830	+	0.167164i	−0.964528	+	0.00677940i
$609$	−1.70175	−	1.70175i	−0.0689585	−	0.0689585i
$610$	8.76434	+	3.50465i	0.354858	+	0.141899i
$611$		−	57.7875i		−	2.33783i
$612$	−5.52669	+	17.1735i	−0.223403	+	0.694199i
$613$	−21.0461	+	21.0461i	−0.850044	+	0.850044i	−0.990138	−	0.140094i	$-0.955260\pi$
$613$	−21.0461	+	21.0461i	−0.850044	+	0.850044i	0.140094	+	0.990138i	$0.455260\pi$
$614$	−16.3878	+	11.9416i	−0.661356	+	0.481925i
$615$	13.5728	+	27.8366i	0.547308	+	1.12248i
$616$	−0.218886	−	0.664119i	−0.00881916	−	0.0267581i
$617$	21.9292	+	21.9292i	0.882838	+	0.882838i	0.993822	−	0.110985i	$-0.0354004\pi$
$617$	21.9292	+	21.9292i	0.882838	+	0.882838i	−0.110985	+	0.993822i	$0.535400\pi$
$618$	16.1125	+	22.1116i	0.648141	+	0.889458i
$619$	−17.6974			−0.711319			−0.355660	−	0.934616i	$-0.615744\pi$
$619$	−17.6974			−0.711319			−0.355660	+	0.934616i	$0.615744\pi$
$620$	−18.0924	−	10.7488i	−0.726609	−	0.431683i
$621$	−0.607589	+	0.607589i	−0.0243817	+	0.0243817i
$622$	19.1156	+	26.2327i	0.766465	+	1.05184i
$623$	−3.06853	−	3.06853i	−0.122938	−	0.122938i
$624$	28.2975	−	39.4123i	1.13281	−	1.57775i
$625$	15.5617	+	19.5661i	0.622467	+	0.782646i
$626$	−14.7478	−	2.31458i	−0.589441	−	0.0925091i
$627$			7.61955i			0.304296i
$628$	−0.924872	−	0.297637i	−0.0369064	−	0.0118770i
$629$	14.4586	+	14.4586i	0.576501	+	0.576501i
$630$	1.45426	+	0.581523i	0.0579389	+	0.0231684i
$631$			32.8381i			1.30726i	0.756812	+	0.653632i	$0.226756\pi$
$631$			32.8381i			1.30726i	−0.756812	+	0.653632i	$0.773244\pi$
$632$	1.69563	+	5.14470i	0.0674487	+	0.204645i
$633$	−33.2157	−	33.2157i	−1.32021	−	1.32021i
$634$	−12.4643	−	1.95619i	−0.495021	−	0.0776904i
$635$	26.0166	−	16.3355i	1.03244	−	0.648253i
$636$	−4.36341	+	13.5588i	−0.173021	+	0.537641i
$637$			38.7666i			1.53599i
$638$	−0.692760	+	4.41407i	−0.0274266	+	0.174755i
$639$	−9.46496	+	9.46496i	−0.374428	+	0.374428i
$640$	24.4715	−	6.41447i	0.967321	−	0.253554i
$641$	−34.3455	+	34.3455i	−1.35657	+	1.35657i	−0.478455	+	0.878112i	$0.658803\pi$
$641$	−34.3455	+	34.3455i	−1.35657	+	1.35657i	−0.878112	+	0.478455i	$0.841197\pi$
$642$	−16.7113	−	22.9333i	−0.659543	−	0.905105i
$643$	−4.81618			−0.189932			−0.0949658	−	0.995481i	$-0.530274\pi$
$643$	−4.81618			−0.189932			−0.0949658	+	0.995481i	$0.530274\pi$
$644$	−0.0809841	−	0.157842i	−0.00319122	−	0.00621983i
$645$	−11.6455	+	7.31202i	−0.458540	+	0.287911i
$646$	−18.8180	−	25.8244i	−0.740385	−	1.01605i
$647$	−3.59621	+	3.59621i	−0.141381	+	0.141381i	−0.774255	−	0.632874i	$-0.781875\pi$
$647$	−3.59621	+	3.59621i	−0.141381	+	0.141381i	0.632874	+	0.774255i	$0.281875\pi$
$648$	28.3318	+	14.2856i	1.11298	+	0.561192i
$649$	−8.44871	+	8.44871i	−0.331641	+	0.331641i
$650$	−22.5575	+	32.6121i	−0.884776	+	1.27915i
$651$	3.00331			0.117709
$652$	34.2032	−	17.5487i	1.33950	−	0.687260i
$653$		−	35.9169i		−	1.40554i	−0.711418	−	0.702769i	$-0.751947\pi$
$653$		−	35.9169i		−	1.40554i	0.711418	−	0.702769i	$-0.248053\pi$
$654$	−16.2071	−	22.2413i	−0.633747	−	0.869704i
$655$	−3.81883	+	16.7062i	−0.149214	+	0.652766i
$656$	−25.5728	+	1.42585i	−0.998449	+	0.0556700i
$657$	−6.47937	+	6.47937i	−0.252784	+	0.252784i
$658$	−0.666708	+	4.24807i	−0.0259910	+	0.165607i
$659$	17.7691	+	17.7691i	0.692185	+	0.692185i	0.962712	−	0.270527i	$-0.0871981\pi$
$659$	17.7691	+	17.7691i	0.692185	+	0.692185i	−0.270527	+	0.962712i	$0.587198\pi$
$660$	−1.99985	−	7.85419i	−0.0778441	−	0.305724i
$661$		−	30.6829i		−	1.19343i	−0.802454	−	0.596714i	$-0.796473\pi$
$661$		−	30.6829i		−	1.19343i	0.802454	−	0.596714i	$-0.203527\pi$
$662$	−22.8912	+	16.6807i	−0.889692	+	0.648312i
$663$	65.1852			2.53158
$664$	4.75230	−	1.56630i	0.184425	−	0.0607844i
$665$	−2.34931	+	1.47510i	−0.0911022	+	0.0572018i
$666$	−7.29960	+	5.31917i	−0.282854	+	0.206113i
$667$			1.13357i			0.0438921i
$668$	−7.07779	+	21.9934i	−0.273848	+	0.850950i
$669$	13.1082	−	13.1082i	0.506793	−	0.506793i
$670$	−4.04934	+	10.1265i	−0.156440	+	0.391220i
$671$	1.76843	+	1.76843i	0.0682693	+	0.0682693i
$672$	−2.53491	+	2.57079i	−0.0977862	+	0.0991706i
$673$	−26.1544			−1.00818			−0.504089	−	0.863652i	$-0.668172\pi$
$673$	−26.1544			−1.00818			−0.504089	+	0.863652i	$0.668172\pi$
$674$	11.5617	+	15.8664i	0.445342	+	0.611152i
$675$	−12.8722	−	6.20931i	−0.495453	−	0.238997i
$676$	−35.1217	−	11.3027i	−1.35083	−	0.434718i
$677$	−13.8939	−	13.8939i	−0.533984	−	0.533984i	0.387771	−	0.921756i	$-0.373245\pi$
$677$	−13.8939	−	13.8939i	−0.533984	−	0.533984i	−0.921756	+	0.387771i	$0.873245\pi$
$678$	−15.2700	−	20.9554i	−0.586442	−	0.804787i
$679$	3.88001			0.148901
$680$	26.1755	+	21.6806i	1.00378	+	0.831412i
$681$	49.6456			1.90242
$682$	−3.28375	−	4.50636i	−0.125741	−	0.172557i
$683$		−	9.79987i		−	0.374982i	−0.982266	−	0.187491i	$-0.939965\pi$
$683$		−	9.79987i		−	0.374982i	0.982266	−	0.187491i	$-0.0600355\pi$
$684$	12.5579	−	6.44313i	0.480165	−	0.246359i
$685$	23.5769	+	5.38938i	0.900827	+	0.205917i
$686$	0.900151	−	5.73550i	0.0343679	−	0.218982i
$687$	17.8625	+	17.8625i	0.681496	+	0.681496i
$688$	−1.84214	−	11.2220i	−0.0702309	−	0.427836i
$689$	18.4642			0.703429
$690$	−0.810183	−	1.88987i	−0.0308431	−	0.0719462i
$691$	−7.23522	−	7.23522i	−0.275241	−	0.275241i	0.555965	−	0.831206i	$-0.312349\pi$
$691$	−7.23522	−	7.23522i	−0.275241	−	0.275241i	−0.831206	+	0.555965i	$0.812349\pi$
$692$	28.8663	−	14.8105i	1.09733	−	0.563011i
$693$	0.293433	+	0.293433i	0.0111466	+	0.0111466i
$694$	41.4740	+	6.50909i	1.57433	+	0.247082i
$695$	2.88779	−	12.6332i	0.109540	−	0.479204i
$696$	21.9100	−	7.22128i	0.830496	−	0.273722i
$697$	−21.5941	−	26.7914i	−0.817934	−	1.01480i
$698$	15.3927	+	2.41578i	0.582621	+	0.0914388i
$699$		−	2.69641i		−	0.101987i
$700$	2.03449	−	2.13713i	0.0768967	−	0.0807759i
$701$	−0.962763			−0.0363630			−0.0181815	−	0.999835i	$-0.505788\pi$
$701$	−0.962763			−0.0363630			−0.0181815	+	0.999835i	$0.505788\pi$
$702$	3.51465	−	22.3943i	0.132652	−	0.845219i
$703$		−	15.9972i		−	0.603345i
$704$	6.62898	+	0.992689i	0.249839	+	0.0374134i
$705$	−11.1063	+	48.5869i	−0.418289	+	1.82989i
$706$	−14.1328	−	19.3947i	−0.531894	−	0.729930i
$707$	1.89930	+	1.89930i	0.0714304	+	0.0714304i
$708$	58.7244	+	18.8984i	2.20700	+	0.710244i
$709$	−6.53364	+	6.53364i	−0.245376	+	0.245376i	−0.819070	−	0.573694i	$-0.805510\pi$
$709$	−6.53364	+	6.53364i	−0.245376	+	0.245376i	0.573694	+	0.819070i	$0.305510\pi$
$710$	9.93617	+	23.1776i	0.372898	+	0.869839i
$711$	−2.27312	−	2.27312i	−0.0852487	−	0.0852487i
$712$	39.5072	−	13.0211i	1.48060	−	0.487987i
$713$	−1.00028	−	1.00028i	−0.0374609	−	0.0374609i
$714$	−4.79189	−	0.752057i	−0.179332	−	0.0281450i
$715$	−8.89782	+	5.58682i	−0.332760	+	0.208935i
$716$	−9.07995	+	4.65867i	−0.339334	+	0.174103i
$717$	35.4316	+	35.4316i	1.32322	+	1.32322i
$718$	−41.7385	−	6.55060i	−1.55767	−	0.244466i
$719$	26.9605	−	26.9605i	1.00546	−	1.00546i	0.00547208	−	0.999985i	$-0.498258\pi$
$719$	26.9605	−	26.9605i	1.00546	−	1.00546i	0.999985	−	0.00547208i	$-0.00174183\pi$
$720$	−11.2536	+	9.93754i	−0.419396	+	0.370350i
$721$	−1.86613	+	1.86613i	−0.0694985	+	0.0694985i
$722$	0.290126	−	1.84860i	0.0107974	−	0.0687977i
$723$			0.399070i			0.0148416i
$724$	−19.4258	+	9.96685i	−0.721956	+	0.370415i
$725$	−17.8001	+	6.21548i	−0.661080	+	0.230837i
$726$	−4.88408	+	31.1199i	−0.181265	+	1.15497i
$727$			30.5494i			1.13302i	0.824056	+	0.566508i	$0.191706\pi$
$727$			30.5494i			1.13302i	−0.824056	+	0.566508i	$0.808294\pi$
$728$	4.17898	+	2.10715i	0.154883	+	0.0780961i
$729$	−0.282400			−0.0104592
$730$	6.80194	+	15.8665i	0.251751	+	0.587247i
$731$	10.8036	−	10.8036i	0.399587	−	0.399587i
$732$	3.95568	−	12.2918i	0.146206	−	0.454318i
$733$	−4.41040	+	4.41040i	−0.162902	+	0.162902i	−0.783851	−	0.620949i	$-0.786747\pi$
$733$	−4.41040	+	4.41040i	−0.162902	+	0.162902i	0.620949	+	0.783851i	$0.286747\pi$
$734$	5.30513	−	3.86581i	0.195816	−	0.142690i
$735$	7.45066	−	32.5944i	0.274822	−	1.20226i
$736$	1.70050	−	0.0119524i	0.0626814	−	0.000440571i
$737$	−2.04327	+	2.04327i	−0.0752649	+	0.0752649i
$738$	13.1700	−	7.58831i	0.484796	−	0.279330i
$739$	5.37329			0.197660			0.0988299	−	0.995104i	$-0.468490\pi$
$739$	5.37329			0.197660			0.0988299	+	0.995104i	$0.468490\pi$
$740$	4.19867	+	16.4898i	0.154346	+	0.606177i
$741$	−36.0610	−	36.0610i	−1.32473	−	1.32473i
$742$	−1.35734	−	0.213026i	−0.0498294	−	0.00782041i
$743$	24.3657	+	24.3657i	0.893892	+	0.893892i	0.994887	−	0.100995i	$-0.0322025\pi$
$743$	24.3657	+	24.3657i	0.893892	+	0.893892i	−0.100995	+	0.994887i	$0.532202\pi$
$744$	−12.9616	+	25.7059i	−0.475194	+	0.942426i
$745$	1.31971	−	0.828629i	0.0483505	−	0.0303586i
$746$	−0.601753	−	0.825798i	−0.0220317	−	0.0302346i
$747$	−2.09975	+	2.09975i	−0.0768257	+	0.0768257i
$748$	4.11089	+	8.01231i	0.150309	+	0.292959i
$749$	1.93549	−	1.93549i	0.0707211	−	0.0707211i
$750$	25.2338	−	23.0844i	0.921407	−	0.842923i
$751$	28.5669	−	28.5669i	1.04242	−	1.04242i	0.0433622	−	0.999059i	$-0.486193\pi$
$751$	28.5669	−	28.5669i	1.04242	−	1.04242i	0.999059	−	0.0433622i	$-0.0138070\pi$
$752$	−33.4827	−	24.0401i	−1.22099	−	0.876653i
$753$	47.8267			1.74290
$754$	−17.6118	−	24.1690i	−0.641383	−	0.880184i
$755$	6.32874	+	10.0794i	0.230326	+	0.366828i
$756$	−0.516737	+	1.60570i	−0.0187935	+	0.0583987i
$757$		−	6.18605i		−	0.224836i	−0.993661	−	0.112418i	$-0.964140\pi$
$757$		−	6.18605i		−	0.224836i	0.993661	−	0.112418i	$-0.0358595\pi$
$758$	44.9404	+	7.05311i	1.63231	+	0.256181i
$759$		−	0.544805i		−	0.0197752i
$760$	−2.48660	−	26.4743i	−0.0901985	−	0.960325i
$761$	3.98484			0.144450			0.0722251	−	0.997388i	$-0.476990\pi$
$761$	3.98484			0.144450			0.0722251	+	0.997388i	$0.476990\pi$
$762$	−24.7492	−	33.9639i	−0.896571	−	1.23038i
$763$	1.87708	−	1.87708i	0.0679550	−	0.0679550i
$764$	20.4916	+	39.9390i	0.741359	+	1.44494i
$765$	−19.6632	−	4.49475i	−0.710924	−	0.162508i
$766$	2.71495	−	17.2988i	0.0980950	−	0.625033i
$767$		−	79.9702i		−	2.88756i
$768$	−11.0639	−	32.7917i	−0.399233	−	1.18327i
$769$			16.5226i			0.595822i	0.954594	+	0.297911i	$0.0962898\pi$
$769$			16.5226i			0.595822i	−0.954594	+	0.297911i	$0.903710\pi$
$770$	0.718552	−	0.308041i	0.0258948	−	0.0111010i
$771$	26.4775			0.953564
$772$	−7.28584	+	22.6399i	−0.262223	+	0.814828i
$773$	35.3417			1.27115			0.635577	−	0.772038i	$-0.280762\pi$
$773$	35.3417			1.27115			0.635577	+	0.772038i	$0.280762\pi$
$774$	3.97455	+	5.45436i	0.142862	+	0.196053i
$775$	10.2225	−	21.1918i	0.367203	−	0.761231i
$776$	−16.7452	+	33.2098i	−0.601117	+	1.19216i
$777$	−1.71713	−	1.71713i	−0.0616016	−	0.0616016i
$778$	6.70349	+	1.05207i	0.240332	+	0.0377186i
$779$	−2.87517	+	26.7672i	−0.103014	+	0.959035i
$780$	46.6361	+	27.7068i	1.66984	+	0.992061i
$781$			6.68154i			0.239084i
$782$	1.34550	+	1.84646i	0.0481152	+	0.0660294i
$783$	7.62135	−	7.62135i	0.272365	−	0.272365i
$784$	22.4618	+	16.1272i	0.802206	+	0.575973i
$785$	0.242062	−	1.05895i	0.00863958	−	0.0377955i
$786$	23.1600	+	3.63482i	0.826090	+	0.129650i
$787$	−5.01916	+	5.01916i	−0.178914	+	0.178914i	−0.790882	−	0.611968i	$-0.790378\pi$
$787$	−5.01916	+	5.01916i	−0.178914	+	0.178914i	0.611968	+	0.790882i	$0.290378\pi$
$788$	24.4325	+	47.6199i	0.870370	+	1.69639i
$789$		−	25.5728i		−	0.910416i
$790$	−5.56637	+	2.38629i	−0.198043	+	0.0849003i
$791$	1.76856	−	1.76856i	0.0628826	−	0.0628826i
$792$	−3.77793	+	1.24516i	−0.134243	+	0.0442449i
$793$	−16.7388			−0.594413
$794$	−18.0476	−	2.83246i	−0.640487	−	0.100520i
$795$	−15.5244	−	3.54868i	−0.550594	−	0.125859i
$796$	33.1643	−	17.0157i	1.17548	−	0.603105i
$797$	39.0883	−	39.0883i	1.38458	−	1.38458i	0.548296	−	0.836284i	$-0.315277\pi$
$797$	39.0883	−	39.0883i	1.38458	−	1.38458i	0.836284	−	0.548296i	$-0.184723\pi$
$798$	2.23487	+	3.06695i	0.0791134	+	0.108569i
$799$		−	55.3781i		−	1.95914i
$800$	9.51171	+	26.6370i	0.336290	+	0.941759i
$801$	−17.4558	+	17.4558i	−0.616770	+	0.616770i
$802$	7.80324	−	49.7199i	0.275542	−	1.75567i
$803$			4.57394i			0.161411i
$804$	14.2022	+	4.57046i	0.500872	+	0.161188i
$805$	0.167977	−	0.105471i	0.00592043	−	0.00371735i
$806$	36.8681	+	5.78622i	1.29862	+	0.203811i
$807$		−	18.5130i		−	0.651687i
$808$	−24.4533	+	8.05954i	−0.860266	+	0.283534i
$809$	−8.49004	+	8.49004i	−0.298494	+	0.298494i	−0.840424	−	0.541930i	$-0.817694\pi$
$809$	−8.49004	+	8.49004i	−0.298494	+	0.298494i	0.541930	+	0.840424i	$0.317694\pi$
$810$	−13.1715	+	32.9390i	−0.462800	+	1.15736i
$811$	−11.7840			−0.413791			−0.206895	−	0.978363i	$-0.566336\pi$
$811$	−11.7840			−0.413791			−0.206895	+	0.978363i	$0.566336\pi$
$812$	1.01583	+	1.97990i	0.0356487	+	0.0694809i
$813$		−	27.2381i		−	0.955281i
$814$	−0.699019	+	4.45394i	−0.0245006	+	0.156111i
$815$	22.8548	+	36.3996i	0.800568	+	1.27502i
$816$	27.1176	−	37.7690i	0.949306	−	1.32218i
$817$	−11.9533			−0.418193
$818$	6.22720	−	39.6779i	0.217729	−	1.38730i
$819$	−2.77745			−0.0970520
$820$	−4.06169	−	28.3461i	−0.141840	−	0.989890i
$821$	−32.6457			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$821$	−32.6457			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$822$	5.12969	−	32.6849i	0.178919	−	1.14002i
$823$	14.1894			0.494612			0.247306	−	0.968937i	$-0.420455\pi$
$823$	14.1894			0.494612			0.247306	+	0.968937i	$0.420455\pi$
$824$	−7.91882	−	24.0264i	−0.275865	−	0.836999i
$825$	8.55490	−	2.98721i	0.297843	−	0.104001i
$826$	−0.922634	+	5.87876i	−0.0321026	+	0.204548i
$827$			5.63679i			0.196011i	0.995186	+	0.0980053i	$0.0312462\pi$
$827$			5.63679i			0.196011i	−0.995186	+	0.0980053i	$0.968754\pi$
$828$	−0.897904	+	0.460689i	−0.0312043	+	0.0160101i
$829$	53.6658			1.86389			0.931945	−	0.362601i	$-0.118111\pi$
$829$	53.6658			1.86389			0.931945	+	0.362601i	$0.118111\pi$
$830$	2.20428	+	5.14182i	0.0765117	+	0.178475i
$831$	19.8090	−	19.8090i	0.687168	−	0.687168i
$832$	−36.0710	+	26.6748i	−1.25054	+	0.924782i
$833$			37.1502i			1.28718i
$834$	−17.5135	−	2.74864i	−0.606444	−	0.0951777i
$835$	−25.1818	−	5.75623i	−0.871451	−	0.199203i
$836$	2.15830	−	6.70665i	0.0746463	−	0.231954i
$837$			13.4504i			0.464915i
$838$	−4.30619	+	27.4378i	−0.148755	+	0.947822i
$839$	3.67736	−	3.67736i	0.126957	−	0.126957i	−0.640773	−	0.767730i	$-0.721386\pi$
$839$	3.67736	−	3.67736i	0.126957	−	0.126957i	0.767730	+	0.640773i	$0.221386\pi$
$840$	−3.10865	−	2.57483i	−0.107259	−	0.0888400i
$841$			14.7809i			0.509688i
$842$	15.5311	+	21.3136i	0.535236	+	0.734516i
$843$	−46.3498	+	46.3498i	−1.59637	+	1.59637i
$844$	19.8275	+	38.6447i	0.682492	+	1.33021i
$845$	9.19225	−	40.2133i	0.316223	−	1.38338i
$846$	24.1657	+	3.79266i	0.830835	+	0.130394i
$847$	−3.03860			−0.104408
$848$	7.68126	−	10.6983i	0.263776	−	0.367382i
$849$	23.9761	−	23.9761i	0.822858	−	0.822858i
$850$	−21.6169	+	31.2524i	−0.741455	+	1.07195i
$851$			1.14381i			0.0392094i
$852$	30.6934	−	15.7479i	1.05154	−	0.539515i
$853$	−3.99055	+	3.99055i	−0.136634	+	0.136634i	−0.772116	−	0.635482i	$-0.780801\pi$
$853$	−3.99055	+	3.99055i	−0.136634	+	0.136634i	0.635482	+	0.772116i	$0.280801\pi$
$854$	1.23050	+	0.193120i	0.0421069	+	0.00660842i
$855$	8.39129	+	13.3644i	0.286976	+	0.457051i
$856$	8.21311	+	24.9193i	0.280718	+	0.851723i
$857$	13.7999	−	13.7999i	0.471394	−	0.471394i	−0.430971	−	0.902366i	$-0.641829\pi$
$857$	13.7999	−	13.7999i	0.471394	−	0.471394i	0.902366	+	0.430971i	$0.141829\pi$
$858$	8.46438	+	11.6158i	0.288969	+	0.396558i
$859$			50.0285i			1.70695i	0.521133	+	0.853475i	$0.325509\pi$
$859$			50.0285i			1.70695i	−0.521133	+	0.853475i	$0.674491\pi$
$860$	12.3214	−	3.13730i	0.420156	−	0.106981i
$861$	2.56456	+	3.18179i	0.0873998	+	0.108435i
$862$	49.2336	+	7.72691i	1.67690	+	0.263180i
$863$	−16.8897	−	16.8897i	−0.574932	−	0.574932i	0.358571	−	0.933503i	$-0.383264\pi$
$863$	−16.8897	−	16.8897i	−0.574932	−	0.574932i	−0.933503	+	0.358571i	$0.883264\pi$
$864$	−11.5134	−	11.3527i	−0.391693	−	0.386225i
$865$	19.2886	+	30.7200i	0.655834	+	1.04451i
$866$	−0.719086	−	0.986817i	−0.0244355	−	0.0335334i
$867$	25.6964			0.872697
$868$	−2.64349	−	0.850712i	−0.0897258	−	0.0288750i
$869$	−1.60465			−0.0544340
$870$	10.1626	+	23.7058i	0.344545	+	0.803702i
$871$		−	19.3403i		−	0.655323i
$872$	7.96528	+	24.1674i	0.269738	+	0.818410i
$873$		−	22.0720i		−	0.747023i
$874$	0.277135	−	1.76582i	0.00937423	−	0.0597298i
$875$	2.57721	+	2.05939i	0.0871256	+	0.0696202i
$876$	21.0116	−	10.7805i	0.709917	−	0.364238i
$877$	−4.14206	+	4.14206i	−0.139867	+	0.139867i	−0.773574	−	0.633706i	$-0.781533\pi$
$877$	−4.14206	+	4.14206i	−0.139867	+	0.139867i	0.633706	+	0.773574i	$0.281533\pi$
$878$	26.5637	+	36.4539i	0.896482	+	1.23026i
$879$	−52.5377			−1.77205
$880$	−0.464512	+	7.47965i	−0.0156587	+	0.252139i
$881$			45.0414i			1.51748i	0.651392	+	0.758741i	$0.274185\pi$
$881$			45.0414i			1.51748i	−0.651392	+	0.758741i	$0.725815\pi$
$882$	−16.2115	−	2.54429i	−0.545870	−	0.0856709i
$883$		−	41.9659i		−	1.41226i	−0.708080	−	0.706132i	$-0.750438\pi$
$883$		−	41.9659i		−	1.41226i	0.708080	−	0.706132i	$-0.249562\pi$
$884$	−57.3753	−	18.4642i	−1.92974	−	0.621018i
$885$	−15.3697	+	67.2377i	−0.516646	+	2.26017i
$886$	−19.8967	−	27.3047i	−0.668443	−	0.917319i
$887$	8.42535			0.282896			0.141448	−	0.989946i	$-0.454824\pi$
$887$	8.42535			0.282896			0.141448	+	0.989946i	$0.454824\pi$
$888$	22.1079	−	7.28652i	0.741893	−	0.244519i
$889$	2.86643	−	2.86643i	0.0961369	−	0.0961369i
$890$	18.3248	+	42.7453i	0.614249	+	1.43283i
$891$	−6.64627	+	6.64627i	−0.222658	+	0.222658i
$892$	−15.2507	+	7.82472i	−0.510632	+	0.261991i
$893$	−30.6356	+	30.6356i	−1.02518	+	1.02518i
$894$	−1.25543	−	1.72285i	−0.0419877	−	0.0576206i
$895$	−6.06728	−	9.66303i	−0.202807	−	0.322999i
$896$	2.95940	−	1.54476i	0.0988665	−	0.0516066i
$897$	2.57839	+	2.57839i	0.0860899	+	0.0860899i
$898$	−11.9523	−	1.87584i	−0.398854	−	0.0625977i
$899$	12.5471	+	12.5471i	0.418471	+	0.418471i
$900$	−12.1573	−	11.5735i	−0.405245	−	0.385783i
$901$	17.6943			0.589483
$902$	1.97014	−	7.32691i	0.0655984	−	0.243959i
$903$	−1.28306	+	1.28306i	−0.0426976	+	0.0426976i
$904$	7.50475	+	22.7701i	0.249604	+	0.757321i
$905$	−12.9805	−	20.6733i	−0.431485	−	0.687203i
$906$	13.1584	−	9.58843i	0.437159	−	0.318554i
$907$	−12.9621	+	12.9621i	−0.430400	+	0.430400i	−0.888764	−	0.458364i	$-0.848436\pi$
$907$	−12.9621	+	12.9621i	−0.430400	+	0.430400i	0.458364	+	0.888764i	$0.348436\pi$
$908$	−43.6975	−	14.0625i	−1.45015	−	0.466680i
$909$	10.8044	−	10.8044i	0.358360	−	0.358360i
$910$	−1.94282	+	4.85854i	−0.0644038	+	0.161059i
$911$	12.1400			0.402215			0.201108	−	0.979569i	$-0.435546\pi$
$911$	12.1400			0.402215			0.201108	+	0.979569i	$0.435546\pi$
$912$	−35.8958	+	5.89242i	−1.18863	+	0.195117i
$913$			1.48226i			0.0490557i
$914$	−6.19300	+	39.4600i	−0.204846	+	1.30522i
$915$	14.0737	+	3.21708i	0.465263	+	0.106353i
$916$	−10.6627	−	20.7820i	−0.352305	−	0.686658i
$917$			2.26138i			0.0746775i
$918$	3.36810	−	21.4606i	0.111164	−	0.708305i
$919$	−7.87823	+	7.87823i	−0.259879	+	0.259879i	−0.825005	−	0.565126i	$-0.808828\pi$
$919$	−7.87823	+	7.87823i	−0.259879	+	0.259879i	0.565126	+	0.825005i	$0.308828\pi$
$920$	0.177794	+	1.89294i	0.00586170	+	0.0624083i
$921$	−21.9296	+	21.9296i	−0.722606	+	0.722606i
$922$	−37.5261	−	5.88948i	−1.23586	−	0.193960i
$923$	−31.6216	−	31.6216i	−1.04084	−	1.04084i
$924$	−0.488218	−	0.951558i	−0.0160612	−	0.0313040i
$925$	−17.9609	+	6.27163i	−0.590551	+	0.206210i
$926$	25.7295	+	4.03808i	0.845523	+	0.132700i
$927$	10.6158	+	10.6158i	0.348667	+	0.348667i
$928$	−21.3304	+	0.149926i	−0.700206	+	0.00492155i
$929$	20.5130	+	20.5130i	0.673011	+	0.673011i	0.958409	−	0.285398i	$-0.0921259\pi$
$929$	20.5130	+	20.5130i	0.673011	+	0.673011i	−0.285398	+	0.958409i	$0.592126\pi$
$930$	−29.8861	−	11.9507i	−0.980003	−	0.391880i
$931$	20.5518	−	20.5518i	0.673558	−	0.673558i
$932$	−0.763778	+	2.37335i	−0.0250184	+	0.0777417i
$933$	35.1038	+	35.1038i	1.14925	+	1.14925i
$934$	−27.3286	−	37.5036i	−0.894219	−	1.22716i
$935$	−8.52683	+	5.35387i	−0.278857	+	0.175090i
$936$	11.9868	−	23.7727i	0.391801	−	0.777036i
$937$			15.7880i			0.515772i	0.966175	+	0.257886i	$0.0830259\pi$
$937$			15.7880i			0.515772i	−0.966175	+	0.257886i	$0.916974\pi$
$938$	−0.223134	+	1.42174i	−0.00728558	+	0.0464216i
$939$	−22.8324			−0.745107
$940$	23.5383	−	39.6197i	0.767734	−	1.29225i
$941$		−	9.90115i		−	0.322768i	−0.986892	−	0.161384i	$-0.948404\pi$
$941$		−	9.90115i		−	0.322768i	0.986892	−	0.161384i	$-0.0515958\pi$
$942$	−1.46803	−	0.230399i	−0.0478311	−	0.00750680i
$943$	0.205577	−	1.91388i	0.00669452	−	0.0623245i
$944$	−46.3355	−	33.2683i	−1.50809	−	1.08279i
$945$	−1.83848	−	0.420252i	−0.0598056	−	0.0136708i
$946$	3.32805	+	0.522316i	0.108204	+	0.0169820i
$947$	32.5623	+	32.5623i	1.05813	+	1.05813i	0.998203	+	0.0599306i	$0.0190879\pi$
$947$	32.5623	+	32.5623i	1.05813	+	1.05813i	0.0599306	+	0.998203i	$0.480912\pi$
$948$	3.78205	+	7.37139i	0.122835	+	0.239412i
$949$	−21.6470	−	21.6470i	−0.702692	−	0.702692i
$950$	29.2477	−	5.33041i	0.948921	−	0.172941i
$951$	−19.2971			−0.625751
$952$	4.00474	+	2.01929i	0.129794	+	0.0654456i
$953$	−6.28887	−	6.28887i	−0.203716	−	0.203716i	0.597874	−	0.801590i	$-0.296012\pi$
$953$	−6.28887	−	6.28887i	−0.203716	−	0.203716i	−0.801590	+	0.597874i	$0.796012\pi$
$954$	−1.21183	+	7.72140i	−0.0392343	+	0.249989i
$955$	−42.5037	+	26.6875i	−1.37539	+	0.863587i
$956$	−21.1502	−	41.2228i	−0.684048	−	1.33324i
$957$			6.83380i			0.220906i
$958$	6.99273	+	9.59628i	0.225925	+	0.310042i
$959$	3.19141			0.103056
$960$	35.4546	−	15.4952i	1.14429	−	0.500105i
$961$	8.85635			0.285689
$962$	−17.7709	−	24.3874i	−0.572956	−	0.786280i
$963$	−11.0103	−	11.0103i	−0.354801	−	0.354801i
$964$	0.113040	−	0.351257i	0.00364076	−	0.0113132i
$965$	−25.9220	−	5.92544i	−0.834458	−	0.190747i
$966$	−0.159795	−	0.219290i	−0.00514131	−	0.00705553i
$967$	−37.3230			−1.20023			−0.600114	−	0.799914i	$-0.704878\pi$
$967$	−37.3230			−1.20023			−0.600114	+	0.799914i	$0.704878\pi$
$968$	13.1139	−	26.0080i	0.421496	−	0.835928i
$969$	−34.5574	−	34.5574i	−1.11014	−	1.11014i
$970$	−38.6101	−	15.4393i	−1.23970	−	0.495725i
$971$	27.7930	−	27.7930i	0.891920	−	0.891920i	−0.102783	−	0.994704i	$-0.532775\pi$
$971$	27.7930	−	27.7930i	0.891920	−	0.891920i	0.994704	+	0.102783i	$0.0327748\pi$
$972$	29.8708	+	9.61285i	0.958107	+	0.308332i
$973$		−	1.71005i		−	0.0548218i
$974$	25.8536	−	18.8393i	0.828401	−	0.603650i
$975$	−26.3501	+	54.6252i	−0.843878	+	1.74941i
$976$	−6.96349	+	9.69864i	−0.222896	+	0.310446i
$977$	−20.6029			−0.659144			−0.329572	−	0.944130i	$-0.606904\pi$
$977$	−20.6029			−0.659144			−0.329572	+	0.944130i	$0.606904\pi$
$978$	47.5186	−	34.6264i	1.51948	−	1.10723i
$979$			12.3224i			0.393827i
$980$	−15.7906	+	26.5788i	−0.504412	+	0.849027i
$981$	−10.6780	−	10.6780i	−0.340924	−	0.340924i
$982$	3.08235	−	19.6398i	0.0983617	−	0.626732i
$983$	20.3951	−	20.3951i	0.650502	−	0.650502i	−0.302612	−	0.953114i	$-0.597859\pi$
$983$	20.3951	−	20.3951i	0.650502	−	0.650502i	0.953114	+	0.302612i	$0.0978586\pi$
$984$	−38.3016	+	8.21868i	−1.22101	+	0.262002i
$985$	−50.6779	+	31.8199i	−1.61473	+	1.01387i
$986$	−16.8775	−	23.1613i	−0.537488	−	0.737606i
$987$			6.57681i			0.209342i
$988$	21.5259	+	41.9550i	0.684832	+	1.33477i
$989$	0.854672			0.0271770
$990$	−1.75233	−	4.08758i	−0.0556928	−	0.129912i
$991$	−6.36284	+	6.36284i	−0.202122	+	0.202122i	−0.800909	−	0.598786i	$-0.795650\pi$
$991$	−6.36284	+	6.36284i	−0.202122	+	0.202122i	0.598786	+	0.800909i	$0.295650\pi$
$992$	18.6901	−	18.9546i	0.593410	−	0.601811i
$993$	−30.6323	+	30.6323i	−0.972088	+	0.972088i
$994$	1.95974	+	2.68939i	0.0621591	+	0.0853023i
$995$	22.1606	+	35.2940i	0.702538	+	1.11889i
$996$	6.80916	−	3.49359i	0.215757	−	0.110699i
$997$	−18.1185			−0.573818			−0.286909	−	0.957958i	$-0.592628\pi$
$997$	−18.1185			−0.573818			−0.286909	+	0.957958i	$0.592628\pi$
$998$	−33.6859	−	46.2279i	−1.06631	−	1.46332i
$999$	7.69020	−	7.69020i	0.243307	−	0.243307i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	820.2.s.c.583.6	yes	240
4.3	odd	2	inner	820.2.s.c.583.56	yes	240
5.2	odd	4		820.2.j.c.747.65	yes	240
20.7	even	4		820.2.j.c.747.115	yes	240
41.32	even	4		820.2.j.c.483.115	yes	240
164.155	odd	4		820.2.j.c.483.65	✓	240
205.32	odd	4	inner	820.2.s.c.647.56	yes	240
820.647	even	4	inner	820.2.s.c.647.6	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
820.2.j.c.483.65	✓	240	164.155	odd	4
820.2.j.c.483.115	yes	240	41.32	even	4
820.2.j.c.747.65	yes	240	5.2	odd	4
820.2.j.c.747.115	yes	240	20.7	even	4
820.2.s.c.583.6	yes	240	1.1	even	1	trivial
820.2.s.c.583.56	yes	240	4.3	odd	2	inner
820.2.s.c.647.6	yes	240	820.647	even	4	inner
820.2.s.c.647.56	yes	240	205.32	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 820 = 2^{2} \cdot 5 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	820.s (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39711 - 0.219268i) q^{2} -2.16299 q^{3} +(1.90384 + 0.612684i) q^{4} +(-0.498284 + 2.17984i) q^{5} +(3.02194 + 0.474275i) q^{6} +0.295068i q^{7} +(-2.52554 - 1.27344i) q^{8} +1.67853 q^{9} +(1.17413 - 2.93623i) q^{10} +(0.592458 - 0.592458i) q^{11} +(-4.11800 - 1.32523i) q^{12} +5.60783i q^{13} +(0.0646989 - 0.412242i) q^{14} +(1.07778 - 4.71498i) q^{15} +(3.24924 + 2.33291i) q^{16} +5.37402i q^{17} +(-2.34510 - 0.368048i) q^{18} +(2.97295 - 2.97295i) q^{19} +(-2.28421 + 3.84479i) q^{20} -0.638229i q^{21} +(-0.957637 + 0.697823i) q^{22} +(-0.212568 + 0.212568i) q^{23} +(5.46272 + 2.75444i) q^{24} +(-4.50343 - 2.17236i) q^{25} +(1.22962 - 7.83477i) q^{26} +2.85832 q^{27} +(-0.180783 + 0.561762i) q^{28} +(2.66637 - 2.66637i) q^{29} +(-2.53963 + 6.35103i) q^{30} +4.70570i q^{31} +(-4.02802 - 3.97179i) q^{32} +(-1.28148 + 1.28148i) q^{33} +(1.17835 - 7.50810i) q^{34} +(-0.643201 - 0.147028i) q^{35} +(3.19566 + 1.02841i) q^{36} +(2.69046 - 2.69046i) q^{37} +(-4.80541 + 3.50167i) q^{38} -12.1297i q^{39} +(4.03433 - 4.87074i) q^{40} +(-4.98535 + 4.01824i) q^{41} +(-0.139943 + 0.891677i) q^{42} +(-2.01035 - 2.01035i) q^{43} +(1.49094 - 0.764957i) q^{44} +(-0.836386 + 3.65894i) q^{45} +(0.343591 - 0.250372i) q^{46} -10.3048 q^{47} +(-7.02807 - 5.04606i) q^{48} +6.91294 q^{49} +(5.81546 + 4.02249i) q^{50} -11.6240i q^{51} +(-3.43583 + 10.6764i) q^{52} -3.29257i q^{53} +(-3.99340 - 0.626739i) q^{54} +(0.996252 + 1.58668i) q^{55} +(0.375751 - 0.745205i) q^{56} +(-6.43046 + 6.43046i) q^{57} +(-4.30987 + 3.14057i) q^{58} -14.2604 q^{59} +(4.94073 - 8.31624i) q^{60} +2.98490i q^{61} +(1.03181 - 6.57439i) q^{62} +0.495280i q^{63} +(4.75670 + 6.43225i) q^{64} +(-12.2242 - 2.79430i) q^{65} +(2.07136 - 1.50938i) q^{66} -3.44881 q^{67} +(-3.29257 + 10.2313i) q^{68} +(0.459783 - 0.459783i) q^{69} +(0.866385 + 0.346447i) q^{70} +(-5.63883 + 5.63883i) q^{71} +(-4.23920 - 2.13751i) q^{72} +(-3.86014 + 3.86014i) q^{73} +(-4.34880 + 3.16894i) q^{74} +(9.74087 + 4.69880i) q^{75} +(7.48150 - 3.83855i) q^{76} +(0.174815 + 0.174815i) q^{77} +(-2.65965 + 16.9465i) q^{78} +(-1.35423 - 1.35423i) q^{79} +(-6.70442 + 5.92037i) q^{80} -11.2181 q^{81} +(7.84617 - 4.52080i) q^{82} +(-1.25094 + 1.25094i) q^{83} +(0.391032 - 1.21509i) q^{84} +(-11.7145 - 2.67779i) q^{85} +(2.36787 + 3.24948i) q^{86} +(-5.76734 + 5.76734i) q^{87} +(-2.25073 + 0.741816i) q^{88} +(-10.3994 + 10.3994i) q^{89} +(1.97081 - 4.92855i) q^{90} -1.65469 q^{91} +(-0.534934 + 0.274460i) q^{92} -10.1784i q^{93} +(14.3969 + 2.25951i) q^{94} +(4.99919 + 7.96193i) q^{95} +(8.71256 + 8.59094i) q^{96} -13.1496i q^{97} +(-9.65814 - 1.51579i) q^{98} +(0.994459 - 0.994459i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{6} - 12 q^{8} + 240 q^{9} - 20 q^{10} + 8 q^{14} + 8 q^{16} - 12 q^{18} - 16 q^{20} - 12 q^{24} - 16 q^{25} - 30 q^{30} - 24 q^{33} + 20 q^{34} - 8 q^{37} - 4 q^{40} - 16 q^{41} + 84 q^{42}+ \cdots - 12 q^{98}+O(q^{100}) \) 240 * q - 4 * q^6 - 12 * q^8 + 240 * q^9 - 20 * q^10 + 8 * q^14 + 8 * q^16 - 12 * q^18 - 16 * q^20 - 12 * q^24 - 16 * q^25 - 30 * q^30 - 24 * q^33 + 20 * q^34 - 8 * q^37 - 4 * q^40 - 16 * q^41 + 84 * q^42 - 80 * q^45 - 224 * q^49 + 12 * q^50 + 28 * q^52 - 48 * q^54 + 24 * q^56 - 8 * q^57 + 28 * q^58 - 26 * q^60 - 40 * q^65 - 8 * q^66 + 96 * q^68 - 16 * q^69 - 14 * q^70 - 96 * q^72 + 72 * q^73 - 112 * q^74 + 20 * q^76 + 56 * q^77 + 4 * q^78 - 60 * q^80 + 48 * q^81 + 20 * q^82 + 32 * q^84 - 16 * q^85 - 8 * q^86 - 16 * q^88 + 64 * q^89 - 76 * q^90 + 20 * q^92 - 48 * q^94 + 24 * q^96 - 12 * q^98

Introduction

L-functions

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