LMFDB - Embedded newform 425.2.r.a.154.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [425,2,Mod(69,425)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("425.69"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(425, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([9, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.r (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$40$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			154.20
Character	$\chi$	$=$	425.154
Dual form			425.2.r.a.69.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.248853 - 0.0808572i) q^{2} +(-0.408373 + 0.562077i) q^{3} +(-1.56264 - 1.13533i) q^{4} +(-1.61719 + 1.54424i) q^{5} +(0.147073 - 0.106855i) q^{6} -1.76904i q^{7} +(0.604668 + 0.832255i) q^{8} +(0.777889 + 2.39410i) q^{9} +(0.527307 - 0.253527i) q^{10} +(1.20206 - 3.69957i) q^{11} +(1.27628 - 0.414689i) q^{12} +(2.08164 - 0.676366i) q^{13} +(-0.143040 + 0.440231i) q^{14} +(-0.207564 - 1.53961i) q^{15} +(1.11057 + 3.41800i) q^{16} +(-0.587785 - 0.809017i) q^{17} -0.658676i q^{18} +(4.31151 - 3.13249i) q^{19} +(4.28032 - 0.577055i) q^{20} +(0.994337 + 0.722428i) q^{21} +(-0.598274 + 0.823454i) q^{22} +(7.61793 + 2.47521i) q^{23} -0.714721 q^{24} +(0.230636 - 4.99468i) q^{25} -0.572712 q^{26} +(-3.64562 - 1.18453i) q^{27} +(-2.00844 + 2.76438i) q^{28} +(-1.72717 - 1.25486i) q^{29} +(-0.0728359 + 0.399920i) q^{30} +(8.32975 - 6.05192i) q^{31} -2.99782i q^{32} +(1.58855 + 2.18646i) q^{33} +(0.0808572 + 0.248853i) q^{34} +(2.73183 + 2.86089i) q^{35} +(1.50252 - 4.62428i) q^{36} +(-3.86926 + 1.25720i) q^{37} +(-1.32622 + 0.430914i) q^{38} +(-0.469916 + 1.44625i) q^{39} +(-2.26307 - 0.412163i) q^{40} +(2.36700 + 7.28488i) q^{41} +(-0.189030 - 0.260178i) q^{42} -4.18236i q^{43} +(-6.07862 + 4.41638i) q^{44} +(-4.95506 - 2.67047i) q^{45} +(-1.69560 - 1.23193i) q^{46} +(-5.92954 + 8.16131i) q^{47} +(-2.37470 - 0.771588i) q^{48} +3.87049 q^{49} +(-0.461250 + 1.22429i) q^{50} +0.694765 q^{51} +(-4.02076 - 1.30642i) q^{52} +(1.99138 - 2.74089i) q^{53} +(0.811444 + 0.589549i) q^{54} +(3.76906 + 7.83920i) q^{55} +(1.47229 - 1.06968i) q^{56} +3.70262i q^{57} +(0.328346 + 0.451930i) q^{58} +(-2.93943 - 9.04665i) q^{59} +(-1.42362 + 2.64152i) q^{60} +(1.67435 - 5.15313i) q^{61} +(-2.56222 + 0.832517i) q^{62} +(4.23526 - 1.37612i) q^{63} +(1.97875 - 6.08997i) q^{64} +(-2.32195 + 4.30837i) q^{65} +(-0.218525 - 0.672552i) q^{66} +(5.25041 + 7.22656i) q^{67} +1.93153i q^{68} +(-4.50221 + 3.27105i) q^{69} +(-0.448500 - 0.932828i) q^{70} +(0.990731 + 0.719808i) q^{71} +(-1.52213 + 2.09504i) q^{72} +(-8.89853 - 2.89131i) q^{73} +1.06453 q^{74} +(2.71321 + 2.16932i) q^{75} -10.2938 q^{76} +(-6.54470 - 2.12650i) q^{77} +(0.233880 - 0.321908i) q^{78} +(-7.05538 - 5.12603i) q^{79} +(-7.07423 - 3.81257i) q^{80} +(-3.95505 + 2.87351i) q^{81} -2.00425i q^{82} +(9.22003 + 12.6903i) q^{83} +(-0.733603 - 2.25780i) q^{84} +(2.19988 + 0.400655i) q^{85} +(-0.338174 + 1.04079i) q^{86} +(1.41066 - 0.458350i) q^{87} +(3.80583 - 1.23659i) q^{88} +(2.92596 - 9.00518i) q^{89} +(1.01715 + 1.06521i) q^{90} +(-1.19652 - 3.68251i) q^{91} +(-9.09393 - 12.5167i) q^{92} +7.15340i q^{93} +(2.13548 - 1.55152i) q^{94} +(-2.13522 + 11.7239i) q^{95} +(1.68501 + 1.22423i) q^{96} +(-0.0568680 + 0.0782721i) q^{97} +(-0.963183 - 0.312957i) q^{98} +9.79220 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) $ 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$e\left(\frac{1}{10}\right)$	$1$

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 $

$2$	−0.248853	−	0.0808572i	−0.175966	−	0.0571747i	0.219709	−	0.975565i	$-0.429489\pi$
$2$	−0.248853	−	0.0808572i	−0.175966	−	0.0571747i	−0.395675	+	0.918391i	$0.629489\pi$
$3$	−0.408373	+	0.562077i	−0.235774	+	0.324515i	−0.910466	−	0.413585i	$-0.864277\pi$
$3$	−0.408373	+	0.562077i	−0.235774	+	0.324515i	0.674692	+	0.738100i	$0.264277\pi$
$4$	−1.56264	−	1.13533i	−0.781322	−	0.567664i
$5$	−1.61719	+	1.54424i	−0.723231	+	0.690606i
$5$	−1.61719	+	1.54424i	−0.723231	+	0.690606i
$6$	0.147073	−	0.106855i	0.0600422	−	0.0436232i
$7$		−	1.76904i		−	0.668635i	−0.942460	−	0.334318i	$-0.891494\pi$
$7$		−	1.76904i		−	0.668635i	0.942460	−	0.334318i	$-0.108506\pi$
$8$	0.604668	+	0.832255i	0.213783	+	0.294246i
$9$	0.777889	+	2.39410i	0.259296	+	0.798032i
$10$	0.527307	−	0.253527i	0.166749	−	0.0801723i
$11$	1.20206	−	3.69957i	0.362436	−	1.11546i	−0.589135	−	0.808034i	$-0.700532\pi$
$11$	1.20206	−	3.69957i	0.362436	−	1.11546i	0.951571	−	0.307428i	$-0.0994684\pi$
$12$	1.27628	−	0.414689i	0.368431	−	0.119710i
$13$	2.08164	−	0.676366i	0.577343	−	0.187590i	−0.00576673	−	0.999983i	$-0.501836\pi$
$13$	2.08164	−	0.676366i	0.577343	−	0.187590i	0.583110	+	0.812393i	$0.301836\pi$
$14$	−0.143040	+	0.440231i	−0.0382290	+	0.117657i
$15$	−0.207564	−	1.53961i	−0.0535929	−	0.397526i
$16$	1.11057	+	3.41800i	0.277644	+	0.854499i
$17$	−0.587785	−	0.809017i	−0.142559	−	0.196215i
$17$	−0.587785	−	0.809017i	−0.142559	−	0.196215i
$18$		−	0.658676i		−	0.155251i
$19$	4.31151	−	3.13249i	0.989128	−	0.718643i	0.0293977	−	0.999568i	$-0.490641\pi$
$19$	4.31151	−	3.13249i	0.989128	−	0.718643i	0.959730	+	0.280925i	$0.0906411\pi$
$20$	4.28032	−	0.577055i	0.957108	−	0.129033i
$21$	0.994337	+	0.722428i	0.216982	+	0.157647i
$22$	−0.598274	+	0.823454i	−0.127552	+	0.175561i
$23$	7.61793	+	2.47521i	1.58845	+	0.516118i	0.964215	−	0.265121i	$-0.0854118\pi$
$23$	7.61793	+	2.47521i	1.58845	+	0.516118i	0.624233	+	0.781239i	$0.285412\pi$
$24$	−0.714721			−0.145892
$25$	0.230636	−	4.99468i	0.0461272	−	0.998936i
$26$	−0.572712			−0.112318
$27$	−3.64562	−	1.18453i	−0.701599	−	0.227963i
$28$	−2.00844	+	2.76438i	−0.379560	+	0.522419i
$29$	−1.72717	−	1.25486i	−0.320727	−	0.233022i	0.415758	−	0.909475i	$-0.363516\pi$
$29$	−1.72717	−	1.25486i	−0.320727	−	0.233022i	−0.736486	+	0.676453i	$0.763516\pi$
$30$	−0.0728359	+	0.399920i	−0.0132980	+	0.0730151i
$31$	8.32975	−	6.05192i	1.49607	−	1.08696i	0.524152	−	0.851624i	$-0.324382\pi$
$31$	8.32975	−	6.05192i	1.49607	−	1.08696i	0.971915	−	0.235332i	$-0.0756178\pi$
$32$		−	2.99782i		−	0.529945i
$33$	1.58855	+	2.18646i	0.276532	+	0.380613i
$34$	0.0808572	+	0.248853i	0.0138669	+	0.0426779i
$35$	2.73183	+	2.86089i	0.461763	+	0.483578i
$36$	1.50252	−	4.62428i	0.250420	−	0.770713i
$37$	−3.86926	+	1.25720i	−0.636103	+	0.206682i	−0.609277	−	0.792958i	$-0.708540\pi$
$37$	−3.86926	+	1.25720i	−0.636103	+	0.206682i	−0.0268261	+	0.999640i	$0.508540\pi$
$38$	−1.32622	+	0.430914i	−0.215141	+	0.0699034i
$39$	−0.469916	+	1.44625i	−0.0752467	+	0.231586i
$40$	−2.26307	−	0.412163i	−0.357823	−	0.0651688i
$41$	2.36700	+	7.28488i	0.369663	+	1.13771i	0.947009	+	0.321207i	$0.104088\pi$
$41$	2.36700	+	7.28488i	0.369663	+	1.13771i	−0.577346	+	0.816500i	$0.695912\pi$
$42$	−0.189030	−	0.260178i	−0.0291680	−	0.0401463i
$43$		−	4.18236i		−	0.637805i	−0.947788	−	0.318902i	$-0.896686\pi$
$43$		−	4.18236i		−	0.637805i	0.947788	−	0.318902i	$-0.103314\pi$
$44$	−6.07862	+	4.41638i	−0.916387	+	0.665794i
$45$	−4.95506	−	2.67047i	−0.738657	−	0.398090i
$46$	−1.69560	−	1.23193i	−0.250003	−	0.181638i
$47$	−5.92954	+	8.16131i	−0.864912	+	1.19045i	0.115464	+	0.993312i	$0.463165\pi$
$47$	−5.92954	+	8.16131i	−0.864912	+	1.19045i	−0.980376	+	0.197137i	$0.936835\pi$
$48$	−2.37470	−	0.771588i	−0.342759	−	0.111369i
$49$	3.87049			0.552927
$50$	−0.461250	+	1.22429i	−0.0652306	+	0.173141i
$51$	0.694765			0.0972866
$52$	−4.02076	−	1.30642i	−0.557579	−	0.181168i
$53$	1.99138	−	2.74089i	0.273536	−	0.376491i	−0.650043	−	0.759897i	$-0.725249\pi$
$53$	1.99138	−	2.74089i	0.273536	−	0.376491i	0.923580	+	0.383407i	$0.125249\pi$
$54$	0.811444	+	0.589549i	0.110424	+	0.0802274i
$55$	3.76906	+	7.83920i	0.508220	+	1.05704i
$56$	1.47229	−	1.06968i	0.196743	−	0.142942i
$57$			3.70262i			0.490424i
$58$	0.328346	+	0.451930i	0.0431140	+	0.0593413i
$59$	−2.93943	−	9.04665i	−0.382682	−	1.17777i	−0.938148	−	0.346234i	$-0.887460\pi$
$59$	−2.93943	−	9.04665i	−0.382682	−	1.17777i	0.555466	−	0.831539i	$-0.312540\pi$
$60$	−1.42362	+	2.64152i	−0.183788	+	0.341019i
$61$	1.67435	−	5.15313i	0.214379	−	0.659791i	−0.784818	−	0.619726i	$-0.787244\pi$
$61$	1.67435	−	5.15313i	0.214379	−	0.659791i	0.999197	−	0.0400646i	$-0.0127564\pi$
$62$	−2.56222	+	0.832517i	−0.325403	+	0.105730i
$63$	4.23526	−	1.37612i	0.533592	−	0.173375i
$64$	1.97875	−	6.08997i	0.247344	−	0.761247i
$65$	−2.32195	+	4.30837i	−0.288002	+	0.534388i
$66$	−0.218525	−	0.672552i	−0.0268986	−	0.0827854i
$67$	5.25041	+	7.22656i	0.641439	+	0.882865i	0.998691	−	0.0511428i	$-0.0162864\pi$
$67$	5.25041	+	7.22656i	0.641439	+	0.882865i	−0.357252	+	0.934008i	$0.616286\pi$
$68$			1.93153i			0.234233i
$69$	−4.50221	+	3.27105i	−0.542003	+	0.393788i
$70$	−0.448500	−	0.932828i	−0.0536060	−	0.111494i
$71$	0.990731	+	0.719808i	0.117578	+	0.0854255i	0.645020	−	0.764165i	$-0.276849\pi$
$71$	0.990731	+	0.719808i	0.117578	+	0.0854255i	−0.527442	+	0.849591i	$0.676849\pi$
$72$	−1.52213	+	2.09504i	−0.179385	+	0.246902i
$73$	−8.89853	−	2.89131i	−1.04149	−	0.338402i	−0.262169	−	0.965022i	$-0.584438\pi$
$73$	−8.89853	−	2.89131i	−1.04149	−	0.338402i	−0.779325	+	0.626620i	$0.784438\pi$
$74$	1.06453			0.123749
$75$	2.71321	+	2.16932i	0.313294	+	0.250492i
$76$	−10.2938			−1.18077
$77$	−6.54470	−	2.12650i	−0.745837	−	0.242337i
$78$	0.233880	−	0.321908i	0.0264817	−	0.0364489i
$79$	−7.05538	−	5.12603i	−0.793792	−	0.576724i	0.115294	−	0.993331i	$-0.463219\pi$
$79$	−7.05538	−	5.12603i	−0.793792	−	0.576724i	−0.909086	+	0.416608i	$0.863219\pi$
$80$	−7.07423	−	3.81257i	−0.790922	−	0.426258i
$81$	−3.95505	+	2.87351i	−0.439450	+	0.319279i
$82$		−	2.00425i		−	0.221333i
$83$	9.22003	+	12.6903i	1.01203	+	1.39294i	0.917644	+	0.397404i	$0.130089\pi$
$83$	9.22003	+	12.6903i	1.01203	+	1.39294i	0.0943865	+	0.995536i	$0.469911\pi$
$84$	−0.733603	−	2.25780i	−0.0800426	−	0.246346i
$85$	2.19988	+	0.400655i	0.238611	+	0.0434572i
$86$	−0.338174	+	1.04079i	−0.0364663	+	0.112232i
$87$	1.41066	−	0.458350i	0.151238	−	0.0491403i
$88$	3.80583	−	1.23659i	0.405703	−	0.131821i
$89$	2.92596	−	9.00518i	0.310151	−	0.954547i	−0.667554	−	0.744562i	$-0.732658\pi$
$89$	2.92596	−	9.00518i	0.310151	−	0.954547i	0.977705	−	0.209985i	$-0.0673415\pi$
$90$	1.01715	+	1.06521i	0.107217	+	0.112283i
$91$	−1.19652	−	3.68251i	−0.125429	−	0.386032i
$92$	−9.09393	−	12.5167i	−0.948108	−	1.30496i
$93$			7.15340i			0.741773i
$94$	2.13548	−	1.55152i	0.220258	−	0.160027i
$95$	−2.13522	+	11.7239i	−0.219069	+	1.20284i
$96$	1.68501	+	1.22423i	0.171975	+	0.124947i
$97$	−0.0568680	+	0.0782721i	−0.00577407	+	0.00794733i	−0.811894	−	0.583804i	$-0.801563\pi$
$97$	−0.0568680	+	0.0782721i	−0.00577407	+	0.00794733i	0.806120	+	0.591752i	$0.201563\pi$
$98$	−0.963183	−	0.312957i	−0.0972962	−	0.0316134i
$99$	9.79220			0.984153
$100$	−6.03100	+	7.54306i	−0.603100	+	0.754306i
$101$	17.4908			1.74040			0.870200	−	0.492699i	$-0.163990\pi$
$101$	17.4908			1.74040			0.870200	+	0.492699i	$0.163990\pi$
$102$	−0.172894	−	0.0561768i	−0.0171191	−	0.00556233i
$103$	−8.09807	+	11.1460i	−0.797927	+	1.09825i	0.195149	+	0.980774i	$0.437481\pi$
$103$	−8.09807	+	11.1460i	−0.797927	+	1.09825i	−0.993075	+	0.117478i	$0.962519\pi$
$104$	1.82161	+	1.32348i	0.178624	+	0.129778i
$105$	−2.72364	+	0.367190i	−0.265800	+	0.0358341i
$106$	−0.717181	+	0.521062i	−0.0696587	+	0.0506100i
$107$		−	7.79549i		−	0.753618i	−0.926291	−	0.376809i	$-0.877021\pi$
$107$		−	7.79549i		−	0.753618i	0.926291	−	0.376809i	$-0.122979\pi$
$108$	4.35197	+	5.98997i	0.418768	+	0.576385i
$109$	−2.65064	−	8.15785i	−0.253886	−	0.781380i	−0.994047	−	0.108951i	$-0.965251\pi$
$109$	−2.65064	−	8.15785i	−0.253886	−	0.781380i	0.740161	−	0.672429i	$-0.234749\pi$
$110$	−0.304086	−	2.25556i	−0.0289934	−	0.215060i
$111$	0.873458	−	2.68823i	0.0829050	−	0.255155i
$112$	6.04658	−	1.96465i	0.571348	−	0.185642i
$113$	−3.07440	+	0.998933i	−0.289215	+	0.0939717i	−0.450032	−	0.893013i	$-0.648587\pi$
$113$	−3.07440	+	0.998933i	−0.289215	+	0.0939717i	0.160816	+	0.986984i	$0.448587\pi$
$114$	0.299384	−	0.921408i	0.0280399	−	0.0862978i
$115$	−16.1420	+	7.76102i	−1.50525	+	0.723719i
$116$	1.27427	+	3.92180i	0.118313	+	0.364130i
$117$	3.23857	+	4.45751i	0.299406	+	0.412097i
$118$			2.48896i			0.229127i
$119$	−1.43119	+	1.03982i	−0.131197	+	0.0953199i
$120$	1.15584	−	1.10370i	0.105514	−	0.100754i
$121$	−3.34268	−	2.42860i	−0.303880	−	0.220782i
$122$	−0.833336	+	1.14699i	−0.0754467	+	0.103843i
$123$	−5.06128	−	1.64451i	−0.456360	−	0.148280i
$124$	−19.8873			−1.78594
$125$	7.34001	+	8.43352i	0.656510	+	0.754317i
$126$	−1.16523			−0.103807
$127$	−2.69660	−	0.876179i	−0.239285	−	0.0777483i	0.186920	−	0.982375i	$-0.440150\pi$
$127$	−2.69660	−	0.876179i	−0.239285	−	0.0777483i	−0.426204	+	0.904627i	$0.640150\pi$
$128$	−4.50899	+	6.20609i	−0.398542	+	0.548546i
$129$	2.35081	+	1.70796i	0.206977	+	0.150378i
$130$	0.926186	−	0.884405i	0.0812319	−	0.0775675i
$131$	−5.66636	+	4.11685i	−0.495072	+	0.359691i	−0.807131	−	0.590372i	$-0.798981\pi$
$131$	−5.66636	+	4.11685i	−0.495072	+	0.359691i	0.312060	+	0.950063i	$0.398981\pi$
$132$		−	5.22018i		−	0.454358i
$133$	−5.54151	−	7.62724i	−0.480510	−	0.661365i
$134$	−0.722259	−	2.22288i	−0.0623937	−	0.192028i
$135$	7.72488	−	3.71409i	0.664851	−	0.319658i
$136$	0.317893	−	0.978374i	0.0272591	−	0.0838949i
$137$	4.25940	−	1.38396i	0.363905	−	0.118240i	−0.121356	−	0.992609i	$-0.538724\pi$
$137$	4.25940	−	1.38396i	0.363905	−	0.118240i	0.485262	+	0.874369i	$0.338724\pi$
$138$	1.38488	−	0.449974i	0.117889	−	0.0383043i
$139$	5.31946	−	16.3716i	0.451190	−	1.38862i	−0.424360	−	0.905494i	$-0.639501\pi$
$139$	5.31946	−	16.3716i	0.451190	−	1.38862i	0.875550	−	0.483127i	$-0.160499\pi$
$140$	−1.02083	−	7.57206i	−0.0862762	−	0.639956i
$141$	−2.16582	−	6.66571i	−0.182395	−	0.561354i
$142$	−0.188345	−	0.259234i	−0.0158055	−	0.0217545i
$143$		−	8.51421i		−	0.711994i
$144$	−7.31911	+	5.31764i	−0.609926	+	0.443137i
$145$	4.73098	−	0.637811i	0.392886	−	0.0529673i
$146$	1.98064	+	1.43902i	0.163919	+	0.119094i
$147$	−1.58060	+	2.17551i	−0.130366	+	0.179433i
$148$	7.47361	+	2.42832i	0.614327	+	0.199607i
$149$	−1.20858			−0.0990107			−0.0495053	−	0.998774i	$-0.515764\pi$
$149$	−1.20858			−0.0990107			−0.0495053	+	0.998774i	$0.515764\pi$
$150$	−0.499784	−	0.759225i	−0.0408072	−	0.0619905i
$151$	−18.4900			−1.50470			−0.752349	−	0.658765i	$-0.771079\pi$
$151$	−18.4900			−1.50470			−0.752349	+	0.658765i	$0.771079\pi$
$152$	5.21406	+	1.69415i	0.422916	+	0.137414i
$153$	1.47963	−	2.03654i	0.119621	−	0.164644i
$154$	1.45672	+	1.05837i	0.117386	+	0.0852860i
$155$	−4.12520	+	22.6503i	−0.331344	+	1.81931i
$156$	2.37628	−	1.72647i	0.190255	−	0.138228i
$157$			10.8964i			0.869629i	0.900520	+	0.434814i	$0.143186\pi$
$157$			10.8964i			0.869629i	−0.900520	+	0.434814i	$0.856814\pi$
$158$	1.34127	+	1.84611i	0.106706	+	0.146868i
$159$	0.727369	+	2.23861i	0.0576841	+	0.177533i
$160$	4.62936	+	4.84806i	0.365983	+	0.383273i
$161$	4.37876	−	13.4764i	0.345095	−	1.06209i
$162$	1.21657	−	0.395288i	0.0955828	−	0.0310567i
$163$	2.08101	−	0.676162i	0.162998	−	0.0529611i	−0.226382	−	0.974039i	$-0.572690\pi$
$163$	2.08101	−	0.676162i	0.162998	−	0.0529611i	0.389379	+	0.921078i	$0.372690\pi$
$164$	4.57194	−	14.0710i	0.357009	−	1.09876i
$165$	−5.94541	−	1.08281i	−0.462850	−	0.0842970i
$166$	−1.26833	−	3.90352i	−0.0984416	−	0.302972i
$167$	1.98166	+	2.72752i	0.153346	+	0.211062i	0.878777	−	0.477232i	$-0.158360\pi$
$167$	1.98166	+	2.72752i	0.153346	+	0.211062i	−0.725432	+	0.688294i	$0.758360\pi$
$168$			1.26437i			0.0975484i
$169$	−6.64146	+	4.82530i	−0.510882	+	0.371177i
$170$	−0.515051	−	0.277581i	−0.0395026	−	0.0212895i
$171$	10.8534	+	7.88543i	0.829977	+	0.603014i
$172$	−4.74835	+	6.53555i	−0.362059	+	0.498331i
$173$	8.47569	+	2.75392i	0.644395	+	0.209377i	0.612941	−	0.790129i	$-0.289986\pi$
$173$	8.47569	+	2.75392i	0.644395	+	0.209377i	0.0314538	+	0.999505i	$0.489986\pi$
$174$	−0.388107			−0.0294223
$175$	−8.83580	−	0.408005i	−0.667923	−	0.0308423i
$176$	13.9801			1.05379
$177$	6.28529	+	2.04222i	0.472432	+	0.153502i
$178$	−1.45627	+	2.00438i	−0.109152	+	0.150235i
$179$	14.8930	+	10.8204i	1.11315	+	0.808753i	0.983157	−	0.182762i	$-0.0585037\pi$
$179$	14.8930	+	10.8204i	1.11315	+	0.808753i	0.129996	+	0.991515i	$0.458504\pi$
$180$	4.71114	+	9.79861i	0.351147	+	0.730345i
$181$	8.77133	−	6.37274i	0.651968	−	0.473682i	−0.211973	−	0.977275i	$-0.567989\pi$
$181$	8.77133	−	6.37274i	0.651968	−	0.473682i	0.863941	+	0.503593i	$0.167989\pi$
$182$			1.01315i			0.0750997i
$183$	2.21269	+	3.04551i	0.163567	+	0.225131i
$184$	2.54631	+	7.83674i	0.187717	+	0.577732i
$185$	4.31593	−	8.00821i	0.317313	−	0.588775i
$186$	0.578404	−	1.78014i	0.0424106	−	0.130526i
$187$	−3.69957	+	1.20206i	−0.270539	+	0.0879036i
$188$	18.5315	−	6.02125i	1.35155	−	0.439145i
$189$	−2.09549	+	6.44925i	−0.152424	+	0.469114i
$190$	1.47931	−	2.74487i	0.107321	−	0.199134i
$191$	2.82238	+	8.68639i	0.204220	+	0.628525i	0.999745	+	0.0226033i	$0.00719548\pi$
$191$	2.82238	+	8.68639i	0.204220	+	0.628525i	−0.795524	+	0.605922i	$0.792805\pi$
$192$	2.61496	+	3.59919i	0.188719	+	0.259749i
$193$		−	13.9103i		−	1.00128i	−0.865654	−	0.500642i	$-0.833097\pi$
$193$		−	13.9103i		−	1.00128i	0.865654	−	0.500642i	$-0.166903\pi$
$194$	0.0204806	−	0.0148801i	0.00147042	−	0.00106833i
$195$	−1.47342	−	3.06453i	−0.105514	−	0.219456i
$196$	−6.04820	−	4.39427i	−0.432014	−	0.313877i
$197$	11.4710	−	15.7884i	0.817273	−	1.12488i	−0.172887	−	0.984942i	$-0.555310\pi$
$197$	11.4710	−	15.7884i	0.817273	−	1.12488i	0.990160	−	0.139938i	$-0.0446905\pi$
$198$	−2.43682	−	0.791770i	−0.173177	−	0.0562687i
$199$	4.57777			0.324510			0.162255	−	0.986749i	$-0.448123\pi$
$199$	4.57777			0.324510			0.162255	+	0.986749i	$0.448123\pi$
$200$	4.29630	−	2.82818i	0.303794	−	0.199982i
$201$	−6.20600			−0.437738
$202$	−4.35264	−	1.41426i	−0.306250	−	0.0995068i
$203$	−2.21990	+	3.05544i	−0.155807	+	0.214449i
$204$	−1.08567	−	0.788786i	−0.0760121	−	0.0552260i
$205$	−15.0775	−	8.12584i	−1.05306	−	0.567533i
$206$	2.91647	−	2.11894i	0.203200	−	0.147633i
$207$			20.1635i			1.40146i
$208$	4.62363	+	6.36389i	0.320591	+	0.441256i
$209$	−6.40618	−	19.7162i	−0.443124	−	1.36380i
$210$	0.707476	+	0.128850i	0.0488205	+	0.00889148i
$211$	2.91290	−	8.96498i	0.200532	−	0.617175i	−0.799335	−	0.600886i	$-0.794815\pi$
$211$	2.91290	−	8.96498i	0.200532	−	0.617175i	0.999867	−	0.0162893i	$-0.00518529\pi$
$212$	−6.22362	+	2.02218i	−0.427440	+	0.138884i
$213$	−0.809175	+	0.262917i	−0.0554438	+	0.0180148i
$214$	−0.630321	+	1.93993i	−0.0430879	+	0.132611i
$215$	6.45858	+	6.76370i	0.440472	+	0.461280i
$216$	−1.21856	−	3.75033i	−0.0829122	−	0.255178i
$217$	−10.7061	−	14.7357i	−0.726777	−	1.00032i
$218$			2.24443i			0.152012i
$219$	5.25905	−	3.82093i	0.355374	−	0.258194i
$220$	3.01036	−	16.5290i	0.202958	−	1.11439i
$221$	−1.77075	−	1.28652i	−0.119114	−	0.0865410i
$222$	−0.434725	+	0.598348i	−0.0291768	+	0.0401585i
$223$	22.1596	+	7.20010i	1.48392	+	0.482154i	0.935281	−	0.353906i	$-0.115147\pi$
$223$	22.1596	+	7.20010i	1.48392	+	0.482154i	0.548638	+	0.836060i	$0.315147\pi$
$224$	−5.30327			−0.354340
$225$	12.1371	−	3.33314i	0.809143	−	0.222209i
$226$	0.845844			0.0562647
$227$	−7.83482	−	2.54569i	−0.520015	−	0.168963i	0.0372371	−	0.999306i	$-0.488144\pi$
$227$	−7.83482	−	2.54569i	−0.520015	−	0.168963i	−0.557252	+	0.830343i	$0.688144\pi$
$228$	4.20369	−	5.78588i	0.278396	−	0.383179i
$229$	14.6013	+	10.6085i	0.964881	+	0.701027i	0.954279	−	0.298917i	$-0.0966253\pi$
$229$	14.6013	+	10.6085i	0.964881	+	0.701027i	0.0106017	+	0.999944i	$0.496625\pi$
$230$	4.64452	−	0.626155i	0.306250	−	0.0412874i
$231$	3.86793	−	2.81022i	0.254491	−	0.184899i
$232$		−	2.19622i		−	0.144189i
$233$	−12.2724	−	16.8915i	−0.803990	−	1.10660i	−0.992223	−	0.124473i	$-0.960276\pi$
$233$	−12.2724	−	16.8915i	−0.803990	−	1.10660i	0.188233	−	0.982124i	$-0.439724\pi$
$234$	−0.445506	−	1.37113i	−0.0291236	−	0.0896333i
$235$	−3.01382	−	22.3551i	−0.196600	−	1.45828i
$236$	−5.67762	+	17.4739i	−0.369581	+	1.13745i
$237$	5.76245	−	1.87233i	0.374311	−	0.121621i
$238$	0.440231	−	0.143040i	0.0285360	−	0.00927189i
$239$	3.52008	−	10.8337i	0.227695	−	0.700773i	−0.770312	−	0.637667i	$-0.779900\pi$
$239$	3.52008	−	10.8337i	0.227695	−	0.700773i	0.998007	−	0.0631055i	$-0.0201005\pi$
$240$	5.03188	−	2.41931i	0.324806	−	0.156166i
$241$	3.99934	+	12.3087i	0.257620	+	0.792873i	0.993302	+	0.115546i	$0.0368618\pi$
$241$	3.99934	+	12.3087i	0.257620	+	0.792873i	−0.735682	+	0.677327i	$0.763138\pi$
$242$	0.635466	+	0.874645i	0.0408493	+	0.0562243i
$243$		−	14.8962i		−	0.955591i
$244$	−8.46691	+	6.15157i	−0.542038	+	0.393814i
$245$	−6.25934	+	5.97697i	−0.399894	+	0.381855i
$246$	1.12654	+	0.818481i	0.0718258	+	0.0521845i
$247$	6.85630	−	9.43688i	0.436256	−	0.600455i
$248$	10.0735	+	3.27307i	0.639666	+	0.207840i
$249$	−10.8981			−0.690641
$250$	−1.14467	−	2.69220i	−0.0723953	−	0.170270i
$251$	−0.618916			−0.0390657			−0.0195328	−	0.999809i	$-0.506218\pi$
$251$	−0.618916			−0.0390657			−0.0195328	+	0.999809i	$0.506218\pi$
$252$	−8.18054	−	2.65802i	−0.515326	−	0.167440i
$253$	18.3145	−	25.2077i	1.15142	−	1.58479i
$254$	0.600212	+	0.436079i	0.0376606	+	0.0273620i
$255$	−1.12357	+	1.07288i	−0.0703607	+	0.0671867i
$256$	−8.73700	+	6.34780i	−0.546063	+	0.396738i
$257$		−	17.1392i		−	1.06912i	−0.845132	−	0.534558i	$-0.820478\pi$
$257$		−	17.1392i		−	1.06912i	0.845132	−	0.534558i	$-0.179522\pi$
$258$	−0.446905	−	0.615112i	−0.0278231	−	0.0382952i
$259$	2.22404	+	6.84489i	0.138195	+	0.425321i
$260$	8.51979	−	4.09628i	0.528375	−	0.254041i
$261$	1.66071	−	5.11115i	0.102796	−	0.316372i
$262$	1.74297	−	0.566324i	0.107681	−	0.0349876i
$263$	−29.7603	+	9.66972i	−1.83510	+	0.596261i	−0.836250	+	0.548348i	$0.815257\pi$
$263$	−29.7603	+	9.66972i	−1.83510	+	0.596261i	−0.998852	+	0.0479126i	$0.984743\pi$
$264$	−0.859140	+	2.64416i	−0.0528764	+	0.162737i
$265$	1.01216	+	7.50772i	0.0621765	+	0.461196i
$266$	0.762304	+	2.34613i	0.0467399	+	0.143851i
$267$	3.86672	+	5.32208i	0.236639	+	0.325706i
$268$		−	17.2535i		−	1.05392i
$269$	−12.9135	+	9.38223i	−0.787352	+	0.572044i	−0.907176	−	0.420751i	$-0.861767\pi$
$269$	−12.9135	+	9.38223i	−0.787352	+	0.572044i	0.119825	+	0.992795i	$0.461767\pi$
$270$	−2.22267	+	0.299651i	−0.135267	+	0.0182362i
$271$	20.4457	+	14.8547i	1.24199	+	0.902358i	0.997729	−	0.0673513i	$-0.0214548\pi$
$271$	20.4457	+	14.8547i	1.24199	+	0.902358i	0.244260	+	0.969710i	$0.421455\pi$
$272$	2.11244	−	2.90752i	0.128085	−	0.176294i
$273$	2.55848	+	0.831300i	0.154846	+	0.0503126i
$274$	−1.17187			−0.0707951
$275$	−18.2009	−	6.85717i	−1.09756	−	0.413503i
$276$	10.7491			0.647018
$277$	−23.1202	−	7.51222i	−1.38916	−	0.451365i	−0.483490	−	0.875350i	$-0.660631\pi$
$277$	−23.1202	−	7.51222i	−1.38916	−	0.451365i	−0.905670	+	0.423984i	$0.860631\pi$
$278$	−2.64752	+	3.64400i	−0.158788	+	0.218553i
$279$	20.9685	+	15.2345i	1.25535	+	0.912066i
$280$	−0.729135	+	4.00346i	−0.0435741	+	0.239253i
$281$	−12.3212	+	8.95187i	−0.735021	+	0.534024i	−0.891148	−	0.453713i	$-0.850099\pi$
$281$	−12.3212	+	8.95187i	−0.735021	+	0.534024i	0.156127	+	0.987737i	$0.450099\pi$
$282$			1.83390i			0.109207i
$283$	−9.72607	−	13.3868i	−0.578155	−	0.795762i	0.415337	−	0.909668i	$-0.363664\pi$
$283$	−9.72607	−	13.3868i	−0.578155	−	0.795762i	−0.993492	+	0.113906i	$0.963664\pi$
$284$	−0.730942	−	2.24961i	−0.0433734	−	0.133490i
$285$	−5.71774	−	5.98786i	−0.338690	−	0.354690i
$286$	−0.688436	+	2.11879i	−0.0407081	+	0.125287i
$287$	12.8873	−	4.18732i	0.760710	−	0.247170i
$288$	7.17708	−	2.33197i	0.422913	−	0.137413i
$289$	−0.309017	+	0.951057i	−0.0181775	+	0.0559445i
$290$	−1.22889	−	0.223813i	−0.0721629	−	0.0131427i
$291$	−0.0207716	−	0.0639284i	−0.00121765	−	0.00374755i
$292$	10.6227	+	14.6208i	0.621644	+	0.855620i
$293$			30.8808i			1.80408i	0.431655	+	0.902039i	$0.357930\pi$
$293$			30.8808i			1.80408i	−0.431655	+	0.902039i	$0.642070\pi$
$294$	0.569243	−	0.413580i	0.0331989	−	0.0241204i
$295$	18.7238	+	10.0910i	1.09014	+	0.587520i
$296$	−3.38593	−	2.46002i	−0.196803	−	0.142986i
$297$	−8.76453	+	12.0633i	−0.508569	+	0.699986i
$298$	0.300758	+	0.0977223i	0.0174225	+	0.00566090i
$299$	17.5319			1.01390
$300$	−1.77688	−	6.47026i	−0.102588	−	0.373561i
$301$	−7.39878			−0.426459
$302$	4.60130	+	1.49505i	0.264775	+	0.0860306i
$303$	−7.14276	+	9.83117i	−0.410341	+	0.564786i
$304$	15.4951	+	11.2578i	0.888705	+	0.645682i
$305$	5.24992	+	10.9192i	0.300610	+	0.625233i
$306$	−0.532880	+	0.387160i	−0.0304627	+	0.0221325i
$307$		−	13.9036i		−	0.793520i	−0.917922	−	0.396760i	$-0.870135\pi$
$307$		−	13.9036i		−	0.793520i	0.917922	−	0.396760i	$-0.129865\pi$
$308$	7.81276	+	10.7533i	0.445173	+	0.612728i
$309$	−2.95790	−	9.10347i	−0.168269	−	0.517879i
$310$	2.85801	−	5.30304i	0.162324	−	0.301192i
$311$	−6.70274	+	20.6289i	−0.380078	+	1.16976i	0.559911	+	0.828553i	$0.310835\pi$
$311$	−6.70274	+	20.6289i	−0.380078	+	1.16976i	−0.939988	+	0.341206i	$0.889165\pi$
$312$	−1.48779	+	0.483413i	−0.0842297	+	0.0273679i
$313$	−22.4900	+	7.30745i	−1.27121	+	0.413042i	−0.865477	−	0.500949i	$-0.832984\pi$
$313$	−22.4900	+	7.30745i	−1.27121	+	0.413042i	−0.405735	+	0.913991i	$0.632984\pi$
$314$	0.881054	−	2.71160i	0.0497207	−	0.153025i
$315$	−4.72417	+	8.76571i	−0.266177	+	0.493892i
$316$	5.20532	+	16.0203i	0.292822	+	0.901214i
$317$	11.5775	+	15.9351i	0.650258	+	0.895004i	0.999110	−	0.0421739i	$-0.0134284\pi$
$317$	11.5775	+	15.9351i	0.650258	+	0.895004i	−0.348852	+	0.937178i	$0.613428\pi$
$318$		−	0.615898i		−	0.0345378i
$319$	−6.71862	+	4.88136i	−0.376170	+	0.273304i
$320$	6.20436	+	12.9043i	0.346834	+	0.721375i
$321$	4.38166	+	3.18346i	0.244560	+	0.177684i
$322$	−2.17933	+	2.99960i	−0.121450	+	0.167161i
$323$	−5.06848	−	1.64685i	−0.282018	−	0.0916331i
$324$	9.44272			0.524595
$325$	−2.89813	−	10.5531i	−0.160759	−	0.585382i
$326$	−0.572539			−0.0317100
$327$	5.66779	+	1.84158i	0.313429	+	0.101839i
$328$	−4.63162	+	6.37488i	−0.255738	+	0.351994i
$329$	14.4377	+	10.4896i	0.795976	+	0.578310i
$330$	1.39198	+	0.750191i	0.0766260	+	0.0412967i
$331$	7.53231	−	5.47254i	0.414013	−	0.300798i	−0.361211	−	0.932484i	$-0.617637\pi$
$331$	7.53231	−	5.47254i	0.414013	−	0.300798i	0.775225	+	0.631686i	$0.217637\pi$
$332$		−	30.2982i		−	1.66283i
$333$	−6.01971	−	8.28542i	−0.329878	−	0.454038i
$334$	−0.272602	−	0.838984i	−0.0149161	−	0.0459071i
$335$	−19.6505	−	3.57886i	−1.07362	−	0.195534i
$336$	−1.36497	+	4.20095i	−0.0744653	+	0.229181i
$337$	−18.8848	+	6.13605i	−1.02872	+	0.334252i	−0.774285	−	0.632837i	$-0.781890\pi$
$337$	−18.8848	+	6.13605i	−1.02872	+	0.334252i	−0.254437	+	0.967089i	$0.581890\pi$
$338$	2.04291	−	0.663781i	0.111120	−	0.0361049i
$339$	0.694024	−	2.13598i	0.0376942	−	0.116011i
$340$	−2.98276	−	3.12367i	−0.161763	−	0.169405i
$341$	−12.3766	−	38.0913i	−0.670231	−	2.06276i
$342$	−2.06330	−	2.83989i	−0.111570	−	0.153563i
$343$		−	19.2304i		−	1.03834i
$344$	3.48079	−	2.52894i	0.187672	−	0.136351i
$345$	2.22966	−	12.2424i	0.120041	−	0.659110i
$346$	−1.88653	−	1.37064i	−0.101420	−	0.0736861i
$347$	−9.46684	+	13.0300i	−0.508207	+	0.699487i	−0.983616	−	0.180278i	$-0.942300\pi$
$347$	−9.46684	+	13.0300i	−0.508207	+	0.699487i	0.475409	+	0.879765i	$0.342300\pi$
$348$	−2.72473	−	0.885319i	−0.146061	−	0.0474581i
$349$	−15.3305			−0.820623			−0.410312	−	0.911945i	$-0.634580\pi$
$349$	−15.3305			−0.820623			−0.410312	+	0.911945i	$0.634580\pi$
$350$	2.16582	+	0.815971i	0.115768	+	0.0436155i
$351$	−8.39004			−0.447827
$352$	−11.0907	−	3.60357i	−0.591134	−	0.192071i
$353$	0.0340891	−	0.0469196i	0.00181438	−	0.00249728i	−0.808109	−	0.589033i	$-0.799509\pi$
$353$	0.0340891	−	0.0469196i	0.00181438	−	0.00249728i	0.809923	+	0.586536i	$0.199509\pi$
$354$	−1.39899	−	1.01642i	−0.0743553	−	0.0540223i
$355$	−2.71376	+	0.365858i	−0.144032	+	0.0194177i
$356$	−14.7961	+	10.7500i	−0.784189	+	0.569747i
$357$		−	1.22907i		−	0.0650492i
$358$	−2.83125	−	3.89689i	−0.149636	−	0.205957i
$359$	5.74049	+	17.6674i	0.302971	+	0.932450i	0.980426	+	0.196886i	$0.0630828\pi$
$359$	5.74049	+	17.6674i	0.302971	+	0.932450i	−0.677455	+	0.735564i	$0.736917\pi$
$360$	−0.773657	−	5.73862i	−0.0407753	−	0.302452i
$361$	2.90526	−	8.94146i	0.152908	−	0.470603i
$362$	−2.69805	+	0.876651i	−0.141807	+	0.0460757i
$363$	2.73012	−	0.887070i	0.143294	−	0.0465591i
$364$	−2.31112	+	7.11290i	−0.121136	+	0.372817i
$365$	18.8555	−	9.06568i	0.986944	−	0.474519i
$366$	−0.304384	−	0.936797i	−0.0159104	−	0.0489672i
$367$	21.1524	+	29.1138i	1.10415	+	1.51973i	0.829770	+	0.558105i	$0.188471\pi$
$367$	21.1524	+	29.1138i	1.10415	+	1.51973i	0.274377	+	0.961622i	$0.411529\pi$
$368$			28.7870i			1.50062i
$369$	−15.5994	+	11.3336i	−0.812074	+	0.590006i
$370$	−1.72155	+	1.64389i	−0.0894993	+	0.0854619i
$371$	−4.84875	−	3.52283i	−0.251735	−	0.182896i
$372$	8.12145	−	11.1782i	0.421077	−	0.579563i
$373$	−22.2606	−	7.23290i	−1.15261	−	0.374505i	−0.330484	−	0.943812i	$-0.607212\pi$
$373$	−22.2606	−	7.23290i	−1.15261	−	0.374505i	−0.822125	+	0.569306i	$0.807212\pi$
$374$	1.01784			0.0526315
$375$	−7.73774	+	0.681626i	−0.399575	+	0.0351990i
$376$	−10.3777			−0.535188
$377$	−4.44409	−	1.44397i	−0.228882	−	0.0743684i
$378$	1.04294	−	1.43548i	0.0536429	−	0.0738331i
$379$	−7.05230	−	5.12380i	−0.362252	−	0.263192i	0.391739	−	0.920077i	$-0.371874\pi$
$379$	−7.05230	−	5.12380i	−0.362252	−	0.263192i	−0.753991	+	0.656885i	$0.771874\pi$
$380$	16.6470	−	15.8960i	0.853973	−	0.815450i
$381$	1.59370	−	1.15789i	0.0816476	−	0.0593204i
$382$		−	2.38984i		−	0.122275i
$383$	6.81187	+	9.37574i	0.348070	+	0.479078i	0.946777	−	0.321891i	$-0.104318\pi$
$383$	6.81187	+	9.37574i	0.348070	+	0.479078i	−0.598706	+	0.800969i	$0.704318\pi$
$384$	−1.64695	−	5.06879i	−0.0840456	−	0.258666i
$385$	13.8679	−	6.66763i	0.706773	−	0.339814i
$386$	−1.12475	+	3.46161i	−0.0572481	+	0.176192i
$387$	10.0130	−	3.25342i	0.508989	−	0.165380i
$388$	0.177729	−	0.0577476i	0.00902282	−	0.00293169i
$389$	−3.68404	+	11.3383i	−0.186788	+	0.574875i	−0.999975	−	0.00712836i	$-0.997731\pi$
$389$	−3.68404	+	11.3383i	−0.186788	+	0.574875i	0.813186	+	0.582003i	$0.197731\pi$
$390$	0.118874	+	0.881754i	0.00601944	+	0.0446494i
$391$	−2.47521	−	7.61793i	−0.125177	−	0.385255i
$392$	2.34036	+	3.22123i	0.118206	+	0.162697i
$393$		−	4.86613i		−	0.245464i
$394$	−4.13120	+	3.00149i	−0.208127	+	0.151213i
$395$	19.3258	−	2.60542i	0.972384	−	0.131093i
$396$	−15.3017	−	11.1174i	−0.768941	−	0.558668i
$397$	−13.3611	+	18.3899i	−0.670572	+	0.922963i	−0.999773	−	0.0212965i	$-0.993221\pi$
$397$	−13.3611	+	18.3899i	−0.670572	+	0.922963i	0.329201	+	0.944260i	$0.393221\pi$
$398$	−1.13919	−	0.370146i	−0.0571025	−	0.0185537i
$399$	6.55009			0.327915
$400$	17.3279	−	4.75865i	0.866396	−	0.237932i
$401$	−22.9853			−1.14783			−0.573916	−	0.818914i	$-0.694576\pi$
$401$	−22.9853			−1.14783			−0.573916	+	0.818914i	$0.694576\pi$
$402$	1.54438	+	0.501800i	0.0770268	+	0.0250275i
$403$	13.2462	−	18.2319i	0.659842	−	0.908195i
$404$	−27.3319	−	19.8578i	−1.35981	−	0.987961i
$405$	1.95869	−	10.7546i	0.0973280	−	0.534400i
$406$	0.799483	−	0.580859i	0.0396777	−	0.0288275i
$407$			15.8258i			0.784458i
$408$	0.420102	+	0.578221i	0.0207982	+	0.0286262i
$409$	5.84501	+	17.9891i	0.289017	+	0.889503i	0.985166	+	0.171605i	$0.0548954\pi$
$409$	5.84501	+	17.9891i	0.289017	+	0.889503i	−0.696149	+	0.717898i	$0.745105\pi$
$410$	3.09505	+	3.24126i	0.152854	+	0.160075i
$411$	−0.961529	+	2.95928i	−0.0474288	+	0.145971i
$412$	25.3088	−	8.22333i	1.24688	−	0.405134i
$413$	−16.0039	+	5.19998i	−0.787500	+	0.255874i
$414$	1.63036	−	5.01774i	0.0801280	−	0.246609i
$415$	−34.5075	−	6.28470i	−1.69390	−	0.308504i
$416$	−2.02763	−	6.24039i	−0.0994125	−	0.305960i
$417$	7.02977	+	9.67565i	0.344250	+	0.473819i
$418$			5.42442i			0.265317i
$419$	−23.8802	+	17.3500i	−1.16662	+	0.847602i	−0.990601	−	0.136784i	$-0.956323\pi$
$419$	−23.8802	+	17.3500i	−1.16662	+	0.847602i	−0.176023	+	0.984386i	$0.556323\pi$
$420$	4.67296	+	2.51844i	0.228017	+	0.122887i
$421$	−19.8702	−	14.4365i	−0.968412	−	0.703593i	−0.0133230	−	0.999911i	$-0.504241\pi$
$421$	−19.8702	−	14.4365i	−0.968412	−	0.703593i	−0.955089	+	0.296319i	$0.904241\pi$
$422$	−1.44977	+	1.99543i	−0.0705736	+	0.0971362i
$423$	−24.1515	−	7.84729i	−1.17428	−	0.381548i
$424$	3.48524			0.169258
$425$	−4.17634	+	2.74921i	−0.202582	+	0.133356i
$426$	0.222624			0.0107862
$427$	−9.11611	−	2.96200i	−0.441159	−	0.143341i
$428$	−8.85043	+	12.1816i	−0.427802	+	0.588818i
$429$	4.78564	+	3.47697i	0.231053	+	0.167870i
$430$	−1.06034	−	2.20539i	−0.0511343	−	0.106353i
$431$	−8.27343	+	6.01100i	−0.398517	+	0.289540i	−0.768937	−	0.639325i	$-0.779214\pi$
$431$	−8.27343	+	6.01100i	−0.398517	+	0.289540i	0.370420	+	0.928865i	$0.379214\pi$
$432$		−	13.7762i		−	0.662808i
$433$	−16.4225	−	22.6036i	−0.789215	−	1.08626i	−0.994205	−	0.107497i	$-0.965716\pi$
$433$	−16.4225	−	22.6036i	−0.789215	−	1.08626i	0.204991	−	0.978764i	$-0.434284\pi$
$434$	1.47276	+	4.53268i	0.0706946	+	0.217576i
$435$	−1.57350	+	2.91964i	−0.0754437	+	0.139986i
$436$	−5.11981	+	15.7572i	−0.245194	+	0.754631i
$437$	40.5983	−	13.1912i	1.94208	−	0.631021i
$438$	−1.61768	+	0.525616i	−0.0772958	+	0.0251149i
$439$	−3.26488	+	10.0483i	−0.155824	+	0.479577i	−0.998243	−	0.0592451i	$-0.981131\pi$
$439$	−3.26488	+	10.0483i	−0.155824	+	0.479577i	0.842419	+	0.538823i	$0.181131\pi$
$440$	−4.24518	+	7.87694i	−0.202381	+	0.375518i
$441$	3.01081	+	9.26632i	0.143372	+	0.441254i
$442$	0.336631	+	0.463333i	0.0160119	+	0.0220385i
$443$			4.10520i			0.195044i	0.995233	+	0.0975219i	$0.0310916\pi$
$443$			4.10520i			0.195044i	−0.995233	+	0.0975219i	$0.968908\pi$
$444$	−4.41692	+	3.20908i	−0.209618	+	0.152296i
$445$	9.17432	+	19.0815i	0.434905	+	0.904550i
$446$	−4.93231	−	3.58353i	−0.233552	−	0.169685i
$447$	0.493551	−	0.679314i	0.0233441	−	0.0321305i
$448$	−10.7734	−	3.50050i	−0.508996	−	0.165383i
$449$	−24.3079			−1.14716			−0.573580	−	0.819149i	$-0.694446\pi$
$449$	−24.3079			−1.14716			−0.573580	+	0.819149i	$0.694446\pi$
$450$	−3.28987	−	0.151914i	−0.155086	−	0.00716131i
$451$	29.7962			1.40305
$452$	5.93831	+	1.92947i	0.279314	+	0.0907548i
$453$	7.55082	−	10.3928i	0.354769	−	0.488297i
$454$	1.74388	+	1.26700i	0.0818444	+	0.0594634i
$455$	7.62169	+	4.10762i	0.357310	+	0.192568i
$456$	−3.08152	+	2.23886i	−0.144306	+	0.104844i
$457$			0.0269860i			0.00126235i	1.00000		0.000631177i	$0.000200910\pi$
$457$			0.0269860i			0.00126235i	−1.00000		0.000631177i	$0.999799\pi$
$458$	−2.77580	−	3.82057i	−0.129705	−	0.178523i
$459$	1.18453	+	3.64562i	0.0552892	+	0.170163i
$460$	34.0355	+	6.19875i	1.58691	+	0.289018i
$461$	−0.782321	+	2.40774i	−0.0364363	+	0.112139i	−0.967620	−	0.252410i	$-0.918777\pi$
$461$	−0.782321	+	2.40774i	−0.0364363	+	0.112139i	0.931184	+	0.364549i	$0.118777\pi$
$462$	−1.18977	+	0.386581i	−0.0553532	+	0.0179854i
$463$	−9.85254	+	3.20128i	−0.457886	+	0.148776i	−0.528873	−	0.848701i	$-0.677385\pi$
$463$	−9.85254	+	3.20128i	−0.457886	+	0.148776i	0.0709866	+	0.997477i	$0.477385\pi$
$464$	2.37096	−	7.29707i	0.110069	−	0.338758i
$465$	−11.0466	−	11.5684i	−0.512273	−	0.536473i
$466$	1.68822	+	5.19581i	0.0782053	+	0.240691i
$467$	−14.1348	−	19.4549i	−0.654080	−	0.900263i	0.345188	−	0.938534i	$-0.387815\pi$
$467$	−14.1348	−	19.4549i	−0.654080	−	0.900263i	−0.999267	+	0.0382703i	$0.987815\pi$
$468$		−	10.6423i		−	0.491942i
$469$	12.7841	−	9.28819i	0.590315	−	0.428889i
$470$	−1.05757	+	5.80681i	−0.0487821	+	0.267848i
$471$	−6.12462	−	4.44980i	−0.282208	−	0.205036i
$472$	5.75173	−	7.91658i	0.264745	−	0.364390i
$473$	−15.4730	−	5.02747i	−0.711447	−	0.231163i
$474$	−1.58539			−0.0728195
$475$	−14.6514	−	22.2571i	−0.672253	−	1.02122i
$476$	3.41697			0.156616
$477$	8.11103	+	2.63543i	0.371379	+	0.120668i
$478$	−1.75196	+	2.41137i	−0.0801329	+	0.110293i
$479$	0.649375	+	0.471799i	0.0296707	+	0.0215570i	0.602522	−	0.798102i	$-0.294163\pi$
$479$	0.649375	+	0.471799i	0.0296707	+	0.0215570i	−0.572851	+	0.819659i	$0.694163\pi$
$480$	−4.61549	+	0.622241i	−0.210667	+	0.0284013i
$481$	−7.20409	+	5.23408i	−0.328478	+	0.238653i
$482$		−	3.38643i		−	0.154248i
$483$	5.78662	+	7.96461i	0.263301	+	0.362402i
$484$	2.46617	+	7.59008i	0.112098	+	0.345004i
$485$	−0.0289044	−	0.214399i	−0.00131248	−	0.00973536i
$486$	−1.20446	+	3.70696i	−0.0546356	+	0.168151i
$487$	11.3312	−	3.68172i	0.513464	−	0.166835i	−0.0408128	−	0.999167i	$-0.512995\pi$
$487$	11.3312	−	3.68172i	0.513464	−	0.166835i	0.554277	+	0.832332i	$0.312995\pi$
$488$	5.30115	−	1.72245i	0.239972	−	0.0779715i
$489$	−0.469774	+	1.44582i	−0.0212439	+	0.0653820i
$490$	2.04094	−	0.981274i	0.0922001	−	0.0443295i
$491$	−3.85177	−	11.8545i	−0.173828	−	0.534988i	0.825750	−	0.564037i	$-0.190752\pi$
$491$	−3.85177	−	11.8545i	−0.173828	−	0.534988i	−0.999578	+	0.0290484i	$0.990752\pi$
$492$	6.04192	+	8.31599i	0.272391	+	0.374914i
$493$			2.13490i			0.0961510i
$494$	−2.46925	+	1.79402i	−0.111097	+	0.0807166i
$495$	−15.8359	+	15.1215i	−0.711770	+	0.679662i
$496$	29.9362	+	21.7499i	1.34418	+	0.976602i
$497$	1.27337	−	1.75265i	0.0571185	−	0.0786169i
$498$	2.71203	+	0.881192i	0.121529	+	0.0394872i
$499$	21.1115			0.945080			0.472540	−	0.881309i	$-0.343337\pi$
$499$	21.1115			0.945080			0.472540	+	0.881309i	$0.343337\pi$
$500$	−1.89501	−	21.5119i	−0.0847473	−	0.962042i
$501$	−2.34233			−0.104648
$502$	0.154019	+	0.0500439i	0.00687421	+	0.00223357i
$503$	12.7079	−	17.4909i	0.566617	−	0.779881i	−0.425532	−	0.904943i	$-0.639913\pi$
$503$	12.7079	−	17.4909i	0.566617	−	0.779881i	0.992149	+	0.125062i	$0.0399130\pi$
$504$	3.70621	+	2.69272i	0.165088	+	0.119943i
$505$	−28.2860	+	27.0100i	−1.25871	+	1.20193i
$506$	−6.59583	+	4.79215i	−0.293221	+	0.213037i
$507$		−	5.70353i		−	0.253303i
$508$	3.21908	+	4.43068i	0.142823	+	0.196580i
$509$	−3.33666	−	10.2692i	−0.147895	−	0.455174i	0.849477	−	0.527626i	$-0.176918\pi$
$509$	−3.33666	−	10.2692i	−0.147895	−	0.455174i	−0.997372	+	0.0724520i	$0.976918\pi$
$510$	0.366354	−	0.176142i	0.0162224	−	0.00779969i
$511$	−5.11485	+	15.7419i	−0.226268	+	0.696380i
$512$	17.2789	−	5.61425i	0.763626	−	0.248117i
$513$	−19.4286	+	6.31275i	−0.857796	+	0.278715i
$514$	−1.38583	+	4.26514i	−0.0611263	+	0.188127i
$515$	−4.11602	−	30.5307i	−0.181374	−	1.34534i
$516$	−1.73438	−	5.33788i	−0.0763519	−	0.234987i
$517$	23.0657	+	31.7472i	1.01443	+	1.39624i
$518$		−	1.88320i		−	0.0827430i
$519$	−5.00915	+	3.63936i	−0.219877	+	0.159750i
$520$	−4.98967	+	0.672686i	−0.218811	+	0.0294992i
$521$	−14.8221	−	10.7689i	−0.649369	−	0.471794i	0.213687	−	0.976902i	$-0.431453\pi$
$521$	−14.8221	−	10.7689i	−0.649369	−	0.471794i	−0.863056	+	0.505108i	$0.831453\pi$
$522$	−0.826547	+	1.13764i	−0.0361770	+	0.0497933i
$523$	24.8110	+	8.06159i	1.08491	+	0.352509i	0.796278	−	0.604932i	$-0.206800\pi$
$523$	24.8110	+	8.06159i	1.08491	+	0.352509i	0.288632	+	0.957440i	$0.406800\pi$
$524$	13.5285			0.590994
$525$	3.83763	−	4.79978i	0.167488	−	0.209479i
$526$	8.18782			0.357006
$527$	−9.79221	−	3.18168i	−0.426555	−	0.138596i
$528$	−5.70909	+	7.85789i	−0.248456	+	0.341971i
$529$	33.2987	+	24.1930i	1.44777	+	1.05187i
$530$	0.355175	−	1.95016i	0.0154278	−	0.0847095i
$531$	19.3720	−	14.0746i	0.840673	−	0.610784i
$532$			18.2101i			0.789507i
$533$	9.85449	+	13.5635i	0.426845	+	0.587502i
$534$	−0.531916	−	1.63707i	−0.0230182	−	0.0708428i
$535$	12.0381	+	12.6068i	0.520453	+	0.545040i
$536$	−2.83959	+	8.73935i	−0.122651	+	0.377482i
$537$	−12.1638	+	3.95225i	−0.524905	+	0.170552i
$538$	3.97219	−	1.29064i	0.171253	−	0.0556436i
$539$	4.65257	−	14.3192i	0.200401	−	0.616770i
$540$	−16.2879	−	2.96646i	−0.700921	−	0.127656i
$541$	−4.71642	−	14.5157i	−0.202775	−	0.624077i	−0.999797	−	0.0201273i	$-0.993593\pi$
$541$	−4.71642	−	14.5157i	−0.202775	−	0.624077i	0.797023	−	0.603949i	$-0.206407\pi$
$542$	−3.88687	−	5.34982i	−0.166955	−	0.229794i
$543$			7.53261i			0.323255i
$544$	−2.42529	+	1.76208i	−0.103983	+	0.0755484i
$545$	16.8843	+	9.09959i	0.723244	+	0.389783i
$546$	−0.569469	−	0.413743i	−0.0243710	−	0.0177066i
$547$	13.5726	−	18.6811i	0.580323	−	0.798747i	−0.413407	−	0.910546i	$-0.635661\pi$
$547$	13.5726	−	18.6811i	0.580323	−	0.798747i	0.993731	+	0.111800i	$0.0356615\pi$
$548$	−8.22718	−	2.67317i	−0.351448	−	0.114192i
$549$	13.6396			0.582122
$550$	3.97490	+	3.17810i	0.169490	+	0.135515i
$551$	−11.3775			−0.484700
$552$	−5.44469	−	1.76909i	−0.231741	−	0.0752974i
$553$	−9.06817	+	12.4813i	−0.385618	+	0.530757i
$554$	5.14612	+	3.73888i	0.218638	+	0.158850i
$555$	2.73872	+	5.69622i	0.116252	+	0.241791i
$556$	−26.8995	+	19.5437i	−1.14079	+	0.828836i
$557$			6.96026i			0.294916i	0.989068	+	0.147458i	$0.0471091\pi$
$557$			6.96026i			0.294916i	−0.989068	+	0.147458i	$0.952891\pi$
$558$	−3.98625	−	5.48661i	−0.168751	−	0.232267i
$559$	−2.82881	−	8.70618i	−0.119646	−	0.368232i
$560$	−6.74460	+	12.5146i	−0.285011	+	0.528839i
$561$	0.835152	−	2.57033i	0.0352601	−	0.108520i
$562$	3.78999	−	1.23144i	0.159871	−	0.0519452i
$563$	11.9467	−	3.88170i	0.503491	−	0.163594i	−0.0462488	−	0.998930i	$-0.514727\pi$
$563$	11.9467	−	3.88170i	0.503491	−	0.163594i	0.549740	+	0.835336i	$0.314727\pi$
$564$	−4.18336	+	12.8750i	−0.176151	+	0.542137i
$565$	3.42931	−	6.36308i	0.144272	−	0.267697i
$566$	1.33794	+	4.11776i	0.0562379	+	0.173083i
$567$	5.08337	+	6.99665i	0.213481	+	0.293832i
$568$			1.25979i			0.0528594i
$569$	−5.58962	+	4.06110i	−0.234329	+	0.170250i	−0.698753	−	0.715363i	$-0.746261\pi$
$569$	−5.58962	+	4.06110i	−0.234329	+	0.170250i	0.464424	+	0.885613i	$0.346261\pi$
$570$	0.938715	+	1.95242i	0.0393185	+	0.0817778i
$571$	−10.4440	−	7.58804i	−0.437069	−	0.317549i	0.347400	−	0.937717i	$-0.387065\pi$
$571$	−10.4440	−	7.58804i	−0.437069	−	0.317549i	−0.784469	+	0.620168i	$0.787065\pi$
$572$	−9.66642	+	13.3047i	−0.404173	+	0.556297i
$573$	−6.03500	−	1.96089i	−0.252116	−	0.0819173i
$574$	−3.54561			−0.147991
$575$	14.1199	−	37.4782i	0.588839	−	1.56295i
$576$	16.1192			0.671635
$577$	31.6933	+	10.2978i	1.31941	+	0.428703i	0.882293	−	0.470701i	$-0.155999\pi$
$577$	31.6933	+	10.2978i	1.31941	+	0.428703i	0.437119	+	0.899404i	$0.355999\pi$
$578$	0.153800	−	0.211687i	0.00639722	−	0.00880502i
$579$	7.81865	+	5.68058i	0.324932	+	0.236077i
$580$	−8.11696	−	4.37454i	−0.337038	−	0.181643i
$581$	22.4497	−	16.3106i	0.931369	−	0.676679i
$582$			0.0175883i			0.000729058i
$583$	−7.74637	−	10.6620i	−0.320822	−	0.441573i
$584$	−2.97436	−	9.15413i	−0.123080	−	0.378800i
$585$	−12.1209	−	2.20753i	−0.501136	−	0.0912700i
$586$	2.49694	−	7.68478i	0.103148	−	0.317456i
$587$	0.0929701	−	0.0302078i	0.00383729	−	0.00124681i	−0.307098	−	0.951678i	$-0.599358\pi$
$587$	0.0929701	−	0.0302078i	0.00383729	−	0.00124681i	0.310935	+	0.950431i	$0.399358\pi$
$588$	4.93984	−	1.60505i	0.203715	−	0.0661912i
$589$	16.9562	−	52.1858i	0.698668	−	2.15028i
$590$	−3.84355	−	4.02513i	−0.158237	−	0.165712i
$591$	4.18988	+	12.8951i	0.172349	+	0.530435i
$592$	−8.59420	−	11.8289i	−0.353220	−	0.486165i
$593$		−	15.4663i		−	0.635124i	−0.948237	−	0.317562i	$-0.897136\pi$
$593$		−	15.4663i		−	0.635124i	0.948237	−	0.317562i	$-0.102864\pi$
$594$	3.15649	−	2.29332i	0.129512	−	0.0940961i
$595$	0.708776	−	3.89168i	0.0290570	−	0.159543i
$596$	1.88858	+	1.37213i	0.0773592	+	0.0562048i
$597$	−1.86944	+	2.57306i	−0.0765109	+	0.105308i
$598$	−4.36288	−	1.41758i	−0.178411	−	0.0579693i
$599$	16.3238			0.666974			0.333487	−	0.942755i	$-0.391775\pi$
$599$	16.3238			0.666974			0.333487	+	0.942755i	$0.391775\pi$
$600$	−0.164840	+	3.56980i	−0.00672958	+	0.145736i
$601$	5.47691			0.223408			0.111704	−	0.993742i	$-0.464369\pi$
$601$	5.47691			0.223408			0.111704	+	0.993742i	$0.464369\pi$
$602$	1.84121	+	0.598245i	0.0750420	+	0.0243826i
$603$	−13.2169	+	18.1914i	−0.538232	+	0.740813i
$604$	28.8933	+	20.9922i	1.17565	+	0.854162i
$605$	9.15611	−	1.23439i	0.372249	−	0.0501851i
$606$	2.57242	−	1.86897i	0.104497	−	0.0759218i
$607$		−	1.92569i		−	0.0781613i	−0.999236	−	0.0390807i	$-0.987557\pi$
$607$		−	1.92569i		−	0.0781613i	0.999236	−	0.0390807i	$-0.0124429\pi$
$608$	−9.39066	−	12.9251i	−0.380842	−	0.524183i
$609$	−0.810841	−	2.49551i	−0.0328569	−	0.101123i
$610$	−0.423561	−	3.14177i	−0.0171495	−	0.127207i
$611$	−6.82314	+	20.9995i	−0.276035	+	0.849547i
$612$	−4.62428	+	1.50252i	−0.186925	+	0.0607357i
$613$	−11.7845	+	3.82902i	−0.475972	+	0.154653i	−0.537172	−	0.843473i	$-0.680507\pi$
$613$	−11.7845	+	3.82902i	−0.475972	+	0.154653i	0.0611998	+	0.998126i	$0.480507\pi$
$614$	−1.12421	+	3.45995i	−0.0453693	+	0.139632i
$615$	10.7246	−	5.15634i	0.432457	−	0.207924i
$616$	−2.18758	−	6.73268i	−0.0881401	−	0.271267i
$617$	22.6540	+	31.1805i	0.912015	+	1.25528i	0.966474	+	0.256765i	$0.0826565\pi$
$617$	22.6540	+	31.1805i	0.912015	+	1.25528i	−0.0544591	+	0.998516i	$0.517343\pi$
$618$			2.50459i			0.100750i
$619$	18.7144	−	13.5968i	0.752194	−	0.546501i	−0.144312	−	0.989532i	$-0.546097\pi$
$619$	18.7144	−	13.5968i	0.752194	−	0.546501i	0.896506	+	0.443031i	$0.146097\pi$
$620$	32.1617	−	30.7109i	1.29165	−	1.23338i
$621$	−24.8401	−	18.0474i	−0.996798	−	0.724216i
$622$	3.33600	−	4.59160i	0.133761	−	0.184107i
$623$	−15.9305	−	5.17615i	−0.638244	−	0.207378i
$624$	−5.46516			−0.218781
$625$	−24.8936	−	2.30390i	−0.995745	−	0.0921562i
$626$	6.18757			0.247305
$627$	13.6981	+	4.45079i	0.547050	+	0.177747i
$628$	12.3710	−	17.0272i	0.493657	−	0.679460i
$629$	3.29139	+	2.39134i	0.131236	+	0.0953488i
$630$	1.88440	−	1.79939i	0.0750761	−	0.0716894i
$631$	−1.05428	+	0.765983i	−0.0419704	+	0.0304933i	−0.608573	−	0.793498i	$-0.708258\pi$
$631$	−1.05428	+	0.765983i	−0.0419704	+	0.0304933i	0.566602	+	0.823991i	$0.308258\pi$
$632$		−	8.97142i		−	0.356864i
$633$	3.84946	+	5.29833i	0.153002	+	0.210590i
$634$	−1.59263	−	4.90162i	−0.0632515	−	0.194668i
$635$	5.71396	−	2.74725i	0.226752	−	0.109021i
$636$	1.40494	−	4.32395i	0.0557094	−	0.171456i
$637$	8.05697	−	2.61787i	0.319229	−	0.103724i
$638$	2.06664	−	0.671492i	0.0818191	−	0.0265846i
$639$	−0.952612	+	2.93184i	−0.0376847	+	0.115982i
$640$	−2.29179	−	16.9994i	−0.0905910	−	0.671961i
$641$	12.2024	+	37.5552i	0.481967	+	1.48334i	0.836326	+	0.548233i	$0.184699\pi$
$641$	12.2024	+	37.5552i	0.481967	+	1.48334i	−0.354358	+	0.935110i	$0.615301\pi$
$642$	−0.832983	−	1.14650i	−0.0328752	−	0.0452489i
$643$			18.2810i			0.720934i	0.932772	+	0.360467i	$0.117383\pi$
$643$			18.2810i			0.720934i	−0.932772	+	0.360467i	$0.882617\pi$
$644$	−22.1426	+	16.0875i	−0.872541	+	0.633938i
$645$	−6.43922	+	0.868109i	−0.253544	+	0.0341818i
$646$	1.12815	+	0.819647i	0.0443863	+	0.0322486i
$647$	1.50536	−	2.07195i	0.0591818	−	0.0814567i	−0.778400	−	0.627768i	$-0.783969\pi$
$647$	1.50536	−	2.07195i	0.0591818	−	0.0814567i	0.837582	+	0.546312i	$0.183969\pi$
$648$	−4.78299	−	1.55409i	−0.187894	−	0.0610503i
$649$	−37.0021			−1.45246
$650$	−0.132088	+	2.86051i	−0.00518091	+	0.112198i
$651$	12.6547			0.495975
$652$	−4.01955	−	1.30603i	−0.157418	−	0.0511481i
$653$	12.1606	−	16.7377i	0.475882	−	0.654996i	−0.501825	−	0.864969i	$-0.667338\pi$
$653$	12.1606	−	16.7377i	0.475882	−	0.654996i	0.977707	+	0.209974i	$0.0673378\pi$
$654$	−1.26154	−	0.916563i	−0.0493301	−	0.0358404i
$655$	2.80619	−	15.4080i	0.109647	−	0.602039i
$656$	−22.2709	+	16.1808i	−0.869534	+	0.631754i
$657$		−	23.5531i		−	0.918892i
$658$	−2.74470	−	3.77776i	−0.107000	−	0.147272i
$659$	−11.9913	−	36.9054i	−0.467115	−	1.43763i	−0.856303	−	0.516473i	$-0.827245\pi$
$659$	−11.9913	−	36.9054i	−0.467115	−	1.43763i	0.389189	−	0.921158i	$-0.372755\pi$
$660$	8.06122	+	8.44205i	0.313782	+	0.328606i
$661$	−1.46535	+	4.50990i	−0.0569957	+	0.175415i	−0.975501	−	0.219993i	$-0.929397\pi$
$661$	−1.46535	+	4.50990i	−0.0569957	+	0.175415i	0.918506	+	0.395407i	$0.129397\pi$
$662$	−2.31693	+	0.752817i	−0.0900501	+	0.0292591i
$663$	1.44625	−	0.469916i	0.0561677	−	0.0182500i
$664$	−4.98649	+	15.3468i	−0.193513	+	0.595572i
$665$	20.7400	+	3.77729i	0.804263	+	0.146477i
$666$	0.828087	+	2.54859i	0.0320877	+	0.0987558i
$667$	−10.0514	−	13.8346i	−0.389192	−	0.535676i
$668$		−	6.51198i		−	0.251956i
$669$	−13.0964	+	9.51509i	−0.506336	+	0.367875i
$670$	4.60070	+	2.47949i	0.177741	+	0.0957912i
$671$	−17.0517	−	12.3888i	−0.658273	−	0.478264i
$672$	2.16571	−	2.98085i	0.0835442	−	0.114989i
$673$	39.8480	+	12.9474i	1.53603	+	0.499086i	0.950277	−	0.311405i	$-0.100800\pi$
$673$	39.8480	+	12.9474i	1.53603	+	0.499086i	0.585751	+	0.810491i	$0.300800\pi$
$674$	5.19569			0.200131
$675$	−6.75717	+	17.9355i	−0.260084	+	0.690337i
$676$	15.8565			0.609867
$677$	−26.6690	−	8.66530i	−1.02497	−	0.333034i	−0.252173	−	0.967682i	$-0.581145\pi$
$677$	−26.6690	−	8.66530i	−1.02497	−	0.333034i	−0.772802	+	0.634648i	$0.781145\pi$
$678$	−0.345420	+	0.475429i	−0.0132658	+	0.0182588i
$679$	0.138467	+	0.100602i	0.00531386	+	0.00386075i
$680$	0.996751	+	2.07312i	0.0382237	+	0.0795007i
$681$	4.63040	−	3.36418i	0.177437	−	0.128916i
$682$			10.4799i			0.401295i
$683$	−6.64883	−	9.15133i	−0.254410	−	0.350166i	0.662639	−	0.748939i	$-0.269436\pi$
$683$	−6.64883	−	9.15133i	−0.254410	−	0.350166i	−0.917050	+	0.398773i	$0.869436\pi$
$684$	−8.00740	−	24.6442i	−0.306171	−	0.942296i
$685$	−4.75111	+	8.81568i	−0.181530	+	0.336830i
$686$	−1.55491	+	4.78553i	−0.0593669	+	0.182712i
$687$	−11.9255	+	3.87484i	−0.454988	+	0.147834i
$688$	14.2953	−	4.64483i	0.545003	−	0.177082i
$689$	2.29148	−	7.05245i	0.0872985	−	0.268677i
$690$	−1.54475	+	2.86628i	−0.0588075	+	0.109117i
$691$	7.83568	+	24.1157i	0.298083	+	0.917406i	0.982168	+	0.188004i	$0.0602016\pi$
$691$	7.83568	+	24.1157i	0.298083	+	0.917406i	−0.684085	+	0.729402i	$0.739798\pi$
$692$	−10.1179	−	13.9261i	−0.384624	−	0.529390i
$693$		−	17.3228i		−	0.658039i
$694$	3.40942	−	2.47709i	0.129420	−	0.0940290i
$695$	16.6791	+	34.6906i	0.632675	+	1.31589i
$696$	1.23444	+	0.896876i	0.0467915	+	0.0339960i
$697$	4.50230	−	6.19689i	0.170537	−	0.234724i
$698$	3.81504	+	1.23958i	0.144401	+	0.0469189i
$699$	14.5060			0.548668
$700$	13.3440	+	10.6691i	0.504355	+	0.403254i
$701$	−8.54625			−0.322787			−0.161394	−	0.986890i	$-0.551599\pi$
$701$	−8.54625			−0.322787			−0.161394	+	0.986890i	$0.551599\pi$
$702$	2.08789	+	0.678396i	0.0788022	+	0.0256044i
$703$	−12.7442	+	17.5409i	−0.480656	+	0.661566i
$704$	−20.1517	−	14.6411i	−0.759496	−	0.551806i
$705$	13.7960	+	7.43520i	0.519588	+	0.280026i
$706$	−0.0122770	+	0.00891974i	−0.000462050	+	0.000335699i
$707$		−	30.9420i		−	1.16369i
$708$	−7.50309	−	10.3271i	−0.281984	−	0.388117i
$709$	0.911087	+	2.80404i	0.0342166	+	0.105308i	0.966706	−	0.255889i	$-0.0823682\pi$
$709$	0.911087	+	2.80404i	0.0342166	+	0.105308i	−0.932490	+	0.361197i	$0.882368\pi$
$710$	0.704910	+	0.128382i	0.0264548	+	0.00481811i
$711$	6.78391	−	20.8787i	0.254417	−	0.783014i
$712$	9.26383	−	3.01000i	0.347177	−	0.112805i
$713$	78.4352	−	25.4852i	2.93742	−	0.954427i
$714$	−0.0993791	+	0.305857i	−0.00371917	+	0.0114464i
$715$	13.1480	+	13.7691i	0.491707	+	0.514937i
$716$	−10.9877	−	33.8168i	−0.410631	−	1.26379i
$717$	4.65186	+	6.40273i	0.173727	+	0.239114i
$718$		−	4.86074i		−	0.181401i
$719$	−0.930260	+	0.675874i	−0.0346929	+	0.0252058i	−0.604997	−	0.796228i	$-0.706826\pi$
$719$	−0.930260	+	0.675874i	−0.0346929	+	0.0252058i	0.570304	+	0.821434i	$0.306826\pi$
$720$	3.62469	−	19.9021i	0.135084	−	0.741709i
$721$	19.7178	+	14.3258i	0.734330	+	0.533522i
$722$	−1.44596	+	1.99020i	−0.0538132	+	0.0740675i
$723$	−8.55165	−	2.77860i	−0.318039	−	0.103337i
$724$	−20.9416			−0.778289
$725$	−6.66598	+	8.33724i	−0.247568	+	0.309637i
$726$	−0.751124			−0.0278768
$727$	43.4907	+	14.1310i	1.61298	+	0.524090i	0.970271	−	0.242019i	$-0.0778097\pi$
$727$	43.4907	+	14.1310i	1.61298	+	0.524090i	0.642711	+	0.766109i	$0.277810\pi$
$728$	2.34129	−	3.22251i	0.0867739	−	0.119434i
$729$	−3.49235	−	2.53734i	−0.129346	−	0.0939756i
$730$	−5.42528	+	0.731414i	−0.200799	+	0.0270708i
$731$	−3.38360	+	2.45833i	−0.125147	+	0.0909247i
$732$		−	7.27119i		−	0.268751i
$733$	−12.9906	−	17.8801i	−0.479820	−	0.660415i	0.498651	−	0.866803i	$-0.333829\pi$
$733$	−12.9906	−	17.8801i	−0.479820	−	0.660415i	−0.978470	+	0.206388i	$0.933829\pi$
$734$	−2.90978	−	8.95538i	−0.107402	−	0.330549i
$735$	−0.803375	−	5.95906i	−0.0296329	−	0.219803i
$736$	7.42025	−	22.8372i	0.273514	−	0.841790i
$737$	33.0465	−	10.7375i	1.21728	−	0.395519i
$738$	4.79837	−	1.55909i	0.176630	−	0.0573907i
$739$	−9.77634	+	30.0885i	−0.359629	+	1.10682i	0.593648	+	0.804725i	$0.297687\pi$
$739$	−9.77634	+	30.0885i	−0.359629	+	1.10682i	−0.953277	+	0.302098i	$0.902313\pi$
$740$	−15.8362	+	7.61399i	−0.582150	+	0.279896i
$741$	2.50433	+	7.70753i	0.0919988	+	0.283143i
$742$	0.921781	+	1.26872i	0.0338396	+	0.0465763i
$743$			29.5982i			1.08585i	0.839780	+	0.542927i	$0.182684\pi$
$743$			29.5982i			1.08585i	−0.839780	+	0.542927i	$0.817316\pi$
$744$	−5.95345	+	4.32543i	−0.218264	+	0.158578i
$745$	1.95451	−	1.86634i	0.0716076	−	0.0683773i
$746$	4.95478	+	3.59986i	0.181407	+	0.131800i
$747$	−23.2096	+	31.9453i	−0.849195	+	1.16882i
$748$	7.14585	+	2.32183i	0.261278	+	0.0848944i
$749$	−13.7905			−0.503895
$750$	1.98067	+	0.456028i	0.0723240	+	0.0166518i
$751$	1.92870			0.0703791			0.0351896	−	0.999381i	$-0.488796\pi$
$751$	1.92870			0.0703791			0.0351896	+	0.999381i	$0.488796\pi$
$752$	−34.4805	−	11.2034i	−1.25737	−	0.408546i
$753$	0.252749	−	0.347879i	0.00921067	−	0.0126774i
$754$	0.989170	+	0.718674i	0.0360234	+	0.0261726i
$755$	29.9020	−	28.5531i	1.08824	−	1.03915i
$756$	10.5965	−	7.69882i	0.385391	−	0.280003i
$757$			40.7460i			1.48094i	0.672089	+	0.740470i	$0.265397\pi$
$757$			40.7460i			1.48094i	−0.672089	+	0.740470i	$0.734603\pi$
$758$	1.34069	+	1.84530i	0.0486961	+	0.0670244i
$759$	6.68953	+	20.5883i	0.242815	+	0.747307i
$760$	−11.0483	+	5.31200i	−0.400765	+	0.192687i
$761$	−11.4943	+	35.3758i	−0.416668	+	1.28237i	0.494082	+	0.869415i	$0.335504\pi$
$761$	−11.4943	+	35.3758i	−0.416668	+	1.28237i	−0.910750	+	0.412958i	$0.864496\pi$
$762$	−0.490220	+	0.159282i	−0.0177588	+	0.00577018i
$763$	−14.4316	+	4.68910i	−0.522458	+	0.169757i
$764$	5.45152	−	16.7781i	0.197229	−	0.607009i
$765$	0.752055	+	5.57839i	0.0271906	+	0.201687i
$766$	−0.937058	−	2.88397i	−0.0338573	−	0.104202i
$767$	−12.2377	−	16.8437i	−0.441877	−	0.608192i
$768$		−	7.50313i		−	0.270746i
$769$	−15.0402	+	10.9273i	−0.542363	+	0.394050i	−0.824962	−	0.565188i	$-0.808803\pi$
$769$	−15.0402	+	10.9273i	−0.542363	+	0.394050i	0.282599	+	0.959238i	$0.408803\pi$
$770$	−3.99019	+	0.537941i	−0.143796	+	0.0193860i
$771$	9.63356	+	6.99919i	0.346944	+	0.252070i
$772$	−15.7927	+	21.7368i	−0.568393	+	0.782325i
$773$	−3.51133	−	1.14090i	−0.126294	−	0.0410354i	0.245188	−	0.969476i	$-0.421150\pi$
$773$	−3.51133	−	1.14090i	−0.126294	−	0.0410354i	−0.371482	+	0.928440i	$0.621150\pi$
$774$	−2.75482			−0.0990200
$775$	−28.3062	−	43.0002i	−1.01679	−	1.54461i
$776$	−0.0995286			−0.00357287
$777$	−4.75559	−	1.54518i	−0.170606	−	0.0554332i
$778$	1.83357	−	2.52369i	0.0657366	−	0.0904787i
$779$	33.0252	+	23.9942i	1.18325	+	0.859681i
$780$	−1.17682	+	6.46158i	−0.0421370	+	0.231362i
$781$	3.85390	−	2.80003i	0.137904	−	0.100193i
$782$			2.09588i			0.0749486i
$783$	4.81017	+	6.62063i	0.171902	+	0.236602i
$784$	4.29847	+	13.2293i	0.153517	+	0.472476i
$785$	−16.8267	−	17.6216i	−0.600571	−	0.628943i
$786$	−0.393462	+	1.21095i	−0.0140343	+	0.0431932i
$787$	−3.00482	+	0.976326i	−0.107110	+	0.0348023i	−0.362082	−	0.932146i	$-0.617934\pi$
$787$	−3.00482	+	0.976326i	−0.107110	+	0.0348023i	0.254971	+	0.966949i	$0.417934\pi$
$788$	−35.8501	+	11.6484i	−1.27711	+	0.414957i
$789$	6.71819	−	20.6764i	0.239174	−	0.736101i
$790$	−5.01994	−	0.914261i	−0.178601	−	0.0325279i
$791$	1.76715	+	5.43874i	0.0628328	+	0.193379i
$792$	5.92103	+	8.14960i	0.210395	+	0.289584i
$793$		−	11.8594i		−	0.421141i
$794$	4.81189	−	3.49605i	0.170768	−	0.124070i
$795$	−4.63325	−	2.49704i	−0.164325	−	0.0885608i
$796$	−7.15343	−	5.19727i	−0.253547	−	0.184212i
$797$	−26.4404	+	36.3921i	−0.936568	+	1.28908i	0.0206733	+	0.999786i	$0.493419\pi$
$797$	−26.4404	+	36.3921i	−0.936568	+	1.28908i	−0.957242	+	0.289289i	$0.906581\pi$
$798$	−1.63001	−	0.529622i	−0.0577017	−	0.0187484i
$799$	10.0879			0.356885
$800$	−14.9732	−	0.691406i	−0.529381	−	0.0244449i
$801$	23.8353			0.842180
$802$	5.71996	+	1.85853i	0.201979	+	0.0656269i
$803$	−21.3932	+	29.4452i	−0.754950	+	1.03910i
$804$	9.69778	+	7.04585i	0.342014	+	0.248488i
$805$	13.7296	+	28.5559i	0.483904	+	1.00646i
$806$	−4.77054	+	3.46600i	−0.168035	+	0.122085i
$807$		−	11.0898i		−	0.390381i
$808$	10.5761	+	14.5568i	0.372067	+	0.512106i
$809$	−8.71238	−	26.8139i	−0.306311	−	0.942728i	−0.979185	−	0.202971i	$-0.934940\pi$
$809$	−8.71238	−	26.8139i	−0.306311	−	0.942728i	0.672874	−	0.739757i	$-0.265060\pi$
$810$	−1.35701	+	2.51794i	−0.0476805	+	0.0884712i
$811$	0.418476	−	1.28794i	0.0146947	−	0.0452256i	−0.943440	−	0.331542i	$-0.892431\pi$
$811$	0.418476	−	1.28794i	0.0146947	−	0.0452256i	0.958135	+	0.286317i	$0.0924310\pi$
$812$	6.93784	−	2.25424i	0.243470	−	0.0791083i
$813$	−16.6990	+	5.42582i	−0.585658	+	0.190292i
$814$	1.27963	−	3.93831i	0.0448511	−	0.138038i
$815$	−2.32125	+	4.30707i	−0.0813097	+	0.150870i
$816$	0.771588	+	2.37470i	0.0270110	+	0.0831313i
$817$	−13.1012	−	18.0323i	−0.458354	−	0.630870i
$818$		−	4.94925i		−	0.173046i
$819$	7.88552	−	5.72917i	0.275543	−	0.200193i
$820$	14.3353	+	29.8157i	0.500610	+	1.04121i
$821$	−16.4592	−	11.9583i	−0.574428	−	0.417347i	0.262283	−	0.964991i	$-0.415525\pi$
$821$	−16.4592	−	11.9583i	−0.574428	−	0.417347i	−0.836711	+	0.547644i	$0.815525\pi$
$822$	0.478559	−	0.658680i	0.0166917	−	0.0229741i
$823$	20.4158	+	6.63349i	0.711649	+	0.231229i	0.642399	−	0.766370i	$-0.277939\pi$
$823$	20.4158	+	6.63349i	0.711649	+	0.231229i	0.0692505	+	0.997599i	$0.477939\pi$
$824$	−14.1730			−0.493739
$825$	11.2870	−	7.43003i	0.392964	−	0.258681i
$826$	4.40307			0.153203
$827$	−8.87824	−	2.88472i	−0.308727	−	0.100311i	0.150556	−	0.988601i	$-0.451894\pi$
$827$	−8.87824	−	2.88472i	−0.308727	−	0.100311i	−0.459283	+	0.888290i	$0.651894\pi$
$828$	22.8922	−	31.5084i	0.795558	−	1.09499i
$829$	34.3794	+	24.9781i	1.19405	+	0.867525i	0.993686	−	0.112197i	$-0.0357888\pi$
$829$	34.3794	+	24.9781i	1.19405	+	0.867525i	0.200360	+	0.979722i	$0.435789\pi$
$830$	8.07912	+	4.35414i	0.280430	+	0.151135i
$831$	13.6641	−	9.92756i	0.474003	−	0.344383i
$832$		−	14.0155i		−	0.485900i
$833$	−2.27502	−	3.13129i	−0.0788247	−	0.108493i
$834$	−0.967034	−	2.97622i	−0.0334856	−	0.103058i
$835$	−7.41669	−	1.35077i	−0.256665	−	0.0467454i
$836$	−12.3737	+	38.0825i	−0.427955	+	1.31711i
$837$	−37.5358	+	12.1961i	−1.29743	+	0.421559i
$838$	7.34553	−	2.38671i	0.253747	−	0.0824474i
$839$	−8.89829	+	27.3861i	−0.307203	+	0.945474i	0.671643	+	0.740875i	$0.265589\pi$
$839$	−8.89829	+	27.3861i	−0.307203	+	0.945474i	−0.978846	+	0.204599i	$0.934411\pi$
$840$	−1.95249	−	2.04473i	−0.0673675	−	0.0705500i
$841$	−7.55306	−	23.2459i	−0.260450	−	0.801583i
$842$	3.77745	+	5.19921i	0.130180	+	0.179177i
$843$		−	10.5812i		−	0.364434i
$844$	−14.7300	+	10.7020i	−0.507028	+	0.368377i
$845$	3.28910	−	18.0595i	0.113148	−	0.621265i
$846$	5.37566	+	3.90564i	0.184819	+	0.134279i
$847$	−4.29630	+	5.91335i	−0.147623	+	0.203185i
$848$	11.5799	+	3.76255i	0.397656	+	0.129206i
$849$	11.4963			0.394551
$850$	1.26159	−	0.346461i	0.0432721	−	0.0118835i
$851$	−32.5876			−1.11709
$852$	1.56295	+	0.507833i	0.0535458	+	0.0173981i
$853$	16.3960	−	22.5672i	0.561389	−	0.772685i	−0.430114	−	0.902775i	$-0.641526\pi$
$853$	16.3960	−	22.5672i	0.561389	−	0.772685i	0.991502	+	0.130090i	$0.0415265\pi$
$854$	2.02907	+	1.47421i	0.0694334	+	0.0504463i
$855$	−29.7290	+	4.00794i	−1.01671	+	0.137069i
$856$	6.48783	−	4.71368i	0.221749	−	0.161110i
$857$		−	15.8926i		−	0.542880i	−0.962455	−	0.271440i	$-0.912500\pi$
$857$		−	15.8926i		−	0.542880i	0.962455	−	0.271440i	$-0.0874998\pi$
$858$	−0.909783	−	1.25221i	−0.0310595	−	0.0427497i
$859$	−7.77436	−	23.9270i	−0.265258	−	0.816380i	−0.991634	−	0.129082i	$-0.958797\pi$
$859$	−7.77436	−	23.9270i	−0.265258	−	0.816380i	0.726376	−	0.687297i	$-0.241203\pi$
$860$	−2.41345	−	17.9019i	−0.0822981	−	0.610448i
$861$	−2.90920	+	8.95361i	−0.0991454	+	0.305138i
$862$	2.54490	−	0.826888i	0.0866797	−	0.0281639i
$863$	−13.2984	+	4.32090i	−0.452681	+	0.147085i	−0.526479	−	0.850188i	$-0.676488\pi$
$863$	−13.2984	+	4.32090i	−0.452681	+	0.147085i	0.0737976	+	0.997273i	$0.476488\pi$
$864$	−3.55102	+	10.9289i	−0.120808	+	0.371809i
$865$	−17.9596	+	8.63489i	−0.610643	+	0.293595i
$866$	2.25912	+	6.95286i	0.0767680	+	0.236268i
$867$	−0.408373	−	0.562077i	−0.0138691	−	0.0190891i
$868$			35.1815i			1.19414i
$869$	−27.4451	+	19.9401i	−0.931012	+	0.676420i
$870$	0.627645	−	0.599331i	0.0212791	−	0.0203192i
$871$	15.8173	+	11.4919i	0.535947	+	0.389389i
$872$	5.18664	−	7.13880i	0.175642	−	0.241750i
$873$	−0.231628	−	0.0752605i	−0.00783942	−	0.00254718i
$874$	−11.1696			−0.377818
$875$	14.9193	−	12.9848i	0.504363	−	0.438966i
$876$	−12.5560			−0.424229
$877$	17.2781	+	5.61401i	0.583441	+	0.189572i	0.585842	−	0.810426i	$-0.300764\pi$
$877$	17.2781	+	5.61401i	0.583441	+	0.189572i	−0.00240042	+	0.999997i	$0.500764\pi$
$878$	1.62495	−	2.23655i	0.0548394	−	0.0754799i
$879$	−17.3574	−	12.6109i	−0.585450	−	0.425355i
$880$	−22.6085	+	21.5887i	−0.762134	+	0.727753i
$881$	43.2655	−	31.4342i	1.45765	−	1.05905i	0.473684	−	0.880695i	$-0.342924\pi$
$881$	43.2655	−	31.4342i	1.45765	−	1.05905i	0.983967	−	0.178350i	$-0.0570760\pi$
$882$		−	2.54940i		−	0.0858427i
$883$	−18.1465	−	24.9766i	−0.610680	−	0.840529i	0.385953	−	0.922518i	$-0.373873\pi$
$883$	−18.1465	−	24.9766i	−0.610680	−	0.840529i	−0.996633	+	0.0819895i	$0.973873\pi$
$884$	1.30642	+	4.02076i	0.0439398	+	0.135233i
$885$	−13.3182	+	6.40335i	−0.447687	+	0.215246i
$886$	0.331935	−	1.02159i	0.0111516	−	0.0343210i
$887$	31.4632	−	10.2230i	1.05643	−	0.343255i	0.271242	−	0.962511i	$-0.412566\pi$
$887$	31.4632	−	10.2230i	1.05643	−	0.343255i	0.785189	+	0.619256i	$0.212566\pi$
$888$	2.76544	−	0.898547i	0.0928022	−	0.0301532i
$889$	−1.55000	+	4.77040i	−0.0519852	+	0.159994i
$890$	−0.740179	−	5.49030i	−0.0248109	−	0.184035i
$891$	5.87654	+	18.0861i	0.196872	+	0.605908i
$892$	−26.4531	−	36.4096i	−0.885717	−	1.21908i
$893$			53.7618i			1.79907i
$894$	−0.177749	+	0.129142i	−0.00594481	+	0.00431916i
$895$	−40.7941	+	5.49969i	−1.36360	+	0.183834i
$896$	10.9788	+	7.97659i	0.366777	+	0.266479i
$897$	−7.15957	+	9.85430i	−0.239051	+	0.329025i
$898$	6.04909	+	1.96547i	0.201861	+	0.0655886i
$899$	−21.9812			−0.733114
$900$	−22.7502	−	8.57112i	−0.758342	−	0.285704i
$901$	−3.38793			−0.112868
$902$	−7.41487	−	2.40924i	−0.246888	−	0.0802188i
$903$	3.02146	−	4.15868i	0.100548	−	0.138392i
$904$	−2.69036	−	1.95466i	−0.0894800	−	0.0650110i
$905$	−4.34389	+	23.8510i	−0.144396	+	0.792835i
$906$	−2.71938	+	1.97574i	−0.0903453	+	0.0656397i
$907$		−	11.5897i		−	0.384829i	−0.981314	−	0.192414i	$-0.938368\pi$
$907$		−	11.5897i		−	0.384829i	0.981314	−	0.192414i	$-0.0616317\pi$
$908$	9.35284	+	12.8731i	0.310385	+	0.427208i
$909$	13.6059	+	41.8746i	0.451279	+	1.38889i
$910$	−1.56455	−	1.63846i	−0.0518643	−	0.0543145i
$911$	6.82326	−	20.9998i	0.226065	−	0.695755i	−0.772117	−	0.635480i	$-0.780802\pi$
$911$	6.82326	−	20.9998i	0.226065	−	0.695755i	0.998182	−	0.0602751i	$-0.0191978\pi$
$912$	−12.6555	+	4.11204i	−0.419067	+	0.136163i
$913$	58.0317	−	18.8556i	1.92057	−	0.624031i
$914$	0.00218202	−	0.00671556i	7.21747e−5	−	0.000222131i
$915$	−8.28137	−	1.50825i	−0.273774	−	0.0498613i
$916$	−10.7726	−	33.1545i	−0.355935	−	1.09546i
$917$	7.28288	+	10.0240i	0.240502	+	0.331022i
$918$		−	1.00300i		−	0.0331039i
$919$	19.1011	−	13.8778i	0.630087	−	0.457785i	−0.226343	−	0.974048i	$-0.572677\pi$
$919$	19.1011	−	13.8778i	0.630087	−	0.457785i	0.856430	+	0.516263i	$0.172677\pi$
$920$	−16.2197	−	8.74141i	−0.534748	−	0.288196i
$921$	7.81489	+	5.67785i	0.257509	+	0.187091i
$922$	0.389366	−	0.535916i	0.0128231	−	0.0176495i
$923$	2.54920	+	0.828286i	0.0839080	+	0.0272634i
$924$	−9.23472			−0.303800
$925$	5.38691	+	19.6157i	0.177121	+	0.644959i
$926$	2.71068			0.0890785
$927$	−32.9841	−	10.7172i	−1.08334	−	0.351998i
$928$	−3.76185	+	5.17775i	−0.123489	+	0.169968i
$929$	−19.1508	−	13.9138i	−0.628316	−	0.456498i	0.227500	−	0.973778i	$-0.426945\pi$
$929$	−19.1508	−	13.9138i	−0.628316	−	0.456498i	−0.855816	+	0.517280i	$0.826945\pi$
$930$	1.81358	+	3.77203i	0.0594696	+	0.123690i
$931$	16.6876	−	12.1243i	0.546915	−	0.397357i
$932$			40.3285i			1.32101i
$933$	−8.85782	−	12.1917i	−0.289992	−	0.399140i
$934$	1.94442	+	5.98430i	0.0636232	+	0.195812i
$935$	4.12665	−	7.65700i	0.134956	−	0.250411i
$936$	−1.75152	+	5.39063i	−0.0572503	+	0.176198i
$937$	−23.8531	+	7.75033i	−0.779246	+	0.253192i	−0.671518	−	0.740988i	$-0.734358\pi$
$937$	−23.8531	+	7.75033i	−0.779246	+	0.253192i	−0.107728	+	0.994180i	$0.534358\pi$
$938$	−3.93238	+	1.27771i	−0.128397	+	0.0417186i
$939$	5.07696	−	15.6253i	0.165680	−	0.509912i
$940$	−20.6708	+	38.3547i	−0.674207	+	1.25099i
$941$	−4.05329	−	12.4747i	−0.132133	−	0.406665i	0.863000	−	0.505204i	$-0.168583\pi$
$941$	−4.05329	−	12.4747i	−0.132133	−	0.406665i	−0.995133	+	0.0985397i	$0.968583\pi$
$942$	1.16433	+	1.60257i	0.0379360	+	0.0522144i
$943$			61.3545i			1.99798i
$944$	27.6569	−	20.0939i	0.900157	−	0.654002i
$945$	−6.57039	−	13.6656i	−0.213735	−	0.444543i
$946$	3.44398	+	2.50220i	0.111974	+	0.0813536i
$947$	19.1500	−	26.3578i	0.622293	−	0.856512i	−0.375225	−	0.926934i	$-0.622434\pi$
$947$	19.1500	−	26.3578i	0.622293	−	0.856512i	0.997517	+	0.0704214i	$0.0224344\pi$
$948$	−11.1304	−	3.61647i	−0.361497	−	0.117458i
$949$	−20.4791			−0.664781
$950$	1.84640	+	6.72341i	0.0599052	+	0.218136i
$951$	−13.6847			−0.443756
$952$	−1.73078	−	0.562366i	−0.0560950	−	0.0182264i
$953$	23.3314	−	32.1130i	0.755780	−	1.04024i	−0.241774	−	0.970333i	$-0.577729\pi$
$953$	23.3314	−	32.1130i	0.755780	−	1.04024i	0.997553	−	0.0699087i	$-0.0222708\pi$
$954$	−1.80536	−	1.31167i	−0.0584507	−	0.0424669i
$955$	−17.9782	−	9.68914i	−0.581761	−	0.313533i
$956$	−17.8004	+	12.9328i	−0.575706	+	0.418275i
$957$		−	5.76979i		−	0.186511i
$958$	−0.123451	−	0.169915i	−0.00398851	−	0.00548971i
$959$	−2.44829	−	7.53506i	−0.0790594	−	0.243320i
$960$	−9.78692	−	1.78245i	−0.315872	−	0.0575284i
$961$	23.1795	−	71.3392i	0.747726	−	2.30126i
$962$	2.21597	−	0.720013i	0.0714458	−	0.0232141i
$963$	18.6631	−	6.06402i	0.601411	−	0.195410i
$964$	7.72486	−	23.7747i	0.248801	−	0.765731i
$965$	21.4808	+	22.4956i	0.691493	+	0.724160i
$966$	−0.796023	−	2.44991i	−0.0256116	−	0.0788244i
$967$	−24.8730	−	34.2347i	−0.799860	−	1.10091i	−0.992810	−	0.119704i	$-0.961805\pi$
$967$	−24.8730	−	34.2347i	−0.799860	−	1.10091i	0.192949	−	0.981209i	$-0.438195\pi$
$968$		−	4.25046i		−	0.136615i
$969$	2.99548	−	2.17635i	0.0962288	−	0.0699143i
$970$	−0.0101428	+	0.0556910i	−0.000325665	+	0.00178813i
$971$	2.27159	+	1.65041i	0.0728988	+	0.0529641i	0.623638	−	0.781713i	$-0.285654\pi$
$971$	2.27159	+	1.65041i	0.0728988	+	0.0529641i	−0.550739	+	0.834678i	$0.685654\pi$
$972$	−16.9121	+	23.2774i	−0.542454	+	0.746624i
$973$	−28.9620	−	9.41034i	−0.928481	−	0.301682i
$974$	−3.11749			−0.0998908
$975$	7.11518	+	2.68063i	0.227868	+	0.0858490i
$976$	19.4729			0.623312
$977$	−28.8794	−	9.38348i	−0.923933	−	0.300204i	−0.191854	−	0.981423i	$-0.561450\pi$
$977$	−28.8794	−	9.38348i	−0.923933	−	0.300204i	−0.732079	+	0.681219i	$0.761450\pi$
$978$	0.233809	−	0.321811i	0.00747639	−	0.0102904i
$979$	−29.7981	−	21.6496i	−0.952352	−	0.691924i
$980$	16.5669	−	2.23348i	0.529211	−	0.0713461i
$981$	17.4688	−	12.6918i	0.557735	−	0.405218i
$982$			3.26148i			0.104078i
$983$	24.4764	+	33.6889i	0.780677	+	1.07451i	0.995207	+	0.0977927i	$0.0311782\pi$
$983$	24.4764	+	33.6889i	0.780677	+	1.07451i	−0.214529	+	0.976718i	$0.568822\pi$
$984$	−1.69174	−	5.20665i	−0.0539308	−	0.165982i
$985$	5.83037	+	43.2469i	0.185771	+	1.37796i
$986$	0.172622	−	0.531276i	0.00549740	−	0.0169193i
$987$	−11.7919	+	3.83143i	−0.375341	+	0.121956i
$988$	−21.4279	+	6.96235i	−0.681713	+	0.221502i
$989$	10.3523	−	31.8610i	0.329182	−	1.01312i
$990$	5.16349	−	2.48259i	0.164107	−	0.0789019i
$991$	15.9232	+	49.0065i	0.505816	+	1.55674i	0.799395	+	0.600806i	$0.205154\pi$
$991$	15.9232	+	49.0065i	0.505816	+	1.55674i	−0.293579	+	0.955935i	$0.594846\pi$
$992$	−18.1426	−	24.9711i	−0.576027	−	0.792834i
$993$			6.46857i			0.205274i
$994$	−0.458596	+	0.333190i	−0.0145458	+	0.0105681i
$995$	−7.40315	+	7.06918i	−0.234696	+	0.224108i
$996$	17.0299	+	12.3729i	0.539613	+	0.392052i
$997$	6.15905	−	8.47721i	0.195059	−	0.268476i	−0.700273	−	0.713875i	$-0.746938\pi$
$997$	6.15905	−	8.47721i	0.195059	−	0.268476i	0.895332	+	0.445399i	$0.146938\pi$
$998$	−5.25365	−	1.70702i	−0.166302	−	0.0540346i
$999$	15.5950			0.493405

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.r.a.154.20	yes	160
25.19	even	10	inner	425.2.r.a.69.20	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.r.a.69.20	✓	160	25.19	even	10	inner
425.2.r.a.154.20	yes	160	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.248853 - 0.0808572i) q^{2} +(-0.408373 + 0.562077i) q^{3} +(-1.56264 - 1.13533i) q^{4} +(-1.61719 + 1.54424i) q^{5} +(0.147073 - 0.106855i) q^{6} -1.76904i q^{7} +(0.604668 + 0.832255i) q^{8} +(0.777889 + 2.39410i) q^{9} +(0.527307 - 0.253527i) q^{10} +(1.20206 - 3.69957i) q^{11} +(1.27628 - 0.414689i) q^{12} +(2.08164 - 0.676366i) q^{13} +(-0.143040 + 0.440231i) q^{14} +(-0.207564 - 1.53961i) q^{15} +(1.11057 + 3.41800i) q^{16} +(-0.587785 - 0.809017i) q^{17} -0.658676i q^{18} +(4.31151 - 3.13249i) q^{19} +(4.28032 - 0.577055i) q^{20} +(0.994337 + 0.722428i) q^{21} +(-0.598274 + 0.823454i) q^{22} +(7.61793 + 2.47521i) q^{23} -0.714721 q^{24} +(0.230636 - 4.99468i) q^{25} -0.572712 q^{26} +(-3.64562 - 1.18453i) q^{27} +(-2.00844 + 2.76438i) q^{28} +(-1.72717 - 1.25486i) q^{29} +(-0.0728359 + 0.399920i) q^{30} +(8.32975 - 6.05192i) q^{31} -2.99782i q^{32} +(1.58855 + 2.18646i) q^{33} +(0.0808572 + 0.248853i) q^{34} +(2.73183 + 2.86089i) q^{35} +(1.50252 - 4.62428i) q^{36} +(-3.86926 + 1.25720i) q^{37} +(-1.32622 + 0.430914i) q^{38} +(-0.469916 + 1.44625i) q^{39} +(-2.26307 - 0.412163i) q^{40} +(2.36700 + 7.28488i) q^{41} +(-0.189030 - 0.260178i) q^{42} -4.18236i q^{43} +(-6.07862 + 4.41638i) q^{44} +(-4.95506 - 2.67047i) q^{45} +(-1.69560 - 1.23193i) q^{46} +(-5.92954 + 8.16131i) q^{47} +(-2.37470 - 0.771588i) q^{48} +3.87049 q^{49} +(-0.461250 + 1.22429i) q^{50} +0.694765 q^{51} +(-4.02076 - 1.30642i) q^{52} +(1.99138 - 2.74089i) q^{53} +(0.811444 + 0.589549i) q^{54} +(3.76906 + 7.83920i) q^{55} +(1.47229 - 1.06968i) q^{56} +3.70262i q^{57} +(0.328346 + 0.451930i) q^{58} +(-2.93943 - 9.04665i) q^{59} +(-1.42362 + 2.64152i) q^{60} +(1.67435 - 5.15313i) q^{61} +(-2.56222 + 0.832517i) q^{62} +(4.23526 - 1.37612i) q^{63} +(1.97875 - 6.08997i) q^{64} +(-2.32195 + 4.30837i) q^{65} +(-0.218525 - 0.672552i) q^{66} +(5.25041 + 7.22656i) q^{67} +1.93153i q^{68} +(-4.50221 + 3.27105i) q^{69} +(-0.448500 - 0.932828i) q^{70} +(0.990731 + 0.719808i) q^{71} +(-1.52213 + 2.09504i) q^{72} +(-8.89853 - 2.89131i) q^{73} +1.06453 q^{74} +(2.71321 + 2.16932i) q^{75} -10.2938 q^{76} +(-6.54470 - 2.12650i) q^{77} +(0.233880 - 0.321908i) q^{78} +(-7.05538 - 5.12603i) q^{79} +(-7.07423 - 3.81257i) q^{80} +(-3.95505 + 2.87351i) q^{81} -2.00425i q^{82} +(9.22003 + 12.6903i) q^{83} +(-0.733603 - 2.25780i) q^{84} +(2.19988 + 0.400655i) q^{85} +(-0.338174 + 1.04079i) q^{86} +(1.41066 - 0.458350i) q^{87} +(3.80583 - 1.23659i) q^{88} +(2.92596 - 9.00518i) q^{89} +(1.01715 + 1.06521i) q^{90} +(-1.19652 - 3.68251i) q^{91} +(-9.09393 - 12.5167i) q^{92} +7.15340i q^{93} +(2.13548 - 1.55152i) q^{94} +(-2.13522 + 11.7239i) q^{95} +(1.68501 + 1.22423i) q^{96} +(-0.0568680 + 0.0782721i) q^{97} +(-0.963183 - 0.312957i) q^{98} +9.79220 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 40 q^{4} - 8 q^{5} + 4 q^{6} - 30 q^{8} + 36 q^{9} - 6 q^{10} + 8 q^{11} - 40 q^{12} - 20 q^{14} - 40 q^{15} - 64 q^{16} + 6 q^{19} + 2 q^{20} - 50 q^{22} + 20 q^{23} + 20 q^{24} + 32 q^{25} + 20 q^{26}+ \cdots + 44 q^{99}+O(q^{100}) \) 160 * q + 40 * q^4 - 8 * q^5 + 4 * q^6 - 30 * q^8 + 36 * q^9 - 6 * q^10 + 8 * q^11 - 40 * q^12 - 20 * q^14 - 40 * q^15 - 64 * q^16 + 6 * q^19 + 2 * q^20 - 50 * q^22 + 20 * q^23 + 20 * q^24 + 32 * q^25 + 20 * q^26 + 30 * q^27 + 60 * q^28 + 16 * q^30 + 12 * q^31 - 40 * q^33 - 4 * q^34 - 54 * q^36 - 40 * q^38 - 12 * q^39 - 52 * q^40 - 2 * q^41 + 30 * q^42 - 20 * q^44 + 42 * q^45 + 48 * q^46 + 40 * q^47 - 100 * q^48 - 184 * q^49 + 46 * q^50 - 32 * q^51 - 10 * q^52 - 20 * q^53 - 40 * q^54 + 18 * q^55 + 24 * q^56 - 120 * q^58 + 6 * q^59 - 40 * q^60 + 12 * q^61 - 10 * q^62 + 90 * q^63 + 58 * q^64 - 20 * q^65 + 48 * q^66 - 90 * q^67 - 74 * q^69 - 120 * q^70 - 16 * q^71 - 10 * q^72 + 52 * q^74 + 76 * q^75 + 96 * q^76 + 80 * q^77 + 40 * q^78 - 60 * q^79 - 24 * q^80 - 118 * q^81 - 76 * q^84 + 2 * q^85 + 44 * q^86 + 40 * q^87 + 140 * q^88 + 50 * q^89 + 224 * q^90 + 28 * q^91 - 170 * q^92 + 96 * q^94 - 44 * q^95 - 116 * q^96 + 110 * q^97 + 70 * q^98 + 44 * q^99

Introduction

L-functions

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